TSTP Solution File: ITP200^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP200^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:23:58 EDT 2024
% Result : Theorem 15.95s 4.88s
% Output : Refutation 16.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 460
% Syntax : Number of formulae : 765 ( 264 unt; 157 typ; 0 def)
% Number of atoms : 1734 (1021 equ; 8 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 5650 ( 415 ~; 18 |; 64 &;3991 @)
% ( 0 <=>;1162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 52 ( 51 usr)
% Number of type conns : 695 ( 695 >; 0 *; 0 +; 0 <<)
% Number of symbols : 112 ( 108 usr; 13 con; 0-3 aty)
% Number of variables : 2118 ( 138 ^1944 !; 36 ?;2118 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1699626005le_trm_type,type,
produc1699626005le_trm: $tType ).
thf(produc1418842292n_game_type,type,
produc1418842292n_game: $tType ).
thf(set_Pr1918373977on_fml_type,type,
set_Pr1918373977on_fml: $tType ).
thf(set_Pr1062384839on_trm_type,type,
set_Pr1062384839on_trm: $tType ).
thf(set_Pr519625031on_fml_type,type,
set_Pr519625031on_fml: $tType ).
thf(set_Pr1588097095on_trm_type,type,
set_Pr1588097095on_trm: $tType ).
thf(set_Pr1045337287on_fml_type,type,
set_Pr1045337287on_fml: $tType ).
thf(produc1928189433on_fml_type,type,
produc1928189433on_fml: $tType ).
thf(produc2024965863on_trm_type,type,
produc2024965863on_trm: $tType ).
thf(produc591588199on_fml_type,type,
produc591588199on_fml: $tType ).
thf(produc1158546023on_trm_type,type,
produc1158546023on_trm: $tType ).
thf(produc1872652007on_fml_type,type,
produc1872652007on_fml: $tType ).
thf(set_Pr1481565921on_trm_type,type,
set_Pr1481565921on_trm: $tType ).
thf(set_Pr1969262145le_trm_type,type,
set_Pr1969262145le_trm: $tType ).
thf(produc2018724225on_trm_type,type,
produc2018724225on_trm: $tType ).
thf(produc1279577057le_trm_type,type,
produc1279577057le_trm: $tType ).
thf(set_Pr1625152599n_game_type,type,
set_Pr1625152599n_game: $tType ).
thf(set_Pr622314946on_fml_type,type,
set_Pr622314946on_fml: $tType ).
thf(set_Pr1471344007on_trm_type,type,
set_Pr1471344007on_trm: $tType ).
thf(set_Pr927595527on_fml_type,type,
set_Pr927595527on_fml: $tType ).
thf(set_Pr181266295riable_type,type,
set_Pr181266295riable: $tType ).
thf(produc1016592119n_game_type,type,
produc1016592119n_game: $tType ).
thf(produc1739631244on_fml_type,type,
produc1739631244on_fml: $tType ).
thf(produc1072747943on_trm_type,type,
produc1072747943on_trm: $tType ).
thf(produc1456309597on_fml_type,type,
produc1456309597on_fml: $tType ).
thf(produc1810527345on_trm_type,type,
produc1810527345on_trm: $tType ).
thf(produc46605351on_fml_type,type,
produc46605351on_fml: $tType ).
thf(produc432717079riable_type,type,
produc432717079riable: $tType ).
thf(set_Pr943832262on_trm_type,type,
set_Pr943832262on_trm: $tType ).
thf(set_Pr1235432374le_trm_type,type,
set_Pr1235432374le_trm: $tType ).
thf(produc1024976764on_trm_type,type,
produc1024976764on_trm: $tType ).
thf(produc1408538418on_fml_type,type,
produc1408538418on_fml: $tType ).
thf(produc464795408on_trm_type,type,
produc464795408on_trm: $tType ).
thf(produc833882726rp_trm_type,type,
produc833882726rp_trm: $tType ).
thf(produc1367888000le_trm_type,type,
produc1367888000le_trm: $tType ).
thf(set_Pr604539619r_char_type,type,
set_Pr604539619r_char: $tType ).
thf(set_Pr491793543rm_trm_type,type,
set_Pr491793543rm_trm: $tType ).
thf(produc1593312387r_char_type,type,
produc1593312387r_char: $tType ).
thf(product_prod_trm_trm_type,type,
product_prod_trm_trm: $tType ).
thf(option_game_type,type,
option_game: $tType ).
thf(option_trm_type,type,
option_trm: $tType ).
thf(option_fml_type,type,
option_fml: $tType ).
thf(denotational_interp_type,type,
denotational_interp: $tType ).
thf(set_variable_type,type,
set_variable: $tType ).
thf(set_char_type,type,
set_char: $tType ).
thf(variable_type,type,
variable: $tType ).
thf(game_type,type,
game: $tType ).
thf(char_type,type,
char: $tType ).
thf(trm_type,type,
trm: $tType ).
thf(fml_type,type,
fml: $tType ).
thf(real_type,type,
real: $tType ).
thf(bNF_Gr1666135339on_trm_type,type,
bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
thf(bNF_Gr852774302le_trm_type,type,
bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
thf(bNF_Gr951178926on_trm_type,type,
bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
thf(bNF_Gr400922303on_trm_type,type,
bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
thf(bNF_Gr1330108682le_trm_type,type,
bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
thf(bNF_Gr1933470746on_trm_type,type,
bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
thf(denota1419872369iation_type,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(none_fml_type,type,
none_fml: option_fml ).
thf(none_game_type,type,
none_game: option_game ).
thf(none_trm_type,type,
none_trm: option_trm ).
thf(some_fml_type,type,
some_fml: fml > option_fml ).
thf(some_game_type,type,
some_game: game > option_game ).
thf(some_trm_type,type,
some_trm: trm > option_trm ).
thf(case_option_o_fml_type,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(case_option_o_game_type,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(case_option_o_trm_type,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(the_fml_type,type,
the_fml: option_fml > fml ).
thf(the_game_type,type,
the_game: option_game > game ).
thf(the_trm_type,type,
the_trm: option_trm > trm ).
thf(ord_le847028878_trm_o_type,type,
ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
thf(ord_le1957133745_trm_o_type,type,
ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
thf(ord_le90123726_trm_o_type,type,
ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
thf(ord_le1721128566_trm_o_type,type,
ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
thf(ord_le157637894_trm_o_type,type,
ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
thf(ord_le1222882015_trm_o_type,type,
ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
thf(ord_le370603054_trm_o_type,type,
ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
thf(ord_le373274227_trm_o_type,type,
ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
thf(ord_le1322722599on_trm_type,type,
ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
thf(ord_le282106107riable_type,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(order_272405634riable_type,type,
order_272405634riable: ( set_variable > $o ) > set_variable ).
thf(produc1132922070rp_trm_type,type,
produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
thf(produc909629463on_fml_type,type,
produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
thf(produc2124676926on_fml_type,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(produc1111617711n_game_type,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(produc709594775on_trm_type,type,
produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
thf(produc2015636557le_trm_type,type,
produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
thf(produc2001752919on_trm_type,type,
produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
thf(produc1056455193le_trm_type,type,
produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
thf(produc444919481on_trm_type,type,
produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
thf(produc1766592463riable_type,type,
produc1766592463riable: set_variable > set_variable > produc432717079riable ).
thf(produc1482344242le_trm_type,type,
produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
thf(produc1500300866on_trm_type,type,
produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
thf(produc19545147r_char_type,type,
produc19545147r_char: char > char > produc1593312387r_char ).
thf(product_Pair_trm_trm_type,type,
product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
thf(produc1205977188on_fml_type,type,
produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
thf(produc1743721902on_trm_type,type,
produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
thf(collect_char_type,type,
collect_char: ( char > $o ) > set_char ).
thf(collect_variable_type,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(geq_type,type,
geq: trm > trm > fml ).
thf(assign_type,type,
assign: variable > trm > game ).
thf(ode_type,type,
ode: char > trm > game ).
thf(test_type,type,
test: fml > game ).
thf(const_type,type,
const: char > trm ).
thf(differential_type,type,
differential: trm > trm ).
thf(func_type,type,
func: char > trm > trm ).
thf(number_type,type,
number: real > trm ).
thf(plus_type,type,
plus: trm > trm > trm ).
thf(times_type,type,
times: trm > trm > trm ).
thf(var_type,type,
var: variable > trm ).
thf(uSubst834381837ssigno_type,type,
uSubst834381837ssigno: variable > option_trm > option_game ).
thf(uSubst157155628no_rel_type,type,
uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
thf(uSubst716837505ntialo_type,type,
uSubst716837505ntialo: option_trm > option_trm ).
thf(uSubst2051024824lo_rel_type,type,
uSubst2051024824lo_rel: option_trm > option_trm > $o ).
thf(uSubst152838031e_Geqo_type,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(uSubst1304144938qo_rel_type,type,
uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(uSubst1827052306e_ODEo_type,type,
uSubst1827052306e_ODEo: char > option_trm > option_game ).
thf(uSubst299938919Eo_rel_type,type,
uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
thf(uSubst141955042_Pluso_type,type,
uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
thf(uSubst691094423so_rel_type,type,
uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(uSubst1367128042_Testo_type,type,
uSubst1367128042_Testo: option_fml > option_game ).
thf(uSubst954181007to_rel_type,type,
uSubst954181007to_rel: option_fml > option_fml > $o ).
thf(uSubst918876924Timeso_type,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(uSubst924844285so_rel_type,type,
uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(uSubst1559070963pconst_type,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(uSubst516392804stappf_type,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(uSubst516392818stappt_type,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(uSubst1917534215pt_rel_type,type,
uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
thf(accp_option_fml_type,type,
accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
thf(accp_option_trm_type,type,
accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
thf(accp_P758790320on_trm_type,type,
accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
thf(accp_P1877119646le_trm_type,type,
accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
thf(accp_P419951815on_trm_type,type,
accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
thf(accp_P394694195on_trm_type,type,
accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
thf(lex_pr114844335on_trm_type,type,
lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
thf(lex_pr1522821402le_trm_type,type,
lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
thf(lex_pr1901327402on_trm_type,type,
lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
thf(member165817296on_trm_type,type,
member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
thf(member602811152on_trm_type,type,
member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
thf(member1150310282le_trm_type,type,
member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
thf(member1950256170on_trm_type,type,
member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
thf(member1978718144riable_type,type,
member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
thf(member2122665623le_trm_type,type,
member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
thf(member694524327on_trm_type,type,
member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
thf(member1866856748r_char_type,type,
member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
thf(member1735386832rm_trm_type,type,
member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
thf(member_char_type,type,
member_char: char > set_char > $o ).
thf(member_variable_type,type,
member_variable: variable > set_variable > $o ).
thf(u_type,type,
u: set_variable ).
thf(ua_type,type,
ua: set_variable ).
thf(eta_type,type,
eta: trm ).
thf(nu_type,type,
nu: variable > real ).
thf(nu2_type,type,
nu2: variable > real ).
thf(omega_type,type,
omega: variable > real ).
thf(omega2_type,type,
omega2: variable > real ).
thf(sigma_type,type,
sigma: produc1418842292n_game ).
thf(theta_type,type,
theta: trm ).
thf(86,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm > $o] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ! [D: produc464795408on_trm] :
( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( accp_P419951815on_trm @ A @ E ) )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_accp_Oinducts) ).
thf(645,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm > $o] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ! [D: produc464795408on_trm] :
( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( accp_P419951815on_trm @ A @ E ) )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(240,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( differential @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( differential @ C ) )
= ( uSubst716837505ntialo
@ ( uSubst516392818stappt @ A
@ ( collect_variable
@ ^ [D: variable] : $true )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_usubstappt_Opsimps_I7_J) ).
thf(1322,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( differential @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( differential @ C ) )
= ( uSubst716837505ntialo
@ ( uSubst516392818stappt @ A
@ ( collect_variable
@ ^ [D: variable] : $true )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(210,axiom,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( times @ A @ B )
= ( times @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_trm_Oinject_I6_J) ).
thf(1168,plain,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( times @ A @ B )
= ( times @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(277,axiom,
! [A: option_trm,B: option_trm > option_game > $o,C: option_game] :
( ( ( A = none_trm )
=> ( B @ A @ C ) )
=> ( ( ( C = none_game )
=> ( B @ A @ C ) )
=> ( ! [D: trm,E: game] :
( ( A
= ( some_trm @ D ) )
=> ( ( C
= ( some_game @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_combine__options__cases) ).
thf(1633,plain,
! [A: option_trm,B: option_trm > option_game > $o,C: option_game] :
( ( ( A = none_trm )
=> ( B @ A @ C ) )
=> ( ( ( C = none_game )
=> ( B @ A @ C ) )
=> ( ! [D: trm,E: game] :
( ( A
= ( some_trm @ D ) )
=> ( ( C
= ( some_game @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(46,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_accp__downward) ).
thf(479,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(67,axiom,
! [A: option_game,B: game] :
( ( A
= ( some_game @ B ) )
=> ( A != none_game ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_option_OdiscI) ).
thf(555,plain,
! [A: option_game,B: game] :
( ( A
= ( some_game @ B ) )
=> ( A != none_game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(74,axiom,
! [A: option_game] :
( ( A = none_game )
= ( case_option_o_game @ $true
@ ^ [B: game] : $false
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_option_Odisc__eq__case_I1_J) ).
thf(582,plain,
! [A: option_game] :
( ( A = none_game )
= ( case_option_o_game @ $true
@ ^ [B: game] : $false
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(265,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( uSubst516392818stappt @ A @ B @ ( plus @ C @ D ) )
= ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_usubstappt_Osimps_I5_J) ).
thf(1522,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( uSubst516392818stappt @ A @ B @ ( plus @ C @ D ) )
= ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(3,axiom,
! [A: set_Pr1471344007on_trm,B: set_Pr1471344007on_trm] :
( ! [C: option_trm,D: option_trm] :
( ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ A )
=> ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ B ) )
=> ( ord_le1322722599on_trm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_subrelI) ).
thf(308,plain,
! [A: set_Pr1471344007on_trm,B: set_Pr1471344007on_trm] :
( ! [C: option_trm,D: option_trm] :
( ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ A )
=> ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ B ) )
=> ( ord_le1322722599on_trm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(184,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( ord_le370603054_trm_o @ A @ B )
=> ( ord_le373274227_trm_o @ ( accp_P394694195on_trm @ B ) @ ( accp_P394694195on_trm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_accp__subset) ).
thf(1073,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm > produc1024976764on_trm > $o] :
( ( ord_le370603054_trm_o @ A @ B )
=> ( ord_le373274227_trm_o @ ( accp_P394694195on_trm @ B ) @ ( accp_P394694195on_trm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(54,axiom,
! [A: option_game] :
( ( A != none_game )
=> ( ( some_game @ ( the_game @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_option_Ocollapse) ).
thf(511,plain,
! [A: option_game] :
( ( A != none_game )
=> ( ( some_game @ ( the_game @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(137,axiom,
! [A: game,B: game] :
( ( ( some_game @ A )
= ( some_game @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_option_Oinject) ).
thf(861,plain,
! [A: game,B: game] :
( ( ( some_game @ A )
= ( some_game @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(295,axiom,
! [A: variable,B: option_trm,C: option_game] :
( ( ( uSubst834381837ssigno @ A @ B )
= C )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( C
!= ( some_game @ ( assign @ A @ D ) ) ) )
=> ~ ( ( B = none_trm )
=> ( C != none_game ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_Assigno_Oelims) ).
thf(1750,plain,
! [A: variable,B: option_trm,C: option_game] :
( ( ( uSubst834381837ssigno @ A @ B )
= C )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( C
!= ( some_game @ ( assign @ A @ D ) ) ) )
=> ~ ( ( B = none_trm )
=> ( C != none_game ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(158,axiom,
! [A: set_variable,B: variable > $o] :
( ord_le282106107riable
@ ( collect_variable
@ ^ [C: variable] :
( ( member_variable @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Collect__subset) ).
thf(977,plain,
! [A: set_variable,B: variable > $o] :
( ord_le282106107riable
@ ( collect_variable
@ ^ [C: variable] :
( ( member_variable @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(140,axiom,
! [A: trm > $o,B: trm] :
( ! [C: variable] : ( A @ ( var @ C ) )
=> ( ! [C: real] : ( A @ ( number @ C ) )
=> ( ! [C: char] : ( A @ ( const @ C ) )
=> ( ! [C: char,D: trm] :
( ( A @ D )
=> ( A @ ( func @ C @ D ) ) )
=> ( ! [C: trm,D: trm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( plus @ C @ D ) ) ) )
=> ( ! [C: trm,D: trm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( times @ C @ D ) ) ) )
=> ( ! [C: trm] :
( ( A @ C )
=> ( A @ ( differential @ C ) ) )
=> ( A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_trm_Oinduct) ).
thf(873,plain,
! [A: trm > $o,B: trm] :
( ! [C: variable] : ( A @ ( var @ C ) )
=> ( ! [C: real] : ( A @ ( number @ C ) )
=> ( ! [C: char] : ( A @ ( const @ C ) )
=> ( ! [C: char,D: trm] :
( ( A @ D )
=> ( A @ ( func @ C @ D ) ) )
=> ( ! [C: trm,D: trm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( plus @ C @ D ) ) ) )
=> ( ! [C: trm,D: trm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( times @ C @ D ) ) ) )
=> ( ! [C: trm] :
( ( A @ C )
=> ( A @ ( differential @ C ) ) )
=> ( A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(44,axiom,
! [A: option_fml,B: option_game] :
( ( ( uSubst1367128042_Testo @ A )
= B )
=> ( ( accp_option_fml @ uSubst954181007to_rel @ A )
=> ( ! [C: fml] :
( ( A
= ( some_fml @ C ) )
=> ( ( B
= ( some_game @ ( test @ C ) ) )
=> ~ ( accp_option_fml @ uSubst954181007to_rel @ ( some_fml @ C ) ) ) )
=> ~ ( ( A = none_fml )
=> ( ( B = none_game )
=> ~ ( accp_option_fml @ uSubst954181007to_rel @ none_fml ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_Testo_Opelims) ).
thf(449,plain,
! [A: option_fml,B: option_game] :
( ( ( uSubst1367128042_Testo @ A )
= B )
=> ( ( accp_option_fml @ uSubst954181007to_rel @ A )
=> ( ! [C: fml] :
( ( A
= ( some_fml @ C ) )
=> ( ( B
= ( some_game @ ( test @ C ) ) )
=> ~ ( accp_option_fml @ uSubst954181007to_rel @ ( some_fml @ C ) ) ) )
=> ~ ( ( A = none_fml )
=> ( ( B = none_game )
=> ~ ( accp_option_fml @ uSubst954181007to_rel @ none_fml ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(258,axiom,
! [A: option_trm] :
( ( uSubst918876924Timeso @ none_trm @ A )
= none_trm ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Timeso_Osimps_I2_J) ).
thf(1497,plain,
! [A: option_trm] :
( ( uSubst918876924Timeso @ none_trm @ A )
= none_trm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(23,axiom,
! [A: set_variable,B: variable > set_variable,C: variable,D: trm,E: variable > trm,F: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_variable @ C @ F )
=> ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ D ) @ ( bNF_Gr1330108682le_trm @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_image2__eqI) ).
thf(385,plain,
! [A: set_variable,B: variable > set_variable,C: variable,D: trm,E: variable > trm,F: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_variable @ C @ F )
=> ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ D ) @ ( bNF_Gr1330108682le_trm @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(280,axiom,
! [A: produc1418842292n_game,B: set_variable,C: real] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( number @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( number @ C ) )
= ( some_trm @ ( number @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_usubstappt_Opsimps_I2_J) ).
thf(1655,plain,
! [A: produc1418842292n_game,B: set_variable,C: real] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( number @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( number @ C ) )
= ( some_trm @ ( number @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(201,axiom,
! [A: option_trm,B: option_trm,C: option_trm,D: option_trm,E: set_Pr1471344007on_trm,F: set_Pr1471344007on_trm] :
( ( member602811152on_trm @ ( produc2001752919on_trm @ ( produc709594775on_trm @ A @ B ) @ ( produc709594775on_trm @ C @ D ) ) @ ( lex_pr114844335on_trm @ E @ F ) )
= ( ( member165817296on_trm @ ( produc709594775on_trm @ A @ C ) @ E )
| ( ( A = C )
& ( member165817296on_trm @ ( produc709594775on_trm @ B @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_in__lex__prod) ).
thf(1137,plain,
! [A: option_trm,B: option_trm,C: option_trm,D: option_trm,E: set_Pr1471344007on_trm,F: set_Pr1471344007on_trm] :
( ( member602811152on_trm @ ( produc2001752919on_trm @ ( produc709594775on_trm @ A @ B ) @ ( produc709594775on_trm @ C @ D ) ) @ ( lex_pr114844335on_trm @ E @ F ) )
= ( ( member165817296on_trm @ ( produc709594775on_trm @ A @ C ) @ E )
| ( ( A = C )
& ( member165817296on_trm @ ( produc709594775on_trm @ B @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(103,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
( ~ ( accp_P394694195on_trm @ A @ B )
=> ~ ! [C: produc1024976764on_trm] :
( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_not__accp__down) ).
thf(715,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
( ~ ( accp_P394694195on_trm @ A @ B )
=> ~ ! [C: produc1024976764on_trm] :
( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(124,axiom,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_order__subst1) ).
thf(814,plain,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(150,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( A = B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ord__eq__le__trans) ).
thf(945,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( A = B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(11,axiom,
! [A: char,B: char > char,C: char,D: option_trm,E: char > option_trm,F: set_char] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_char @ C @ F )
=> ( member694524327on_trm @ ( produc1500300866on_trm @ A @ D ) @ ( bNF_Gr951178926on_trm @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_image2__eqI) ).
thf(340,plain,
! [A: char,B: char > char,C: char,D: option_trm,E: char > option_trm,F: set_char] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_char @ C @ F )
=> ( member694524327on_trm @ ( produc1500300866on_trm @ A @ D ) @ ( bNF_Gr951178926on_trm @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(261,axiom,
! [A: option_trm] :
( ( A != none_trm )
= ( case_option_o_trm @ $false
@ ^ [B: trm] : $true
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_option_Odisc__eq__case_I2_J) ).
thf(1507,plain,
! [A: option_trm] :
( ( A != none_trm )
= ( case_option_o_trm @ $false
@ ^ [B: trm] : $true
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(28,axiom,
! [A: set_variable,B: set_variable] :
( ! [C: variable] :
( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) )
=> ( ord_le282106107riable @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_subsetI) ).
thf(404,plain,
! [A: set_variable,B: set_variable] :
( ! [C: variable] :
( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) )
=> ( ord_le282106107riable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(216,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ A )
=> ( ord_le282106107riable @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_dual__order_Otrans) ).
thf(1196,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ C @ A )
=> ( ord_le282106107riable @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(143,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm > $o] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ! [D: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ D )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_accp__induct__rule) ).
thf(898,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm > $o] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ! [D: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ D )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(300,axiom,
! [A: trm] :
( ( uSubst918876924Timeso @ ( some_trm @ A ) @ none_trm )
= none_trm ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Timeso_Osimps_I3_J) ).
thf(1782,plain,
! [A: trm] :
( ( uSubst918876924Timeso @ ( some_trm @ A ) @ none_trm )
= none_trm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(278,axiom,
! [A: variable,B: option_trm] :
( ( ( uSubst834381837ssigno @ A @ B )
= none_game )
= ( B = none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_Assigno__undef) ).
thf(1650,plain,
! [A: variable,B: option_trm] :
( ( ( uSubst834381837ssigno @ A @ B )
= none_game )
= ( B = none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(275,axiom,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst141955042_Pluso @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( C
!= ( some_trm @ ( plus @ D @ E ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( C != none_trm ) )
=> ~ ( ? [D: trm] :
( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( C != none_trm ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Pluso_Oelims) ).
thf(1601,plain,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst141955042_Pluso @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( C
!= ( some_trm @ ( plus @ D @ E ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( C != none_trm ) )
=> ~ ( ? [D: trm] :
( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( C != none_trm ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(256,axiom,
! [A: option_trm,B: trm] :
( ( A
= ( some_trm @ B ) )
=> ( A != none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_option_OdiscI) ).
thf(1475,plain,
! [A: option_trm,B: trm] :
( ( A
= ( some_trm @ B ) )
=> ( A != none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(231,axiom,
! [A: produc1072747943on_trm] :
( ! [B: trm,C: trm] :
( A
!= ( produc709594775on_trm @ ( some_trm @ B ) @ ( some_trm @ C ) ) )
=> ( ! [B: option_trm] :
( A
!= ( produc709594775on_trm @ none_trm @ B ) )
=> ~ ! [B: trm] :
( A
!= ( produc709594775on_trm @ ( some_trm @ B ) @ none_trm ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Timeso_Ocases) ).
thf(1254,plain,
! [A: produc1072747943on_trm] :
( ! [B: trm,C: trm] :
( A
!= ( produc709594775on_trm @ ( some_trm @ B ) @ ( some_trm @ C ) ) )
=> ( ! [B: option_trm] :
( A
!= ( produc709594775on_trm @ none_trm @ B ) )
=> ~ ! [B: trm] :
( A
!= ( produc709594775on_trm @ ( some_trm @ B ) @ none_trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(87,axiom,
! [A: option_trm > $o,B: option_trm > option_trm > $o,C: option_trm,D: option_trm > $o] :
( ( ord_le1957133745_trm_o @ A @ ( accp_option_trm @ B ) )
=> ( ! [E: option_trm,F: option_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: option_trm] :
( ( A @ E )
=> ( ! [F: option_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_accp__subset__induct) ).
thf(651,plain,
! [A: option_trm > $o,B: option_trm > option_trm > $o,C: option_trm,D: option_trm > $o] :
( ( ord_le1957133745_trm_o @ A @ ( accp_option_trm @ B ) )
=> ( ! [E: option_trm,F: option_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: option_trm] :
( ( A @ E )
=> ( ! [F: option_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(6,axiom,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml > $o] :
( ( accp_option_fml @ A @ B )
=> ( ! [D: option_fml] :
( ( accp_option_fml @ A @ D )
=> ( ! [E: option_fml] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_accp__induct__rule) ).
thf(320,plain,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml > $o] :
( ( accp_option_fml @ A @ B )
=> ( ! [D: option_fml] :
( ( accp_option_fml @ A @ D )
=> ( ! [E: option_fml] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(70,axiom,
! [A: variable,B: trm,C: fml] :
( ( assign @ A @ B )
!= ( test @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_game_Odistinct_I15_J) ).
thf(565,plain,
! [A: variable,B: trm,C: fml] :
( ( assign @ A @ B )
!= ( test @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(177,axiom,
! [A: option_trm > option_trm > $o,B: option_trm] :
( ( accp_option_trm @ A @ B )
=> ! [C: option_trm] :
( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_accp_Ocases) ).
thf(1055,plain,
! [A: option_trm > option_trm > $o,B: option_trm] :
( ( accp_option_trm @ A @ B )
=> ! [C: option_trm] :
( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(234,axiom,
! [A: produc1024976764on_trm] :
( ! [B: variable,C: trm] :
( A
!= ( produc1743721902on_trm @ B @ ( some_trm @ C ) ) )
=> ~ ! [B: variable] :
( A
!= ( produc1743721902on_trm @ B @ none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_Assigno_Ocases) ).
thf(1264,plain,
! [A: produc1024976764on_trm] :
( ! [B: variable,C: trm] :
( A
!= ( produc1743721902on_trm @ B @ ( some_trm @ C ) ) )
=> ~ ! [B: variable] :
( A
!= ( produc1743721902on_trm @ B @ none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(109,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_set__eq__subset) ).
thf(751,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(122,axiom,
! [A: produc464795408on_trm > $o,B: produc464795408on_trm > produc464795408on_trm > $o,C: produc464795408on_trm,D: produc464795408on_trm > $o] :
( ( ord_le1222882015_trm_o @ A @ ( accp_P419951815on_trm @ B ) )
=> ( ! [E: produc464795408on_trm,F: produc464795408on_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E )
=> ( ! [F: produc464795408on_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_accp__subset__induct) ).
thf(802,plain,
! [A: produc464795408on_trm > $o,B: produc464795408on_trm > produc464795408on_trm > $o,C: produc464795408on_trm,D: produc464795408on_trm > $o] :
( ( ord_le1222882015_trm_o @ A @ ( accp_P419951815on_trm @ B ) )
=> ( ! [E: produc464795408on_trm,F: produc464795408on_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E )
=> ( ! [F: produc464795408on_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(179,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ B )
=> ! [C: produc1024976764on_trm] :
( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_accp_Ocases) ).
thf(1059,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ B )
=> ! [C: produc1024976764on_trm] :
( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(269,axiom,
! [A: produc1418842292n_game,B: set_variable,C: variable] :
( ( uSubst516392818stappt @ A @ B @ ( var @ C ) )
= ( some_trm @ ( var @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_usubstappt_Osimps_I1_J) ).
thf(1545,plain,
! [A: produc1418842292n_game,B: set_variable,C: variable] :
( ( uSubst516392818stappt @ A @ B @ ( var @ C ) )
= ( some_trm @ ( var @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(229,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: set_variable] :
( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ D @ C )
!= none_trm )
=> ( ( uSubst516392818stappt @ A @ B @ C )
= ( uSubst516392818stappt @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_usubstappt__det) ).
thf(1247,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: set_variable] :
( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ D @ C )
!= none_trm )
=> ( ( uSubst516392818stappt @ A @ B @ C )
= ( uSubst516392818stappt @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(32,axiom,
! [A: char,B: variable > char,C: variable,D: option_trm,E: variable > option_trm,F: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_variable @ C @ F )
=> ( member694524327on_trm @ ( produc1500300866on_trm @ A @ D ) @ ( bNF_Gr1933470746on_trm @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_image2__eqI) ).
thf(416,plain,
! [A: char,B: variable > char,C: variable,D: option_trm,E: variable > option_trm,F: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_variable @ C @ F )
=> ( member694524327on_trm @ ( produc1500300866on_trm @ A @ D ) @ ( bNF_Gr1933470746on_trm @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(5,axiom,
! [A: char,B: trm,C: trm] :
( ( func @ A @ B )
!= ( differential @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_trm_Odistinct_I35_J) ).
thf(316,plain,
! [A: char,B: trm,C: trm] :
( ( func @ A @ B )
!= ( differential @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(192,axiom,
! [A: trm,B: trm] :
( ( uSubst152838031e_Geqo @ ( some_trm @ A ) @ ( some_trm @ B ) )
= ( some_fml @ ( geq @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Geqo_Osimps_I1_J) ).
thf(1100,plain,
! [A: trm,B: trm] :
( ( uSubst152838031e_Geqo @ ( some_trm @ A ) @ ( some_trm @ B ) )
= ( some_fml @ ( geq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(224,axiom,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_subset__refl) ).
thf(1232,plain,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(239,axiom,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm] :
( ! [D: trm,E: trm] : ( A @ ( some_trm @ D ) @ ( some_trm @ E ) )
=> ( ! [D: option_trm] : ( A @ none_trm @ D )
=> ( ! [D: trm] : ( A @ ( some_trm @ D ) @ none_trm )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Timeso_Oinduct) ).
thf(1319,plain,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm] :
( ! [D: trm,E: trm] : ( A @ ( some_trm @ D ) @ ( some_trm @ E ) )
=> ( ! [D: option_trm] : ( A @ none_trm @ D )
=> ( ! [D: trm] : ( A @ ( some_trm @ D ) @ none_trm )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(33,axiom,
! [A: set_variable] :
( ( collect_variable
@ ^ [B: variable] : ( member_variable @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Collect__mem__eq) ).
thf(421,plain,
! [A: set_variable] :
( ( collect_variable
@ ^ [B: variable] : ( member_variable @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(139,axiom,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm] :
( ( accp_option_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_accp__downward) ).
thf(870,plain,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm] :
( ( accp_option_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(196,axiom,
! [A: produc1408538418on_fml] :
( ! [B: variable,C: fml] :
( A
!= ( produc1205977188on_fml @ B @ ( some_fml @ C ) ) )
=> ~ ! [B: variable] :
( A
!= ( produc1205977188on_fml @ B @ none_fml ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_Existso_Ocases) ).
thf(1115,plain,
! [A: produc1408538418on_fml] :
( ! [B: variable,C: fml] :
( A
!= ( produc1205977188on_fml @ B @ ( some_fml @ C ) ) )
=> ~ ! [B: variable] :
( A
!= ( produc1205977188on_fml @ B @ none_fml ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(7,axiom,
! [A: char,B: trm,C: char,D: trm] :
( ( ( func @ A @ B )
= ( func @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_trm_Oinject_I4_J) ).
thf(325,plain,
! [A: char,B: trm,C: char,D: trm] :
( ( ( func @ A @ B )
= ( func @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,axiom,
! [A: option_fml,B: option_game] :
( ( ( uSubst1367128042_Testo @ A )
= B )
=> ( ! [C: fml] :
( ( A
= ( some_fml @ C ) )
=> ( B
!= ( some_game @ ( test @ C ) ) ) )
=> ~ ( ( A = none_fml )
=> ( B != none_game ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_Testo_Oelims) ).
thf(492,plain,
! [A: option_fml,B: option_game] :
( ( ( uSubst1367128042_Testo @ A )
= B )
=> ( ! [C: fml] :
( ( A
= ( some_fml @ C ) )
=> ( B
!= ( some_game @ ( test @ C ) ) ) )
=> ~ ( ( A = none_fml )
=> ( B != none_game ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(283,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( uSubst516392818stappt @ A @ B @ ( times @ C @ D ) )
= ( uSubst918876924Timeso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_usubstappt_Osimps_I6_J) ).
thf(1664,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( uSubst516392818stappt @ A @ B @ ( times @ C @ D ) )
= ( uSubst918876924Timeso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(41,axiom,
( ( '?' @ option_fml )
= ( ^ [A: option_fml > $o] :
( ( A @ none_fml )
| ? [B: fml] : ( A @ ( some_fml @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_split__option__ex) ).
thf(443,plain,
( ( '?' @ option_fml )
= ( ^ [A: option_fml > $o] :
( ( A @ none_fml )
| ? [B: fml] : ( A @ ( some_fml @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(21,axiom,
! [A: variable,B: char,C: trm] :
( ( var @ A )
!= ( func @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_trm_Odistinct_I5_J) ).
thf(376,plain,
! [A: variable,B: char,C: trm] :
( ( var @ A )
!= ( func @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(55,axiom,
! [A: option_game] :
( ( ! [B: game] :
( A
!= ( some_game @ B ) ) )
= ( A = none_game ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_not__Some__eq) ).
thf(514,plain,
! [A: option_game] :
( ( ! [B: game] :
( A
!= ( some_game @ B ) ) )
= ( A = none_game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(273,axiom,
! [A: option_trm,B: option_trm > option_trm > $o,C: option_trm] :
( ( ( A = none_trm )
=> ( B @ A @ C ) )
=> ( ( ( C = none_trm )
=> ( B @ A @ C ) )
=> ( ! [D: trm,E: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( C
= ( some_trm @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_combine__options__cases) ).
thf(1581,plain,
! [A: option_trm,B: option_trm > option_trm > $o,C: option_trm] :
( ( ( A = none_trm )
=> ( B @ A @ C ) )
=> ( ( ( C = none_trm )
=> ( B @ A @ C ) )
=> ( ! [D: trm,E: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( C
= ( some_trm @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(14,axiom,
! [A: option_fml > option_fml > $o,B: option_fml] :
( ! [C: option_fml] :
( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) )
=> ( accp_option_fml @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_accp_Ointros) ).
thf(353,plain,
! [A: option_fml > option_fml > $o,B: option_fml] :
( ! [C: option_fml] :
( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) )
=> ( accp_option_fml @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(76,axiom,
! [A: option_game] :
( ( A != none_game )
= ( case_option_o_game @ $false
@ ^ [B: game] : $true
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_option_Odisc__eq__case_I2_J) ).
thf(602,plain,
! [A: option_game] :
( ( A != none_game )
= ( case_option_o_game @ $false
@ ^ [B: game] : $true
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(219,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_accp__downward) ).
thf(1215,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(153,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_order_Otrans) ).
thf(956,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(197,axiom,
! [A: char,B: trm,C: trm] :
( ( const @ A )
!= ( plus @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_trm_Odistinct_I25_J) ).
thf(1119,plain,
! [A: char,B: trm,C: trm] :
( ( const @ A )
!= ( plus @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(30,axiom,
! [A: set_Pr1471344007on_trm,B: set_Pr1471344007on_trm] :
( ( ( ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ A ) )
= ( ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_pred__equals__eq2) ).
thf(411,plain,
! [A: set_Pr1471344007on_trm,B: set_Pr1471344007on_trm] :
( ( ( ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ A ) )
= ( ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
! [C: variable] :
( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_subset__eq) ).
thf(428,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
! [C: variable] :
( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,axiom,
! [A: variable,B: real] :
( ( var @ A )
!= ( number @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_trm_Odistinct_I1_J) ).
thf(507,plain,
! [A: variable,B: real] :
( ( var @ A )
!= ( number @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(22,axiom,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml > $o] :
( ( accp_option_fml @ A @ B )
=> ( ! [D: option_fml] :
( ( accp_option_fml @ A @ D )
=> ( ! [E: option_fml] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_accp__induct) ).
thf(380,plain,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml > $o] :
( ( accp_option_fml @ A @ B )
=> ( ! [D: option_fml] :
( ( accp_option_fml @ A @ D )
=> ( ! [E: option_fml] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(149,axiom,
! [A: set_variable,B: trm,C: set_variable,D: trm,E: set_Pr181266295riable,F: set_Pr491793543rm_trm] :
( ( member1150310282le_trm @ ( produc1056455193le_trm @ ( produc1482344242le_trm @ A @ B ) @ ( produc1482344242le_trm @ C @ D ) ) @ ( lex_pr1522821402le_trm @ E @ F ) )
= ( ( member1978718144riable @ ( produc1766592463riable @ A @ C ) @ E )
| ( ( A = C )
& ( member1735386832rm_trm @ ( product_Pair_trm_trm @ B @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_in__lex__prod) ).
thf(942,plain,
! [A: set_variable,B: trm,C: set_variable,D: trm,E: set_Pr181266295riable,F: set_Pr491793543rm_trm] :
( ( member1150310282le_trm @ ( produc1056455193le_trm @ ( produc1482344242le_trm @ A @ B ) @ ( produc1482344242le_trm @ C @ D ) ) @ ( lex_pr1522821402le_trm @ E @ F ) )
= ( ( member1978718144riable @ ( produc1766592463riable @ A @ C ) @ E )
| ( ( A = C )
& ( member1735386832rm_trm @ ( product_Pair_trm_trm @ B @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(64,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_order__class_Oorder_Oantisym) ).
thf(546,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(148,axiom,
! [A: option_game,B: option_game > option_fml > $o,C: option_fml] :
( ( ( A = none_game )
=> ( B @ A @ C ) )
=> ( ( ( C = none_fml )
=> ( B @ A @ C ) )
=> ( ! [D: game,E: fml] :
( ( A
= ( some_game @ D ) )
=> ( ( C
= ( some_fml @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_combine__options__cases) ).
thf(925,plain,
! [A: option_game,B: option_game > option_fml > $o,C: option_fml] :
( ( ( A = none_game )
=> ( B @ A @ C ) )
=> ( ( ( C = none_fml )
=> ( B @ A @ C ) )
=> ( ! [D: game,E: fml] :
( ( A
= ( some_game @ D ) )
=> ( ( C
= ( some_fml @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(217,axiom,
! [A: fml,B: char,C: trm] :
( ( test @ A )
!= ( ode @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_game_Odistinct_I35_J) ).
thf(1199,plain,
! [A: fml,B: char,C: trm] :
( ( test @ A )
!= ( ode @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(205,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
( ! [C: produc464795408on_trm] :
( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) )
=> ( accp_P419951815on_trm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_accp_Ointros) ).
thf(1153,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
( ! [C: produc464795408on_trm] :
( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) )
=> ( accp_P419951815on_trm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(123,axiom,
! [A: real,B: trm,C: trm] :
( ( number @ A )
!= ( times @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_trm_Odistinct_I19_J) ).
thf(810,plain,
! [A: real,B: trm,C: trm] :
( ( number @ A )
!= ( times @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(61,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_antisym__conv) ).
thf(534,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(182,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
( ~ ( accp_P758790320on_trm @ A @ B )
=> ~ ! [C: produc1072747943on_trm] :
( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_not__accp__down) ).
thf(1067,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
( ~ ( accp_P758790320on_trm @ A @ B )
=> ~ ! [C: produc1072747943on_trm] :
( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(290,axiom,
! [A: variable] :
( ( uSubst834381837ssigno @ A @ none_trm )
= none_game ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_Assigno_Osimps_I2_J) ).
thf(1736,plain,
! [A: variable] :
( ( uSubst834381837ssigno @ A @ none_trm )
= none_game ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(289,axiom,
! [A: option_trm > $o,B: option_trm] :
( ! [C: trm] : ( A @ ( some_trm @ C ) )
=> ( ( A @ none_trm )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Differentialo_Oinduct) ).
thf(1730,plain,
! [A: option_trm > $o,B: option_trm] :
( ! [C: trm] : ( A @ ( some_trm @ C ) )
=> ( ( A @ none_trm )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(178,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_order__class_Oorder_Oeq__iff) ).
thf(1057,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(142,axiom,
! [A: variable,B: char] :
( ( var @ A )
!= ( const @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_trm_Odistinct_I3_J) ).
thf(894,plain,
! [A: variable,B: char] :
( ( var @ A )
!= ( const @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(152,axiom,
! [A: char,B: trm,C: trm] :
( ( const @ A )
!= ( times @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_trm_Odistinct_I27_J) ).
thf(952,plain,
! [A: char,B: trm,C: trm] :
( ( const @ A )
!= ( times @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(198,axiom,
! [A: produc1072747943on_trm > $o,B: produc1072747943on_trm > produc1072747943on_trm > $o,C: produc1072747943on_trm,D: produc1072747943on_trm > $o] :
( ( ord_le1721128566_trm_o @ A @ ( accp_P758790320on_trm @ B ) )
=> ( ! [E: produc1072747943on_trm,F: produc1072747943on_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E )
=> ( ! [F: produc1072747943on_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_accp__subset__induct) ).
thf(1123,plain,
! [A: produc1072747943on_trm > $o,B: produc1072747943on_trm > produc1072747943on_trm > $o,C: produc1072747943on_trm,D: produc1072747943on_trm > $o] :
( ( ord_le1721128566_trm_o @ A @ ( accp_P758790320on_trm @ B ) )
=> ( ! [E: produc1072747943on_trm,F: produc1072747943on_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E )
=> ( ! [F: produc1072747943on_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(212,axiom,
! [A: game] :
( none_game
!= ( some_game @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_option_Odistinct_I1_J) ).
thf(1174,plain,
! [A: game] :
( none_game
!= ( some_game @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(25,axiom,
! [A: option_fml > option_fml > $o,B: option_fml] :
( ~ ( accp_option_fml @ A @ B )
=> ~ ! [C: option_fml] :
( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_not__accp__down) ).
thf(392,plain,
! [A: option_fml > option_fml > $o,B: option_fml] :
( ~ ( accp_option_fml @ A @ B )
=> ~ ! [C: option_fml] :
( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
! [A: char,B: trm,C: trm,D: trm] :
( ( func @ A @ B )
!= ( times @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_trm_Odistinct_I33_J) ).
thf(424,plain,
! [A: char,B: trm,C: trm,D: trm] :
( ( func @ A @ B )
!= ( times @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(226,axiom,
! [A: char,B: option_trm] :
( ( ( uSubst1827052306e_ODEo @ A @ B )
= none_game )
= ( B = none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_ODEo__undef) ).
thf(1238,plain,
! [A: char,B: option_trm] :
( ( ( uSubst1827052306e_ODEo @ A @ B )
= none_game )
= ( B = none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(171,axiom,
! [A: trm,B: trm,C: trm,D: trm] :
( ( plus @ A @ B )
!= ( times @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_trm_Odistinct_I37_J) ).
thf(1021,plain,
! [A: trm,B: trm,C: trm,D: trm] :
( ( plus @ A @ B )
!= ( times @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(115,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ B @ A )
& ( ord_le282106107riable @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_dual__order_Oeq__iff) ).
thf(778,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ B @ A )
& ( ord_le282106107riable @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(29,axiom,
! [A: char,B: char,C: trm] :
( ( const @ A )
!= ( func @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_trm_Odistinct_I23_J) ).
thf(407,plain,
! [A: char,B: char,C: trm] :
( ( const @ A )
!= ( func @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(97,axiom,
! [A: produc46605351on_fml] :
( ! [B: fml,C: fml] :
( A
!= ( produc909629463on_fml @ ( some_fml @ B ) @ ( some_fml @ C ) ) )
=> ( ! [B: option_fml] :
( A
!= ( produc909629463on_fml @ none_fml @ B ) )
=> ~ ! [B: fml] :
( A
!= ( produc909629463on_fml @ ( some_fml @ B ) @ none_fml ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_Ando_Ocases) ).
thf(693,plain,
! [A: produc46605351on_fml] :
( ! [B: fml,C: fml] :
( A
!= ( produc909629463on_fml @ ( some_fml @ B ) @ ( some_fml @ C ) ) )
=> ( ! [B: option_fml] :
( A
!= ( produc909629463on_fml @ none_fml @ B ) )
=> ~ ! [B: fml] :
( A
!= ( produc909629463on_fml @ ( some_fml @ B ) @ none_fml ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(38,axiom,
! [A: char > $o,B: char > $o] :
( ! [C: char] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_char @ A )
= ( collect_char @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Collect__cong) ).
thf(435,plain,
! [A: char > $o,B: char > $o] :
( ! [C: char] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_char @ A )
= ( collect_char @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(213,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
( ~ ( accp_P419951815on_trm @ A @ B )
=> ~ ! [C: produc464795408on_trm] :
( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_not__accp__down) ).
thf(1178,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
( ~ ( accp_P419951815on_trm @ A @ B )
=> ~ ! [C: produc464795408on_trm] :
( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(173,axiom,
( accp_option_trm
= ( ^ [A: option_trm > option_trm > $o,B: option_trm] :
? [C: option_trm] :
( ( B = C )
& ! [D: option_trm] :
( ( A @ D @ C )
=> ( accp_option_trm @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_accp_Osimps) ).
thf(1027,plain,
( accp_option_trm
= ( ^ [A: option_trm > option_trm > $o,B: option_trm] :
? [C: option_trm] :
( ( B = C )
& ! [D: option_trm] :
( ( A @ D @ C )
=> ( accp_option_trm @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(168,axiom,
! [A: trm] :
( ( the_trm @ ( some_trm @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_option_Osel) ).
thf(1012,plain,
! [A: trm] :
( ( the_trm @ ( some_trm @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(194,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm > $o] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ! [D: produc1072747943on_trm] :
( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( accp_P758790320on_trm @ A @ E ) )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_accp_Oinducts) ).
thf(1106,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm > $o] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ! [D: produc1072747943on_trm] :
( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( accp_P758790320on_trm @ A @ E ) )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(133,axiom,
! [A: char,B: trm] :
( ( const @ A )
!= ( differential @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_trm_Odistinct_I29_J) ).
thf(847,plain,
! [A: char,B: trm] :
( ( const @ A )
!= ( differential @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(48,axiom,
! [A: char,B: option_trm,C: char,D: option_trm,E: set_Pr604539619r_char,F: set_Pr1471344007on_trm] :
( ( member1950256170on_trm @ ( produc444919481on_trm @ ( produc1500300866on_trm @ A @ B ) @ ( produc1500300866on_trm @ C @ D ) ) @ ( lex_pr1901327402on_trm @ E @ F ) )
= ( ( member1866856748r_char @ ( produc19545147r_char @ A @ C ) @ E )
| ( ( A = C )
& ( member165817296on_trm @ ( produc709594775on_trm @ B @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_in__lex__prod) ).
thf(484,plain,
! [A: char,B: option_trm,C: char,D: option_trm,E: set_Pr604539619r_char,F: set_Pr1471344007on_trm] :
( ( member1950256170on_trm @ ( produc444919481on_trm @ ( produc1500300866on_trm @ A @ B ) @ ( produc1500300866on_trm @ C @ D ) ) @ ( lex_pr1901327402on_trm @ E @ F ) )
= ( ( member1866856748r_char @ ( produc19545147r_char @ A @ C ) @ E )
| ( ( A = C )
& ( member165817296on_trm @ ( produc709594775on_trm @ B @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(203,axiom,
! [A: set_variable > $o,B: set_variable,C: set_variable > $o] :
( ( A @ B )
=> ( ! [D: set_variable] :
( ( A @ D )
=> ( ord_le282106107riable @ D @ B ) )
=> ( ! [D: set_variable] :
( ( A @ D )
=> ( ! [E: set_variable] :
( ( A @ E )
=> ( ord_le282106107riable @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_272405634riable @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_GreatestI2__order) ).
thf(1143,plain,
! [A: set_variable > $o,B: set_variable,C: set_variable > $o] :
( ( A @ B )
=> ( ! [D: set_variable] :
( ( A @ D )
=> ( ord_le282106107riable @ D @ B ) )
=> ( ! [D: set_variable] :
( ( A @ D )
=> ( ! [E: set_variable] :
( ( A @ E )
=> ( ord_le282106107riable @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_272405634riable @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(181,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_subset__antisym) ).
thf(1064,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(98,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
( ! [C: produc1024976764on_trm] :
( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) )
=> ( accp_P394694195on_trm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_accp_Ointros) ).
thf(697,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
( ! [C: produc1024976764on_trm] :
( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) )
=> ( accp_P394694195on_trm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(225,axiom,
! [A: real,B: trm,C: trm] :
( ( number @ A )
!= ( plus @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_trm_Odistinct_I17_J) ).
thf(1234,plain,
! [A: real,B: trm,C: trm] :
( ( number @ A )
!= ( plus @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(302,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
!= none_fml )
=> ( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
& ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_usubstappf__geq__conv) ).
thf(1794,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
!= none_fml )
=> ( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
& ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(170,axiom,
! [A: option_fml] :
( ( A != none_fml )
=> ~ ! [B: fml] :
( A
!= ( some_fml @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_option_Oexhaust) ).
thf(1017,plain,
! [A: option_fml] :
( ( A != none_fml )
=> ~ ! [B: fml] :
( A
!= ( some_fml @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(286,axiom,
! [A: produc1418842292n_game,B: set_variable,C: variable] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( var @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( var @ C ) )
= ( some_trm @ ( var @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_usubstappt_Opsimps_I1_J) ).
thf(1719,plain,
! [A: produc1418842292n_game,B: set_variable,C: variable] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( var @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( var @ C ) )
= ( some_trm @ ( var @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(15,axiom,
! [A: set_Pr1471344007on_trm,B: set_Pr1471344007on_trm] :
( ( ord_le847028878_trm_o
@ ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ A )
@ ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ B ) )
= ( ord_le1322722599on_trm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_pred__subset__eq2) ).
thf(356,plain,
! [A: set_Pr1471344007on_trm,B: set_Pr1471344007on_trm] :
( ( ord_le847028878_trm_o
@ ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ A )
@ ^ [C: option_trm,D: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ C @ D ) @ B ) )
= ( ord_le1322722599on_trm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(136,axiom,
! [A: trm,B: trm,C: trm] :
( ( times @ A @ B )
!= ( differential @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_trm_Odistinct_I41_J) ).
thf(857,plain,
! [A: trm,B: trm,C: trm] :
( ( times @ A @ B )
!= ( differential @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(246,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
= ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_usubstappf_Osimps_I2_J) ).
thf(1397,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
= ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(8,axiom,
! [A: real,B: char,C: trm] :
( ( number @ A )
!= ( func @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_trm_Odistinct_I15_J) ).
thf(328,plain,
! [A: real,B: char,C: trm] :
( ( number @ A )
!= ( func @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(207,axiom,
( ( '!' @ option_game )
= ( ^ [A: option_game > $o] :
( ( A @ none_game )
& ! [B: game] : ( A @ ( some_game @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_split__option__all) ).
thf(1160,plain,
( ( '!' @ option_game )
= ( ^ [A: option_game > $o] :
( ( A @ none_game )
& ! [B: game] : ( A @ ( some_game @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(187,axiom,
! [A: fml] :
( ( uSubst1367128042_Testo @ ( some_fml @ A ) )
= ( some_game @ ( test @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Testo_Osimps_I1_J) ).
thf(1082,plain,
! [A: fml] :
( ( uSubst1367128042_Testo @ ( some_fml @ A ) )
= ( some_game @ ( test @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(110,axiom,
! [A: $o,B: fml > $o,C: option_fml] :
( ( case_option_o_fml @ A @ B @ C )
=> ( ( ( C = none_fml )
=> ~ A )
=> ~ ! [D: fml] :
( ( C
= ( some_fml @ D ) )
=> ~ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_case__optionE) ).
thf(753,plain,
! [A: $o,B: fml > $o,C: option_fml] :
( ( case_option_o_fml @ A @ B @ C )
=> ( ( ( C = none_fml )
=> ~ A )
=> ~ ! [D: fml] :
( ( C
= ( some_fml @ D ) )
=> ~ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(185,axiom,
( accp_P758790320on_trm
= ( ^ [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
? [C: produc1072747943on_trm] :
( ( B = C )
& ! [D: produc1072747943on_trm] :
( ( A @ D @ C )
=> ( accp_P758790320on_trm @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_accp_Osimps) ).
thf(1075,plain,
( accp_P758790320on_trm
= ( ^ [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
? [C: produc1072747943on_trm] :
( ( B = C )
& ! [D: produc1072747943on_trm] :
( ( A @ D @ C )
=> ( accp_P758790320on_trm @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(85,axiom,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_ord__eq__le__subst) ).
thf(637,plain,
! [A: set_variable,B: set_variable > set_variable,C: set_variable,D: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( ord_le282106107riable @ C @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le282106107riable @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(50,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_antisym) ).
thf(489,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(94,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm > $o] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ! [D: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ D )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_accp__induct__rule) ).
thf(679,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm > $o] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ! [D: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ D )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(291,axiom,
! [A: option_trm] :
( ( A != none_trm )
=> ( ( some_trm @ ( the_trm @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_option_Ocollapse) ).
thf(1739,plain,
! [A: option_trm] :
( ( A != none_trm )
=> ( ( some_trm @ ( the_trm @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(62,axiom,
! [A: option_fml] :
( ( ( uSubst1367128042_Testo @ A )
= none_game )
= ( A = none_fml ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Testo__undef) ).
thf(537,plain,
! [A: option_fml] :
( ( ( uSubst1367128042_Testo @ A )
= none_game )
= ( A = none_fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(204,axiom,
! [A: option_game] :
( ( A != none_game )
= ( ? [B: game] :
( A
= ( some_game @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_undefg__equiv) ).
thf(1150,plain,
! [A: option_game] :
( ( A != none_game )
= ( ? [B: game] :
( A
= ( some_game @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(253,axiom,
! [A: option_fml,B: option_fml > option_trm > $o,C: option_trm] :
( ( ( A = none_fml )
=> ( B @ A @ C ) )
=> ( ( ( C = none_trm )
=> ( B @ A @ C ) )
=> ( ! [D: fml,E: trm] :
( ( A
= ( some_fml @ D ) )
=> ( ( C
= ( some_trm @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_combine__options__cases) ).
thf(1451,plain,
! [A: option_fml,B: option_fml > option_trm > $o,C: option_trm] :
( ( ( A = none_fml )
=> ( B @ A @ C ) )
=> ( ( ( C = none_trm )
=> ( B @ A @ C ) )
=> ( ! [D: fml,E: trm] :
( ( A
= ( some_fml @ D ) )
=> ( ( C
= ( some_trm @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(199,axiom,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_dual__order_Oantisym) ).
thf(1131,plain,
! [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(303,axiom,
! [A: option_trm,B: option_trm,C: option_fml] :
( ( ( uSubst152838031e_Geqo @ A @ B )
= C )
=> ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( ( C
= ( some_fml @ ( geq @ D @ E ) ) )
=> ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ ( some_trm @ E ) ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( ( C = none_fml )
=> ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ B ) ) ) )
=> ~ ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( ( C = none_fml )
=> ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ none_trm ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Geqo_Opelims) ).
thf(1799,plain,
! [A: option_trm,B: option_trm,C: option_fml] :
( ( ( uSubst152838031e_Geqo @ A @ B )
= C )
=> ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( ( C
= ( some_fml @ ( geq @ D @ E ) ) )
=> ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ ( some_trm @ E ) ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( ( C = none_fml )
=> ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ B ) ) ) )
=> ~ ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( ( C = none_fml )
=> ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ none_trm ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(165,axiom,
! [A: option_fml > $o,B: option_fml] :
( ! [C: fml] : ( A @ ( some_fml @ C ) )
=> ( ( A @ none_fml )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Testo_Oinduct) ).
thf(1002,plain,
! [A: option_fml > $o,B: option_fml] :
( ! [C: fml] : ( A @ ( some_fml @ C ) )
=> ( ( A @ none_fml )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(71,axiom,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ ( C @ B ) @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_order__subst2) ).
thf(569,plain,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ ( C @ B ) @ D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(77,axiom,
! [A: variable,B: variable] :
( ( ( var @ A )
= ( var @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_trm_Oinject_I1_J) ).
thf(605,plain,
! [A: variable,B: variable] :
( ( ( var @ A )
= ( var @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(266,axiom,
! [A: option_trm] :
( ( ! [B: trm] :
( A
!= ( some_trm @ B ) ) )
= ( A = none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_not__Some__eq) ).
thf(1525,plain,
! [A: option_trm] :
( ( ! [B: trm] :
( A
!= ( some_trm @ B ) ) )
= ( A = none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(82,axiom,
! [A: option_fml,B: option_fml] :
( ( ( A = none_fml )
= ( B = none_fml ) )
=> ( ( ( A != none_fml )
=> ( ( B != none_fml )
=> ( ( the_fml @ A )
= ( the_fml @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_option_Oexpand) ).
thf(622,plain,
! [A: option_fml,B: option_fml] :
( ( ( A = none_fml )
= ( B = none_fml ) )
=> ( ( ( A != none_fml )
=> ( ( B != none_fml )
=> ( ( the_fml @ A )
= ( the_fml @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(130,axiom,
! [A: option_fml] :
( ( A != none_fml )
=> ( ( some_fml @ ( the_fml @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_option_Ocollapse) ).
thf(837,plain,
! [A: option_fml] :
( ( A != none_fml )
=> ( ( some_fml @ ( the_fml @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(227,axiom,
! [A: produc1418842292n_game,B: set_variable,C: char] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( const @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( const @ C ) )
= ( uSubst1559070963pconst @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_usubstappt_Opsimps_I3_J) ).
thf(1241,plain,
! [A: produc1418842292n_game,B: set_variable,C: char] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( const @ C ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( const @ C ) )
= ( uSubst1559070963pconst @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(4,axiom,
! [A: option_trm,B: variable > option_trm,C: variable,D: option_trm,E: variable > option_trm,F: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_variable @ C @ F )
=> ( member165817296on_trm @ ( produc709594775on_trm @ A @ D ) @ ( bNF_Gr400922303on_trm @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_image2__eqI) ).
thf(311,plain,
! [A: option_trm,B: variable > option_trm,C: variable,D: option_trm,E: variable > option_trm,F: set_variable] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_variable @ C @ F )
=> ( member165817296on_trm @ ( produc709594775on_trm @ A @ D ) @ ( bNF_Gr400922303on_trm @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(111,axiom,
! [A: trm] :
( ! [B: variable] :
( A
!= ( var @ B ) )
=> ( ! [B: real] :
( A
!= ( number @ B ) )
=> ( ! [B: char] :
( A
!= ( const @ B ) )
=> ( ! [B: char,C: trm] :
( A
!= ( func @ B @ C ) )
=> ( ! [B: trm,C: trm] :
( A
!= ( plus @ B @ C ) )
=> ( ! [B: trm,C: trm] :
( A
!= ( times @ B @ C ) )
=> ~ ! [B: trm] :
( A
!= ( differential @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_trm_Oexhaust) ).
thf(765,plain,
! [A: trm] :
( ! [B: variable] :
( A
!= ( var @ B ) )
=> ( ! [B: real] :
( A
!= ( number @ B ) )
=> ( ! [B: char] :
( A
!= ( const @ B ) )
=> ( ! [B: char,C: trm] :
( A
!= ( func @ B @ C ) )
=> ( ! [B: trm,C: trm] :
( A
!= ( plus @ B @ C ) )
=> ( ! [B: trm,C: trm] :
( A
!= ( times @ B @ C ) )
=> ~ ! [B: trm] :
( A
!= ( differential @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(175,axiom,
! [A: option_fml,B: option_fml > option_fml > $o,C: option_fml] :
( ( ( A = none_fml )
=> ( B @ A @ C ) )
=> ( ( ( C = none_fml )
=> ( B @ A @ C ) )
=> ( ! [D: fml,E: fml] :
( ( A
= ( some_fml @ D ) )
=> ( ( C
= ( some_fml @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_combine__options__cases) ).
thf(1035,plain,
! [A: option_fml,B: option_fml > option_fml > $o,C: option_fml] :
( ( ( A = none_fml )
=> ( B @ A @ C ) )
=> ( ( ( C = none_fml )
=> ( B @ A @ C ) )
=> ( ! [D: fml,E: fml] :
( ( A
= ( some_fml @ D ) )
=> ( ( C
= ( some_fml @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(93,axiom,
! [A: set_variable,B: set_variable,C: variable > $o,D: variable > $o] :
( ( ord_le282106107riable @ A @ B )
=> ( ! [E: variable] :
( ( member_variable @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le282106107riable
@ ( collect_variable
@ ^ [E: variable] :
( ( member_variable @ E @ A )
& ( C @ E ) ) )
@ ( collect_variable
@ ^ [E: variable] :
( ( member_variable @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subset__CollectI) ).
thf(674,plain,
! [A: set_variable,B: set_variable,C: variable > $o,D: variable > $o] :
( ( ord_le282106107riable @ A @ B )
=> ( ! [E: variable] :
( ( member_variable @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le282106107riable
@ ( collect_variable
@ ^ [E: variable] :
( ( member_variable @ E @ A )
& ( C @ E ) ) )
@ ( collect_variable
@ ^ [E: variable] :
( ( member_variable @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(120,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( B = C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_ord__le__eq__trans) ).
thf(794,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( B = C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(84,axiom,
! [A: variable,B: trm,C: trm] :
( ( var @ A )
!= ( plus @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_trm_Odistinct_I7_J) ).
thf(633,plain,
! [A: variable,B: trm,C: trm] :
( ( var @ A )
!= ( plus @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(299,axiom,
! [A: produc1418842292n_game,B: set_variable,C: char] :
( ( uSubst516392818stappt @ A @ B @ ( const @ C ) )
= ( uSubst1559070963pconst @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_usubstappt_Osimps_I3_J) ).
thf(1779,plain,
! [A: produc1418842292n_game,B: set_variable,C: char] :
( ( uSubst516392818stappt @ A @ B @ ( const @ C ) )
= ( uSubst1559070963pconst @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(89,axiom,
! [A: set_variable,B: variable > $o] :
( ord_le282106107riable
@ ( collect_variable
@ ^ [C: variable] :
( ( member_variable @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Collect__restrict) ).
thf(662,plain,
! [A: set_variable,B: variable > $o] :
( ord_le282106107riable
@ ( collect_variable
@ ^ [C: variable] :
( ( member_variable @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(104,axiom,
! [A: option_game] :
( ! [B: game] :
( A
!= ( some_game @ B ) )
=> ( A = none_game ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Loopo_Ocases) ).
thf(718,plain,
! [A: option_game] :
( ! [B: game] :
( A
!= ( some_game @ B ) )
=> ( A = none_game ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(262,axiom,
! [A: char] :
( ( uSubst1827052306e_ODEo @ A @ none_trm )
= none_game ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_ODEo_Osimps_I2_J) ).
thf(1510,plain,
! [A: char] :
( ( uSubst1827052306e_ODEo @ A @ none_trm )
= none_game ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(230,axiom,
! [A: option_trm,B: option_trm] :
( ( ( uSubst918876924Timeso @ A @ B )
= none_trm )
= ( ( A = none_trm )
| ( B = none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Timeso__undef) ).
thf(1251,plain,
! [A: option_trm,B: option_trm] :
( ( ( uSubst918876924Timeso @ A @ B )
= none_trm )
= ( ( A = none_trm )
| ( B = none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(36,axiom,
! [A: variable,B: variable > $o] :
( ( member_variable @ A @ ( collect_variable @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_mem__Collect__eq) ).
thf(430,plain,
! [A: variable,B: variable > $o] :
( ( member_variable @ A @ ( collect_variable @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(193,axiom,
! [A: option_fml] :
( ( A != none_fml )
= ( case_option_o_fml @ $false
@ ^ [B: fml] : $true
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_option_Odisc__eq__case_I2_J) ).
thf(1103,plain,
! [A: option_fml] :
( ( A != none_fml )
= ( case_option_o_fml @ $false
@ ^ [B: fml] : $true
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(294,axiom,
! [A: variable > option_trm > $o,B: variable,C: option_trm] :
( ! [D: variable,E: trm] : ( A @ D @ ( some_trm @ E ) )
=> ( ! [D: variable] : ( A @ D @ none_trm )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Assigno_Oinduct) ).
thf(1747,plain,
! [A: variable > option_trm > $o,B: variable,C: option_trm] :
( ! [D: variable,E: trm] : ( A @ D @ ( some_trm @ E ) )
=> ( ! [D: variable] : ( A @ D @ none_trm )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(270,axiom,
! [A: option_trm,B: option_trm] :
( ( ( uSubst141955042_Pluso @ A @ B )
= none_trm )
= ( ( A = none_trm )
| ( B = none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Pluso__undef) ).
thf(1548,plain,
! [A: option_trm,B: option_trm] :
( ( ( uSubst141955042_Pluso @ A @ B )
= none_trm )
= ( ( A = none_trm )
| ( B = none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(72,axiom,
! [A: option_fml > $o,B: option_fml] :
( ( A @ none_fml )
=> ( ! [C: fml] : ( A @ ( some_fml @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_option_Oinducts) ).
thf(573,plain,
! [A: option_fml > $o,B: option_fml] :
( ( A @ none_fml )
=> ( ! [C: fml] : ( A @ ( some_fml @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(69,axiom,
! [A: trm,B: trm] :
( ( uSubst918876924Timeso @ ( some_trm @ A ) @ ( some_trm @ B ) )
= ( some_trm @ ( times @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Timeso_Osimps_I1_J) ).
thf(562,plain,
! [A: trm,B: trm] :
( ( uSubst918876924Timeso @ ( some_trm @ A ) @ ( some_trm @ B ) )
= ( some_trm @ ( times @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(132,axiom,
! [A: trm,B: trm,C: trm] :
( ( plus @ A @ B )
!= ( differential @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_trm_Odistinct_I39_J) ).
thf(843,plain,
! [A: trm,B: trm,C: trm] :
( ( plus @ A @ B )
!= ( differential @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(113,axiom,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( geq @ A @ B )
= ( geq @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fml_Oinject_I2_J) ).
thf(772,plain,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( geq @ A @ B )
= ( geq @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(107,axiom,
! [A: set_variable,B: trm,C: set_Pr1235432374le_trm,D: trm] :
( ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ B ) @ C )
=> ( ( D = B )
=> ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_ssubst__Pair__rhs) ).
thf(743,plain,
! [A: set_variable,B: trm,C: set_Pr1235432374le_trm,D: trm] :
( ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ B ) @ C )
=> ( ( D = B )
=> ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(73,axiom,
! [A: variable,B: trm,C: variable,D: trm] :
( ( ( assign @ A @ B )
= ( assign @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_game_Oinject_I2_J) ).
thf(579,plain,
! [A: variable,B: trm,C: variable,D: trm] :
( ( ( assign @ A @ B )
= ( assign @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(248,axiom,
! [A: option_trm,B: option_trm] :
( ( ( uSubst716837505ntialo @ A )
= B )
=> ( ( accp_option_trm @ uSubst2051024824lo_rel @ A )
=> ( ! [C: trm] :
( ( A
= ( some_trm @ C ) )
=> ( ( B
= ( some_trm @ ( differential @ C ) ) )
=> ~ ( accp_option_trm @ uSubst2051024824lo_rel @ ( some_trm @ C ) ) ) )
=> ~ ( ( A = none_trm )
=> ( ( B = none_trm )
=> ~ ( accp_option_trm @ uSubst2051024824lo_rel @ none_trm ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Differentialo_Opelims) ).
thf(1403,plain,
! [A: option_trm,B: option_trm] :
( ( ( uSubst716837505ntialo @ A )
= B )
=> ( ( accp_option_trm @ uSubst2051024824lo_rel @ A )
=> ( ! [C: trm] :
( ( A
= ( some_trm @ C ) )
=> ( ( B
= ( some_trm @ ( differential @ C ) ) )
=> ~ ( accp_option_trm @ uSubst2051024824lo_rel @ ( some_trm @ C ) ) ) )
=> ~ ( ( A = none_trm )
=> ( ( B = none_trm )
=> ~ ( accp_option_trm @ uSubst2051024824lo_rel @ none_trm ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(260,axiom,
! [A: trm] :
( none_trm
!= ( some_trm @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_option_Odistinct_I1_J) ).
thf(1503,plain,
! [A: trm] :
( none_trm
!= ( some_trm @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(42,axiom,
some_trm = some_trm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Aterm__Some) ).
thf(445,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(236,axiom,
! [A: variable,B: option_trm,C: option_game] :
( ( ( uSubst834381837ssigno @ A @ B )
= C )
=> ( ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( ( C
= ( some_game @ ( assign @ A @ D ) ) )
=> ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ A @ ( some_trm @ D ) ) ) ) )
=> ~ ( ( B = none_trm )
=> ( ( C = none_game )
=> ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ A @ none_trm ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_Assigno_Opelims) ).
thf(1271,plain,
! [A: variable,B: option_trm,C: option_game] :
( ( ( uSubst834381837ssigno @ A @ B )
= C )
=> ( ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( ( C
= ( some_game @ ( assign @ A @ D ) ) )
=> ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ A @ ( some_trm @ D ) ) ) ) )
=> ~ ( ( B = none_trm )
=> ( ( C = none_game )
=> ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ A @ none_trm ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(243,axiom,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst918876924Timeso @ A @ B )
= C )
=> ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( ( C
= ( some_trm @ ( times @ D @ E ) ) )
=> ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ ( some_trm @ E ) ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ B ) ) ) )
=> ~ ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ none_trm ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_Timeso_Opelims) ).
thf(1332,plain,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst918876924Timeso @ A @ B )
= C )
=> ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( ( C
= ( some_trm @ ( times @ D @ E ) ) )
=> ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ ( some_trm @ E ) ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ B ) ) ) )
=> ~ ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ none_trm ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(10,axiom,
! [A: option_trm,B: char > option_trm,C: char,D: option_trm,E: char > option_trm,F: set_char] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_char @ C @ F )
=> ( member165817296on_trm @ ( produc709594775on_trm @ A @ D ) @ ( bNF_Gr1666135339on_trm @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_image2__eqI) ).
thf(335,plain,
! [A: option_trm,B: char > option_trm,C: char,D: option_trm,E: char > option_trm,F: set_char] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_char @ C @ F )
=> ( member165817296on_trm @ ( produc709594775on_trm @ A @ D ) @ ( bNF_Gr1666135339on_trm @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(146,axiom,
! [A: produc1016592119n_game] :
( ! [B: game,C: game] :
( A
!= ( produc1111617711n_game @ ( some_game @ B ) @ ( some_game @ C ) ) )
=> ( ! [B: option_game] :
( A
!= ( produc1111617711n_game @ B @ none_game ) )
=> ~ ! [B: game] :
( A
!= ( produc1111617711n_game @ none_game @ ( some_game @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_Composeo_Ocases) ).
thf(919,plain,
! [A: produc1016592119n_game] :
( ! [B: game,C: game] :
( A
!= ( produc1111617711n_game @ ( some_game @ B ) @ ( some_game @ C ) ) )
=> ( ! [B: option_game] :
( A
!= ( produc1111617711n_game @ B @ none_game ) )
=> ~ ! [B: game] :
( A
!= ( produc1111617711n_game @ none_game @ ( some_game @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(222,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm > $o] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ! [D: produc1024976764on_trm] :
( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( accp_P394694195on_trm @ A @ E ) )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_accp_Oinducts) ).
thf(1224,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm > $o] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ! [D: produc1024976764on_trm] :
( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( accp_P394694195on_trm @ A @ E ) )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(13,axiom,
! [A: set_variable,B: set_variable,C: variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_subsetD) ).
thf(350,plain,
! [A: set_variable,B: set_variable,C: variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(63,axiom,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm > $o] :
( ( accp_option_trm @ A @ B )
=> ( ! [D: option_trm] :
( ! [E: option_trm] :
( ( A @ E @ D )
=> ( accp_option_trm @ A @ E ) )
=> ( ! [E: option_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_accp_Oinducts) ).
thf(540,plain,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm > $o] :
( ( accp_option_trm @ A @ B )
=> ( ! [D: option_trm] :
( ! [E: option_trm] :
( ( A @ E @ D )
=> ( accp_option_trm @ A @ E ) )
=> ( ! [E: option_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(79,axiom,
! [A: variable > real,B: set_variable] : ( denota1419872369iation @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Uvariation__refl) ).
thf(611,plain,
! [A: variable > real,B: set_variable] : ( denota1419872369iation @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(118,axiom,
! [A: variable,B: trm,C: trm] :
( ( var @ A )
!= ( times @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_trm_Odistinct_I9_J) ).
thf(787,plain,
! [A: variable,B: trm,C: trm] :
( ( var @ A )
!= ( times @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(232,axiom,
! [A: option_trm] :
( ( A != none_trm )
= ( ? [B: trm] :
( A
= ( some_trm @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_not__None__eq) ).
thf(1258,plain,
! [A: option_trm] :
( ( A != none_trm )
= ( ? [B: trm] :
( A
= ( some_trm @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(100,axiom,
! [A: variable,B: set_variable,C: set_variable,D: variable > $o] :
( ( member_variable @ A @ B )
=> ( ( ord_le282106107riable @ B
@ ( collect_variable
@ ^ [E: variable] :
( ( member_variable @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_prop__restrict) ).
thf(704,plain,
! [A: variable,B: set_variable,C: set_variable,D: variable > $o] :
( ( member_variable @ A @ B )
=> ( ( ord_le282106107riable @ B
@ ( collect_variable
@ ^ [E: variable] :
( ( member_variable @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(159,axiom,
! [A: real,B: char] :
( ( number @ A )
!= ( const @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_trm_Odistinct_I13_J) ).
thf(979,plain,
! [A: real,B: char] :
( ( number @ A )
!= ( const @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(215,axiom,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_eq__iff) ).
thf(1194,plain,
( ( (=) @ set_variable )
= ( ^ [A: set_variable,B: set_variable] :
( ( ord_le282106107riable @ A @ B )
& ( ord_le282106107riable @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(117,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_order__trans) ).
thf(784,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(17,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real,C: set_variable] :
! [D: variable] :
( ~ ( member_variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Uvariation__def) ).
thf(362,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real,C: set_variable] :
! [D: variable] :
( ~ ( member_variable @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(287,axiom,
! [A: option_trm,B: option_trm] :
( ( ( uSubst152838031e_Geqo @ A @ B )
= none_fml )
= ( ( A = none_trm )
| ( B = none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Geqo__undef) ).
thf(1722,plain,
! [A: option_trm,B: option_trm] :
( ( ( uSubst152838031e_Geqo @ A @ B )
= none_fml )
= ( ( A = none_trm )
| ( B = none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(284,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm] :
( ( ( uSubst516392818stappt @ A @ B @ ( differential @ C ) )
!= none_trm )
=> ( ( uSubst516392818stappt @ A
@ ( collect_variable
@ ^ [D: variable] : $true )
@ C )
!= none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_usubstappt__differential__conv) ).
thf(1667,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm] :
( ( ( uSubst516392818stappt @ A @ B @ ( differential @ C ) )
!= none_trm )
=> ( ( uSubst516392818stappt @ A
@ ( collect_variable
@ ^ [D: variable] : $true )
@ C )
!= none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(45,axiom,
( ( uSubst1367128042_Testo @ none_fml )
= none_game ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Testo_Osimps_I2_J) ).
thf(477,plain,
( ( uSubst1367128042_Testo @ none_fml )
= none_game ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(255,axiom,
! [A: produc464795408on_trm] :
( ! [B: char,C: trm] :
( A
!= ( produc1500300866on_trm @ B @ ( some_trm @ C ) ) )
=> ~ ! [B: char] :
( A
!= ( produc1500300866on_trm @ B @ none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_ODEo_Ocases) ).
thf(1471,plain,
! [A: produc464795408on_trm] :
( ! [B: char,C: trm] :
( A
!= ( produc1500300866on_trm @ B @ ( some_trm @ C ) ) )
=> ~ ! [B: char] :
( A
!= ( produc1500300866on_trm @ B @ none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(83,axiom,
( ( '?' @ option_game )
= ( ^ [A: option_game > $o] :
( ( A @ none_game )
| ? [B: game] : ( A @ ( some_game @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_split__option__ex) ).
thf(631,plain,
( ( '?' @ option_game )
= ( ^ [A: option_game > $o] :
( ( A @ none_game )
| ? [B: game] : ( A @ ( some_game @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(99,axiom,
! [A: produc1418842292n_game,B: set_variable,C: fml,D: set_variable] :
( ( ( uSubst516392804stappf @ A @ B @ C )
!= none_fml )
=> ( ( ( uSubst516392804stappf @ A @ D @ C )
!= none_fml )
=> ( ( uSubst516392804stappf @ A @ B @ C )
= ( uSubst516392804stappf @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_usubstappf__det) ).
thf(700,plain,
! [A: produc1418842292n_game,B: set_variable,C: fml,D: set_variable] :
( ( ( uSubst516392804stappf @ A @ B @ C )
!= none_fml )
=> ( ( ( uSubst516392804stappf @ A @ D @ C )
!= none_fml )
=> ( ( uSubst516392804stappf @ A @ B @ C )
= ( uSubst516392804stappf @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(241,axiom,
denota1419872369iation @ nu2 @ omega2 @ ua,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Geq_Oprems_I2_J) ).
thf(1325,plain,
denota1419872369iation @ nu2 @ omega2 @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(174,axiom,
! [A: option_game > $o,B: option_game] :
( ( A @ none_game )
=> ( ! [C: game] : ( A @ ( some_game @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_option_Oinducts) ).
thf(1029,plain,
! [A: option_game > $o,B: option_game] :
( ( A @ none_game )
=> ( ! [C: game] : ( A @ ( some_game @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(156,axiom,
! [A: produc1024976764on_trm > $o,B: produc1024976764on_trm > produc1024976764on_trm > $o,C: produc1024976764on_trm,D: produc1024976764on_trm > $o] :
( ( ord_le373274227_trm_o @ A @ ( accp_P394694195on_trm @ B ) )
=> ( ! [E: produc1024976764on_trm,F: produc1024976764on_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E )
=> ( ! [F: produc1024976764on_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_accp__subset__induct) ).
thf(964,plain,
! [A: produc1024976764on_trm > $o,B: produc1024976764on_trm > produc1024976764on_trm > $o,C: produc1024976764on_trm,D: produc1024976764on_trm > $o] :
( ( ord_le373274227_trm_o @ A @ ( accp_P394694195on_trm @ B ) )
=> ( ! [E: produc1024976764on_trm,F: produc1024976764on_trm] :
( ( A @ E )
=> ( ( B @ F @ E )
=> ( A @ F ) ) )
=> ( ( A @ C )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E )
=> ( ! [F: produc1024976764on_trm] :
( ( B @ F @ E )
=> ( D @ F ) )
=> ( D @ E ) ) )
=> ( D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(112,axiom,
! [A: char,B: trm,C: char,D: trm] :
( ( ( ode @ A @ B )
= ( ode @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_game_Oinject_I8_J) ).
thf(769,plain,
! [A: char,B: trm,C: char,D: trm] :
( ( ( ode @ A @ B )
= ( ode @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(244,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm )
=> ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
= ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ C ) ) @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_usubstappf__geq) ).
thf(1381,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm )
=> ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
= ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ C ) ) @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(180,axiom,
! [A: fml,B: fml] :
( ( ( some_fml @ A )
= ( some_fml @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_option_Oinject) ).
thf(1061,plain,
! [A: fml,B: fml] :
( ( ( some_fml @ A )
= ( some_fml @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(195,axiom,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( plus @ A @ B )
= ( plus @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_trm_Oinject_I5_J) ).
thf(1112,plain,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( plus @ A @ B )
= ( plus @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(12,axiom,
! [A: set_variable,B: char > set_variable,C: char,D: trm,E: char > trm,F: set_char] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_char @ C @ F )
=> ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ D ) @ ( bNF_Gr852774302le_trm @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_image2__eqI) ).
thf(345,plain,
! [A: set_variable,B: char > set_variable,C: char,D: trm,E: char > trm,F: set_char] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_char @ C @ F )
=> ( member2122665623le_trm @ ( produc1482344242le_trm @ A @ D ) @ ( bNF_Gr852774302le_trm @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml > $o] :
( ( accp_option_fml @ A @ B )
=> ( ! [D: option_fml] :
( ! [E: option_fml] :
( ( A @ E @ D )
=> ( accp_option_fml @ A @ E ) )
=> ( ! [E: option_fml] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_accp_Oinducts) ).
thf(367,plain,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml > $o] :
( ( accp_option_fml @ A @ B )
=> ( ! [D: option_fml] :
( ! [E: option_fml] :
( ( A @ E @ D )
=> ( accp_option_fml @ A @ E ) )
=> ( ! [E: option_fml] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(66,axiom,
! [A: game] :
( ( the_game @ ( some_game @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_option_Osel) ).
thf(552,plain,
! [A: game] :
( ( the_game @ ( some_game @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(121,axiom,
! [A: option_game > option_fml > $o,B: option_game,C: option_fml] :
( ! [D: game,E: fml] : ( A @ ( some_game @ D ) @ ( some_fml @ E ) )
=> ( ! [D: option_fml] : ( A @ none_game @ D )
=> ( ! [D: game] : ( A @ ( some_game @ D ) @ none_fml )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Diamondo_Oinduct) ).
thf(799,plain,
! [A: option_game > option_fml > $o,B: option_game,C: option_fml] :
( ! [D: game,E: fml] : ( A @ ( some_game @ D ) @ ( some_fml @ E ) )
=> ( ! [D: option_fml] : ( A @ none_game @ D )
=> ( ! [D: game] : ( A @ ( some_game @ D ) @ none_fml )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(208,axiom,
! [A: option_game > option_game > $o,B: option_game,C: option_game] :
( ! [D: game,E: game] : ( A @ ( some_game @ D ) @ ( some_game @ E ) )
=> ( ! [D: option_game] : ( A @ D @ none_game )
=> ( ! [D: game] : ( A @ none_game @ ( some_game @ D ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Composeo_Oinduct) ).
thf(1162,plain,
! [A: option_game > option_game > $o,B: option_game,C: option_game] :
( ! [D: game,E: game] : ( A @ ( some_game @ D ) @ ( some_game @ E ) )
=> ( ! [D: option_game] : ( A @ D @ none_game )
=> ( ! [D: game] : ( A @ none_game @ ( some_game @ D ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(106,axiom,
! [A: option_fml,B: option_fml > option_game > $o,C: option_game] :
( ( ( A = none_fml )
=> ( B @ A @ C ) )
=> ( ( ( C = none_game )
=> ( B @ A @ C ) )
=> ( ! [D: fml,E: game] :
( ( A
= ( some_fml @ D ) )
=> ( ( C
= ( some_game @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_combine__options__cases) ).
thf(726,plain,
! [A: option_fml,B: option_fml > option_game > $o,C: option_game] :
( ( ( A = none_fml )
=> ( B @ A @ C ) )
=> ( ( ( C = none_game )
=> ( B @ A @ C ) )
=> ( ! [D: fml,E: game] :
( ( A
= ( some_fml @ D ) )
=> ( ( C
= ( some_game @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(160,axiom,
! [A: set_Pr1235432374le_trm,B: set_Pr1235432374le_trm] :
( ( ( ^ [C: set_variable,D: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ C @ D ) @ A ) )
= ( ^ [C: set_variable,D: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_pred__equals__eq2) ).
thf(983,plain,
! [A: set_Pr1235432374le_trm,B: set_Pr1235432374le_trm] :
( ( ( ^ [C: set_variable,D: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ C @ D ) @ A ) )
= ( ^ [C: set_variable,D: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(27,axiom,
! [A: option_trm,B: option_trm,C: set_Pr1471344007on_trm,D: option_trm] :
( ( member165817296on_trm @ ( produc709594775on_trm @ A @ B ) @ C )
=> ( ( D = B )
=> ( member165817296on_trm @ ( produc709594775on_trm @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_ssubst__Pair__rhs) ).
thf(399,plain,
! [A: option_trm,B: option_trm,C: set_Pr1471344007on_trm,D: option_trm] :
( ( member165817296on_trm @ ( produc709594775on_trm @ A @ B ) @ C )
=> ( ( D = B )
=> ( member165817296on_trm @ ( produc709594775on_trm @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(154,axiom,
! [A: variable > real,B: variable > real] :
( denota1419872369iation @ A @ B
@ ( collect_variable
@ ^ [C: variable] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Uvariation__univ) ).
thf(959,plain,
! [A: variable > real,B: variable > real] :
( denota1419872369iation @ A @ B
@ ( collect_variable
@ ^ [C: variable] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(127,axiom,
! [A: set_variable > $o,B: set_variable] :
( ( A @ B )
=> ( ! [C: set_variable] :
( ( A @ C )
=> ( ord_le282106107riable @ C @ B ) )
=> ( ( order_272405634riable @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Greatest__equality) ).
thf(827,plain,
! [A: set_variable > $o,B: set_variable] :
( ( A @ B )
=> ( ! [C: set_variable] :
( ( A @ C )
=> ( ord_le282106107riable @ C @ B ) )
=> ( ( order_272405634riable @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(267,axiom,
! [A: option_trm] :
( ( A != none_trm )
=> ~ ! [B: trm] :
( A
!= ( some_trm @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_option_Oexhaust) ).
thf(1528,plain,
! [A: option_trm] :
( ( A != none_trm )
=> ~ ! [B: trm] :
( A
!= ( some_trm @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(116,axiom,
! [A: produc1739631244on_fml] :
( ! [B: game,C: fml] :
( A
!= ( produc2124676926on_fml @ ( some_game @ B ) @ ( some_fml @ C ) ) )
=> ( ! [B: option_fml] :
( A
!= ( produc2124676926on_fml @ none_game @ B ) )
=> ~ ! [B: game] :
( A
!= ( produc2124676926on_fml @ ( some_game @ B ) @ none_fml ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Diamondo_Ocases) ).
thf(780,plain,
! [A: produc1739631244on_fml] :
( ! [B: game,C: fml] :
( A
!= ( produc2124676926on_fml @ ( some_game @ B ) @ ( some_fml @ C ) ) )
=> ( ! [B: option_fml] :
( A
!= ( produc2124676926on_fml @ none_game @ B ) )
=> ~ ! [B: game] :
( A
!= ( produc2124676926on_fml @ ( some_game @ B ) @ none_fml ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(169,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm > produc464795408on_trm > $o] :
( ( ord_le157637894_trm_o @ A @ B )
=> ( ord_le1222882015_trm_o @ ( accp_P419951815on_trm @ B ) @ ( accp_P419951815on_trm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_accp__subset) ).
thf(1015,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm > produc464795408on_trm > $o] :
( ( ord_le157637894_trm_o @ A @ B )
=> ( ord_le1222882015_trm_o @ ( accp_P419951815on_trm @ B ) @ ( accp_P419951815on_trm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(78,axiom,
! [A: option_fml] :
( ( A = none_fml )
= ( case_option_o_fml @ $true
@ ^ [B: fml] : $false
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_option_Odisc__eq__case_I1_J) ).
thf(608,plain,
! [A: option_fml] :
( ( A = none_fml )
= ( case_option_o_fml @ $true
@ ^ [B: fml] : $false
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(161,axiom,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm > $o] :
( ( accp_option_trm @ A @ B )
=> ( ! [D: option_trm] :
( ( accp_option_trm @ A @ D )
=> ( ! [E: option_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_accp__induct) ).
thf(986,plain,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm > $o] :
( ( accp_option_trm @ A @ B )
=> ( ! [D: option_trm] :
( ( accp_option_trm @ A @ D )
=> ( ! [E: option_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(251,axiom,
! [A: option_trm,B: option_trm] :
( ( ( uSubst716837505ntialo @ A )
= B )
=> ( ! [C: trm] :
( ( A
= ( some_trm @ C ) )
=> ( B
!= ( some_trm @ ( differential @ C ) ) ) )
=> ~ ( ( A = none_trm )
=> ( B != none_trm ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Differentialo_Oelims) ).
thf(1435,plain,
! [A: option_trm,B: option_trm] :
( ( ( uSubst716837505ntialo @ A )
= B )
=> ( ! [C: trm] :
( ( A
= ( some_trm @ C ) )
=> ( B
!= ( some_trm @ ( differential @ C ) ) ) )
=> ~ ( ( A = none_trm )
=> ( B != none_trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(134,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_accp__downward) ).
thf(851,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_P394694195on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(145,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ~ ( ( ord_le282106107riable @ A @ B )
=> ~ ( ord_le282106107riable @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_equalityE) ).
thf(912,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ~ ( ( ord_le282106107riable @ A @ B )
=> ~ ( ord_le282106107riable @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(57,axiom,
! [A: char,B: char] :
( ( ( const @ A )
= ( const @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_trm_Oinject_I3_J) ).
thf(521,plain,
! [A: char,B: char] :
( ( ( const @ A )
= ( const @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(211,axiom,
! [A: trm,B: trm] :
( ( uSubst141955042_Pluso @ ( some_trm @ A ) @ ( some_trm @ B ) )
= ( some_trm @ ( plus @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Pluso_Osimps_I1_J) ).
thf(1171,plain,
! [A: trm,B: trm] :
( ( uSubst141955042_Pluso @ ( some_trm @ A ) @ ( some_trm @ B ) )
= ( some_trm @ ( plus @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(52,axiom,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_order__refl) ).
thf(505,plain,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(39,axiom,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml] :
( ( accp_option_fml @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_accp__downward) ).
thf(438,plain,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml] :
( ( accp_option_fml @ A @ B )
=> ( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(105,axiom,
! [A: produc1699626005le_trm] :
( ! [B: produc1418842292n_game,C: set_variable,D: variable] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( var @ D ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: real] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( number @ D ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: char] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( const @ D ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: char,E: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( func @ D @ E ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: trm,E: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( plus @ D @ E ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: trm,E: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( times @ D @ E ) ) ) )
=> ~ ! [B: produc1418842292n_game,C: set_variable,D: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( differential @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_usubstappt_Ocases) ).
thf(722,plain,
! [A: produc1699626005le_trm] :
( ! [B: produc1418842292n_game,C: set_variable,D: variable] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( var @ D ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: real] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( number @ D ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: char] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( const @ D ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: char,E: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( func @ D @ E ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: trm,E: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( plus @ D @ E ) ) ) )
=> ( ! [B: produc1418842292n_game,C: set_variable,D: trm,E: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( times @ D @ E ) ) ) )
=> ~ ! [B: produc1418842292n_game,C: set_variable,D: trm] :
( A
!= ( produc2015636557le_trm @ B @ ( produc1482344242le_trm @ C @ ( differential @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(218,axiom,
! [A: $o,B: game > $o,C: option_game] :
( ( case_option_o_game @ A @ B @ C )
=> ( ( ( C = none_game )
=> ~ A )
=> ~ ! [D: game] :
( ( C
= ( some_game @ D ) )
=> ~ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_case__optionE) ).
thf(1203,plain,
! [A: $o,B: game > $o,C: option_game] :
( ( case_option_o_game @ A @ B @ C )
=> ( ( ( C = none_game )
=> ~ A )
=> ~ ! [D: game] :
( ( C
= ( some_game @ D ) )
=> ~ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(60,axiom,
! [A: set_Pr943832262on_trm,B: set_Pr943832262on_trm] :
( ( ( ^ [C: char,D: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ C @ D ) @ A ) )
= ( ^ [C: char,D: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_pred__equals__eq2) ).
thf(531,plain,
! [A: set_Pr943832262on_trm,B: set_Pr943832262on_trm] :
( ( ( ^ [C: char,D: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ C @ D ) @ A ) )
= ( ^ [C: char,D: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm > $o] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ! [D: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ D )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_accp__induct) ).
thf(617,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm,C: produc1072747943on_trm > $o] :
( ( accp_P758790320on_trm @ A @ B )
=> ( ! [D: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ D )
=> ( ! [E: produc1072747943on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(214,axiom,
! [A: denotational_interp > trm > $o,B: denotational_interp,C: trm] :
( ! [D: denotational_interp,E: variable] : ( A @ D @ ( var @ E ) )
=> ( ! [D: denotational_interp,E: real] : ( A @ D @ ( number @ E ) )
=> ( ! [D: denotational_interp,E: char] : ( A @ D @ ( const @ E ) )
=> ( ! [D: denotational_interp,E: char,F: trm] :
( ( A @ D @ F )
=> ( A @ D @ ( func @ E @ F ) ) )
=> ( ! [D: denotational_interp,E: trm] :
( ( A @ D @ E )
=> ! [F: trm] :
( ( A @ D @ F )
=> ( A @ D @ ( plus @ E @ F ) ) ) )
=> ( ! [D: denotational_interp,E: trm] :
( ( A @ D @ E )
=> ! [F: trm] :
( ( A @ D @ F )
=> ( A @ D @ ( times @ E @ F ) ) ) )
=> ( ! [D: denotational_interp,E: trm] :
( ( ? [F: char] :
( member_char @ F
@ ( collect_char
@ ^ [G: char] : $true ) )
=> ( A @ D @ E ) )
=> ( A @ D @ ( differential @ E ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_term__sem_Oinduct) ).
thf(1181,plain,
! [A: denotational_interp > trm > $o,B: denotational_interp,C: trm] :
( ! [D: denotational_interp,E: variable] : ( A @ D @ ( var @ E ) )
=> ( ! [D: denotational_interp,E: real] : ( A @ D @ ( number @ E ) )
=> ( ! [D: denotational_interp,E: char] : ( A @ D @ ( const @ E ) )
=> ( ! [D: denotational_interp,E: char,F: trm] :
( ( A @ D @ F )
=> ( A @ D @ ( func @ E @ F ) ) )
=> ( ! [D: denotational_interp,E: trm] :
( ( A @ D @ E )
=> ! [F: trm] :
( ( A @ D @ F )
=> ( A @ D @ ( plus @ E @ F ) ) ) )
=> ( ! [D: denotational_interp,E: trm] :
( ( A @ D @ E )
=> ! [F: trm] :
( ( A @ D @ F )
=> ( A @ D @ ( times @ E @ F ) ) ) )
=> ( ! [D: denotational_interp,E: trm] :
( ( ? [F: char] :
( member_char @ F
@ ( collect_char
@ ^ [G: char] : $true ) )
=> ( A @ D @ E ) )
=> ( A @ D @ ( differential @ E ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(271,axiom,
! [A: char,B: option_trm,C: option_game] :
( ( ( uSubst1827052306e_ODEo @ A @ B )
= C )
=> ( ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( ( C
= ( some_game @ ( ode @ A @ D ) ) )
=> ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ A @ ( some_trm @ D ) ) ) ) )
=> ~ ( ( B = none_trm )
=> ( ( C = none_game )
=> ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ A @ none_trm ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_ODEo_Opelims) ).
thf(1551,plain,
! [A: char,B: option_trm,C: option_game] :
( ( ( uSubst1827052306e_ODEo @ A @ B )
= C )
=> ( ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( ( C
= ( some_game @ ( ode @ A @ D ) ) )
=> ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ A @ ( some_trm @ D ) ) ) ) )
=> ~ ( ( B = none_trm )
=> ( ( C = none_game )
=> ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ A @ none_trm ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(200,axiom,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Collect__mono) ).
thf(1134,plain,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(49,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( ord_le90123726_trm_o @ A @ B )
=> ( ord_le1721128566_trm_o @ ( accp_P758790320on_trm @ B ) @ ( accp_P758790320on_trm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_accp__subset) ).
thf(487,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm > produc1072747943on_trm > $o] :
( ( ord_le90123726_trm_o @ A @ B )
=> ( ord_le1721128566_trm_o @ ( accp_P758790320on_trm @ B ) @ ( accp_P758790320on_trm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(102,axiom,
! [A: option_trm > option_trm > $o,B: option_trm] :
( ~ ( accp_option_trm @ A @ B )
=> ~ ! [C: option_trm] :
( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_not__accp__down) ).
thf(712,plain,
! [A: option_trm > option_trm > $o,B: option_trm] :
( ~ ( accp_option_trm @ A @ B )
=> ~ ! [C: option_trm] :
( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(274,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( plus @ C @ D ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( plus @ C @ D ) )
= ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_usubstappt_Opsimps_I5_J) ).
thf(1598,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( plus @ C @ D ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( plus @ C @ D ) )
= ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(172,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ B )
=> ! [C: produc1072747943on_trm] :
( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_accp_Ocases) ).
thf(1025,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
( ( accp_P758790320on_trm @ A @ B )
=> ! [C: produc1072747943on_trm] :
( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(183,axiom,
! [A: variable > $o,B: variable > $o] :
( ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) )
= ( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Collect__mono__iff) ).
thf(1070,plain,
! [A: variable > $o,B: variable > $o] :
( ( ord_le282106107riable @ ( collect_variable @ A ) @ ( collect_variable @ B ) )
= ( ! [C: variable] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(206,axiom,
! [A: real,B: trm] :
( ( number @ A )
!= ( differential @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_trm_Odistinct_I21_J) ).
thf(1156,plain,
! [A: real,B: trm] :
( ( number @ A )
!= ( differential @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(31,axiom,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
! [C: variable] :
( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_subset__iff) ).
thf(414,plain,
( ord_le282106107riable
= ( ^ [A: set_variable,B: set_variable] :
! [C: variable] :
( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(223,axiom,
! [A: option_trm > option_trm > $o,B: option_trm > option_trm > $o] :
( ( ord_le847028878_trm_o @ A @ B )
=> ( ord_le1957133745_trm_o @ ( accp_option_trm @ B ) @ ( accp_option_trm @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_accp__subset) ).
thf(1230,plain,
! [A: option_trm > option_trm > $o,B: option_trm > option_trm > $o] :
( ( ord_le847028878_trm_o @ A @ B )
=> ( ord_le1957133745_trm_o @ ( accp_option_trm @ B ) @ ( accp_option_trm @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(247,axiom,
! [A: trm] :
( ( uSubst141955042_Pluso @ ( some_trm @ A ) @ none_trm )
= none_trm ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Pluso_Osimps_I3_J) ).
thf(1400,plain,
! [A: trm] :
( ( uSubst141955042_Pluso @ ( some_trm @ A ) @ none_trm )
= none_trm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(101,axiom,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm > $o] :
( ( accp_option_trm @ A @ B )
=> ( ! [D: option_trm] :
( ( accp_option_trm @ A @ D )
=> ( ! [E: option_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_accp__induct__rule) ).
thf(707,plain,
! [A: option_trm > option_trm > $o,B: option_trm,C: option_trm > $o] :
( ( accp_option_trm @ A @ B )
=> ( ! [D: option_trm] :
( ( accp_option_trm @ A @ D )
=> ( ! [E: option_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(250,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( times @ C @ D ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( times @ C @ D ) )
= ( uSubst918876924Timeso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_usubstappt_Opsimps_I6_J) ).
thf(1432,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A @ ( produc1482344242le_trm @ B @ ( times @ C @ D ) ) ) )
=> ( ( uSubst516392818stappt @ A @ B @ ( times @ C @ D ) )
= ( uSubst918876924Timeso @ ( uSubst516392818stappt @ A @ B @ C ) @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(119,axiom,
! [A: option_game] :
( ( A != none_game )
= ( ? [B: game] :
( A
= ( some_game @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_not__None__eq) ).
thf(791,plain,
! [A: option_game] :
( ( A != none_game )
= ( ? [B: game] :
( A
= ( some_game @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(40,axiom,
( accp_P419951815on_trm
= ( ^ [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
? [C: produc464795408on_trm] :
( ( B = C )
& ! [D: produc464795408on_trm] :
( ( A @ D @ C )
=> ( accp_P419951815on_trm @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_accp_Osimps) ).
thf(441,plain,
( accp_P419951815on_trm
= ( ^ [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
? [C: produc464795408on_trm] :
( ( B = C )
& ! [D: produc464795408on_trm] :
( ( A @ D @ C )
=> ( accp_P419951815on_trm @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(75,axiom,
! [A: option_game,B: option_game > option_game > $o,C: option_game] :
( ( ( A = none_game )
=> ( B @ A @ C ) )
=> ( ( ( C = none_game )
=> ( B @ A @ C ) )
=> ( ! [D: game,E: game] :
( ( A
= ( some_game @ D ) )
=> ( ( C
= ( some_game @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_combine__options__cases) ).
thf(585,plain,
! [A: option_game,B: option_game > option_game > $o,C: option_game] :
( ( ( A = none_game )
=> ( B @ A @ C ) )
=> ( ( ( C = none_game )
=> ( B @ A @ C ) )
=> ( ! [D: game,E: game] :
( ( A
= ( some_game @ D ) )
=> ( ( C
= ( some_game @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(296,axiom,
! [A: char > option_trm > $o,B: char,C: option_trm] :
( ! [D: char,E: trm] : ( A @ D @ ( some_trm @ E ) )
=> ( ! [D: char] : ( A @ D @ none_trm )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_ODEo_Oinduct) ).
thf(1763,plain,
! [A: char > option_trm > $o,B: char,C: option_trm] :
( ! [D: char,E: trm] : ( A @ D @ ( some_trm @ E ) )
=> ( ! [D: char] : ( A @ D @ none_trm )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(16,axiom,
! [A: set_variable,B: set_variable,C: variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_in__mono) ).
thf(359,plain,
! [A: set_variable,B: set_variable,C: variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( member_variable @ C @ A )
=> ( member_variable @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(272,axiom,
( ( '!' @ option_trm )
= ( ^ [A: option_trm > $o] :
( ( A @ none_trm )
& ! [B: trm] : ( A @ ( some_trm @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_split__option__all) ).
thf(1579,plain,
( ( '!' @ option_trm )
= ( ^ [A: option_trm > $o] :
( ( A @ none_trm )
& ! [B: trm] : ( A @ ( some_trm @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(220,axiom,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_dual__order_Orefl) ).
thf(1218,plain,
! [A: set_variable] : ( ord_le282106107riable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(221,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_equalityD1) ).
thf(1220,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(131,axiom,
! [A: trm,B: trm] :
( ( ( differential @ A )
= ( differential @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_trm_Oinject_I7_J) ).
thf(840,plain,
! [A: trm,B: trm] :
( ( ( differential @ A )
= ( differential @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(301,axiom,
! [A: option_trm,B: option_trm] :
( ( ( A = none_trm )
= ( B = none_trm ) )
=> ( ( ( A != none_trm )
=> ( ( B != none_trm )
=> ( ( the_trm @ A )
= ( the_trm @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_option_Oexpand) ).
thf(1785,plain,
! [A: option_trm,B: option_trm] :
( ( ( A = none_trm )
= ( B = none_trm ) )
=> ( ( ( A != none_trm )
=> ( ( B != none_trm )
=> ( ( the_trm @ A )
= ( the_trm @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(188,axiom,
! [A: option_trm > option_trm > $o,B: option_trm] :
( ! [C: option_trm] :
( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) )
=> ( accp_option_trm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_accp_Ointros) ).
thf(1085,plain,
! [A: option_trm > option_trm > $o,B: option_trm] :
( ! [C: option_trm] :
( ( A @ C @ B )
=> ( accp_option_trm @ A @ C ) )
=> ( accp_option_trm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(281,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
!= none_fml )
=> ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
= ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ C ) ) @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_usubstappf__geqr) ).
thf(1658,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
!= none_fml )
=> ( ( uSubst516392804stappf @ A @ B @ ( geq @ C @ D ) )
= ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ C ) ) @ ( the_trm @ ( uSubst516392818stappt @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(297,axiom,
! [A: option_trm] :
( ( uSubst141955042_Pluso @ none_trm @ A )
= none_trm ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Pluso_Osimps_I2_J) ).
thf(1766,plain,
! [A: option_trm] :
( ( uSubst141955042_Pluso @ none_trm @ A )
= none_trm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(80,axiom,
! [A: set_variable,B: set_variable,C: variable > $o] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ A
@ ( collect_variable
@ ^ [D: variable] :
( ( member_variable @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: variable] :
( ( member_variable @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subset__Collect__iff) ).
thf(613,plain,
! [A: set_variable,B: set_variable,C: variable > $o] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ A
@ ( collect_variable
@ ^ [D: variable] :
( ( member_variable @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: variable] :
( ( member_variable @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(176,axiom,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_subset__trans) ).
thf(1052,plain,
! [A: set_variable,B: set_variable,C: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ord_le282106107riable @ B @ C )
=> ( ord_le282106107riable @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(138,axiom,
! [A: option_game > $o,B: option_game] :
( ! [C: game] : ( A @ ( some_game @ C ) )
=> ( ( A @ none_game )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Loopo_Oinduct) ).
thf(864,plain,
! [A: option_game > $o,B: option_game] :
( ! [C: game] : ( A @ ( some_game @ C ) )
=> ( ( A @ none_game )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(202,axiom,
! [A: trm] :
( ( uSubst716837505ntialo @ ( some_trm @ A ) )
= ( some_trm @ ( differential @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Differentialo_Osimps_I1_J) ).
thf(1140,plain,
! [A: trm] :
( ( uSubst716837505ntialo @ ( some_trm @ A ) )
= ( some_trm @ ( differential @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(285,axiom,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst141955042_Pluso @ A @ B )
= C )
=> ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( ( C
= ( some_trm @ ( plus @ D @ E ) ) )
=> ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ ( some_trm @ E ) ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ B ) ) ) )
=> ~ ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ none_trm ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_Pluso_Opelims) ).
thf(1670,plain,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst141955042_Pluso @ A @ B )
= C )
=> ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ A @ B ) )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( ( C
= ( some_trm @ ( plus @ D @ E ) ) )
=> ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ ( some_trm @ E ) ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ B ) ) ) )
=> ~ ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( ( C = none_trm )
=> ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ D ) @ none_trm ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(166,axiom,
denota1419872369iation @ nu @ omega @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_vaouter) ).
thf(1008,plain,
denota1419872369iation @ nu @ omega @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(43,axiom,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
( ! [C: produc1072747943on_trm] :
( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) )
=> ( accp_P758790320on_trm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_accp_Ointros) ).
thf(446,plain,
! [A: produc1072747943on_trm > produc1072747943on_trm > $o,B: produc1072747943on_trm] :
( ! [C: produc1072747943on_trm] :
( ( A @ C @ B )
=> ( accp_P758790320on_trm @ A @ C ) )
=> ( accp_P758790320on_trm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(162,axiom,
! [A: option_game] :
( ( A != none_game )
=> ~ ! [B: game] :
( A
!= ( some_game @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_option_Oexhaust) ).
thf(991,plain,
! [A: option_game] :
( ( A != none_game )
=> ~ ! [B: game] :
( A
!= ( some_game @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(238,axiom,
( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
!= none_fml ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Geq_Oprems_I1_J) ).
thf(1316,plain,
( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
!= none_fml ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(47,axiom,
( ( '!' @ option_fml )
= ( ^ [A: option_fml > $o] :
( ( A @ none_fml )
& ! [B: fml] : ( A @ ( some_fml @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_split__option__all) ).
thf(482,plain,
( ( '!' @ option_fml )
= ( ^ [A: option_fml > $o] :
( ( A @ none_fml )
& ! [B: fml] : ( A @ ( some_fml @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(92,axiom,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_variable @ A )
= ( collect_variable @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Collect__cong) ).
thf(671,plain,
! [A: variable > $o,B: variable > $o] :
( ! [C: variable] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_variable @ A )
= ( collect_variable @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(58,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_eq__refl) ).
thf(524,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(264,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392818stappt @ A @ B @ ( plus @ C @ D ) )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
& ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_usubstappt__plus__conv) ).
thf(1517,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392818stappt @ A @ B @ ( plus @ C @ D ) )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
& ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(252,axiom,
! [A: option_trm] :
( ( ( uSubst716837505ntialo @ A )
= none_trm )
= ( A = none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Differentialo__undef) ).
thf(1448,plain,
! [A: option_trm] :
( ( ( uSubst716837505ntialo @ A )
= none_trm )
= ( A = none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(96,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm > $o] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ! [D: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ D )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_accp__induct__rule) ).
thf(688,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm > $o] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ! [D: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ D )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(144,axiom,
! [A: option_game,B: option_game] :
( ( ( A = none_game )
= ( B = none_game ) )
=> ( ( ( A != none_game )
=> ( ( B != none_game )
=> ( ( the_game @ A )
= ( the_game @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_option_Oexpand) ).
thf(903,plain,
! [A: option_game,B: option_game] :
( ( ( A = none_game )
= ( B = none_game ) )
=> ( ( ( A != none_game )
=> ( ( B != none_game )
=> ( ( the_game @ A )
= ( the_game @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(242,axiom,
! [A: option_trm > $o,B: option_trm] :
( ( A @ none_trm )
=> ( ! [C: trm] : ( A @ ( some_trm @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_option_Oinducts) ).
thf(1326,plain,
! [A: option_trm > $o,B: option_trm] :
( ( A @ none_trm )
=> ( ! [C: trm] : ( A @ ( some_trm @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(56,axiom,
! [A: variable,B: trm] :
( ( var @ A )
!= ( differential @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_trm_Odistinct_I11_J) ).
thf(517,plain,
! [A: variable,B: trm] :
( ( var @ A )
!= ( differential @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(108,axiom,
! [A: option_game] :
( ( A != none_game )
=> ( A
= ( some_game @ ( the_game @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_option_Oexhaust__sel) ).
thf(748,plain,
! [A: option_game] :
( ( A != none_game )
=> ( A
= ( some_game @ ( the_game @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(24,axiom,
! [A: option_fml > option_fml > $o,B: option_fml] :
( ( accp_option_fml @ A @ B )
=> ! [C: option_fml] :
( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_accp_Ocases) ).
thf(390,plain,
! [A: option_fml > option_fml > $o,B: option_fml] :
( ( accp_option_fml @ A @ B )
=> ! [C: option_fml] :
( ( A @ C @ B )
=> ( accp_option_fml @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(276,axiom,
! [A: option_trm] :
( ! [B: trm] :
( A
!= ( some_trm @ B ) )
=> ( A = none_trm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Differentialo_Ocases) ).
thf(1629,plain,
! [A: option_trm] :
( ! [B: trm] :
( A
!= ( some_trm @ B ) )
=> ( A = none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(293,axiom,
( ( '?' @ option_trm )
= ( ^ [A: option_trm > $o] :
( ( A @ none_trm )
| ? [B: trm] : ( A @ ( some_trm @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_split__option__ex) ).
thf(1745,plain,
( ( '?' @ option_trm )
= ( ^ [A: option_trm > $o] :
( ( A @ none_trm )
| ? [B: trm] : ( A @ ( some_trm @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(228,axiom,
! [A: option_trm] :
( ( A != none_trm )
=> ( A
= ( some_trm @ ( the_trm @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_option_Oexhaust__sel) ).
thf(1244,plain,
! [A: option_trm] :
( ( A != none_trm )
=> ( A
= ( some_trm @ ( the_trm @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(163,axiom,
! [A: produc833882726rp_trm] :
( ! [B: denotational_interp,C: variable] :
( A
!= ( produc1132922070rp_trm @ B @ ( var @ C ) ) )
=> ( ! [B: denotational_interp,C: real] :
( A
!= ( produc1132922070rp_trm @ B @ ( number @ C ) ) )
=> ( ! [B: denotational_interp,C: char] :
( A
!= ( produc1132922070rp_trm @ B @ ( const @ C ) ) )
=> ( ! [B: denotational_interp,C: char,D: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( func @ C @ D ) ) )
=> ( ! [B: denotational_interp,C: trm,D: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( plus @ C @ D ) ) )
=> ( ! [B: denotational_interp,C: trm,D: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( times @ C @ D ) ) )
=> ~ ! [B: denotational_interp,C: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( differential @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_term__sem_Ocases) ).
thf(995,plain,
! [A: produc833882726rp_trm] :
( ! [B: denotational_interp,C: variable] :
( A
!= ( produc1132922070rp_trm @ B @ ( var @ C ) ) )
=> ( ! [B: denotational_interp,C: real] :
( A
!= ( produc1132922070rp_trm @ B @ ( number @ C ) ) )
=> ( ! [B: denotational_interp,C: char] :
( A
!= ( produc1132922070rp_trm @ B @ ( const @ C ) ) )
=> ( ! [B: denotational_interp,C: char,D: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( func @ C @ D ) ) )
=> ( ! [B: denotational_interp,C: trm,D: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( plus @ C @ D ) ) )
=> ( ! [B: denotational_interp,C: trm,D: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( times @ C @ D ) ) )
=> ~ ! [B: denotational_interp,C: trm] :
( A
!= ( produc1132922070rp_trm @ B @ ( differential @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(155,axiom,
! [A: fml] :
( ( the_fml @ ( some_fml @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_option_Osel) ).
thf(961,plain,
! [A: fml] :
( ( the_fml @ ( some_fml @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(245,axiom,
! [A: $o,B: trm > $o,C: option_trm] :
( ( case_option_o_trm @ A @ B @ C )
=> ( ( ( C = none_trm )
=> ~ A )
=> ~ ! [D: trm] :
( ( C
= ( some_trm @ D ) )
=> ~ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_case__optionE) ).
thf(1385,plain,
! [A: $o,B: trm > $o,C: option_trm] :
( ( case_option_o_trm @ A @ B @ C )
=> ( ( ( C = none_trm )
=> ~ A )
=> ~ ! [D: trm] :
( ( C
= ( some_trm @ D ) )
=> ~ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(37,axiom,
( accp_option_fml
= ( ^ [A: option_fml > option_fml > $o,B: option_fml] :
? [C: option_fml] :
( ( B = C )
& ! [D: option_fml] :
( ( A @ D @ C )
=> ( accp_option_fml @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_accp_Osimps) ).
thf(433,plain,
( accp_option_fml
= ( ^ [A: option_fml > option_fml > $o,B: option_fml] :
? [C: option_fml] :
( ( B = C )
& ! [D: option_fml] :
( ( A @ D @ C )
=> ( accp_option_fml @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(91,axiom,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_equalityD2) ).
thf(667,plain,
! [A: set_variable,B: set_variable] :
( ( A = B )
=> ( ord_le282106107riable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(186,axiom,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm > $o] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ! [D: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ D )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_accp__induct) ).
thf(1077,plain,
! [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm,C: produc1024976764on_trm > $o] :
( ( accp_P394694195on_trm @ A @ B )
=> ( ! [D: produc1024976764on_trm] :
( ( accp_P394694195on_trm @ A @ D )
=> ( ! [E: produc1024976764on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(263,axiom,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: trm] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( uSubst516392818stappt @ C @ B @ D )
!= none_trm )
=> ( ( uSubst516392818stappt @ C @ B @ D )
= ( uSubst516392818stappt @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_usubstappt__antimon) ).
thf(1513,plain,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: trm] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( uSubst516392818stappt @ C @ B @ D )
!= none_trm )
=> ( ( uSubst516392818stappt @ C @ B @ D )
= ( uSubst516392818stappt @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(282,axiom,
! [A: produc1418842292n_game,B: set_variable,C: real] :
( ( uSubst516392818stappt @ A @ B @ ( number @ C ) )
= ( some_trm @ ( number @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_usubstappt_Osimps_I2_J) ).
thf(1661,plain,
! [A: produc1418842292n_game,B: set_variable,C: real] :
( ( uSubst516392818stappt @ A @ B @ ( number @ C ) )
= ( some_trm @ ( number @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(65,axiom,
! [A: variable,B: trm] :
( ( uSubst834381837ssigno @ A @ ( some_trm @ B ) )
= ( some_game @ ( assign @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_Assigno_Osimps_I1_J) ).
thf(549,plain,
! [A: variable,B: trm] :
( ( uSubst834381837ssigno @ A @ ( some_trm @ B ) )
= ( some_game @ ( assign @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(128,axiom,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml] :
( ! [D: fml,E: fml] : ( A @ ( some_fml @ D ) @ ( some_fml @ E ) )
=> ( ! [D: option_fml] : ( A @ none_fml @ D )
=> ( ! [D: fml] : ( A @ ( some_fml @ D ) @ none_fml )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Ando_Oinduct) ).
thf(832,plain,
! [A: option_fml > option_fml > $o,B: option_fml,C: option_fml] :
( ! [D: fml,E: fml] : ( A @ ( some_fml @ D ) @ ( some_fml @ E ) )
=> ( ! [D: option_fml] : ( A @ none_fml @ D )
=> ( ! [D: fml] : ( A @ ( some_fml @ D ) @ none_fml )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(95,axiom,
! [A: option_fml] :
( ! [B: fml] :
( A
!= ( some_fml @ B ) )
=> ( A = none_fml ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Testo_Ocases) ).
thf(684,plain,
! [A: option_fml] :
( ! [B: fml] :
( A
!= ( some_fml @ B ) )
=> ( A = none_fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(164,axiom,
! [A: option_fml] :
( ( A != none_fml )
= ( ? [B: fml] :
( A
= ( some_fml @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_undeff__equiv) ).
thf(999,plain,
! [A: option_fml] :
( ( A != none_fml )
= ( ? [B: fml] :
( A
= ( some_fml @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(288,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392818stappt @ A @ B @ ( times @ C @ D ) )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
& ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_usubstappt__times__conv) ).
thf(1725,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm,D: trm] :
( ( ( uSubst516392818stappt @ A @ B @ ( times @ C @ D ) )
!= none_trm )
=> ( ( ( uSubst516392818stappt @ A @ B @ C )
!= none_trm )
& ( ( uSubst516392818stappt @ A @ B @ D )
!= none_trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(125,axiom,
! [A: fml] :
( none_fml
!= ( some_fml @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_option_Odistinct_I1_J) ).
thf(818,plain,
! [A: fml] :
( none_fml
!= ( some_fml @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(135,axiom,
! [A: option_fml] :
( ( ! [B: fml] :
( A
!= ( some_fml @ B ) ) )
= ( A = none_fml ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_not__Some__eq) ).
thf(854,plain,
! [A: option_fml] :
( ( ! [B: fml] :
( A
!= ( some_fml @ B ) ) )
= ( A = none_fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(257,axiom,
! [A: option_trm,B: option_trm > option_fml > $o,C: option_fml] :
( ( ( A = none_trm )
=> ( B @ A @ C ) )
=> ( ( ( C = none_fml )
=> ( B @ A @ C ) )
=> ( ! [D: trm,E: fml] :
( ( A
= ( some_trm @ D ) )
=> ( ( C
= ( some_fml @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_combine__options__cases) ).
thf(1480,plain,
! [A: option_trm,B: option_trm > option_fml > $o,C: option_fml] :
( ( ( A = none_trm )
=> ( B @ A @ C ) )
=> ( ( ( C = none_fml )
=> ( B @ A @ C ) )
=> ( ! [D: trm,E: fml] :
( ( A
= ( some_trm @ D ) )
=> ( ( C
= ( some_fml @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(20,axiom,
! [A: set_char] :
( ( collect_char
@ ^ [B: char] : ( member_char @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(373,plain,
! [A: set_char] :
( ( collect_char
@ ^ [B: char] : ( member_char @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(151,axiom,
! [A: variable > real,B: variable > real,C: set_variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( denota1419872369iation @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Uvariation__sym__rel) ).
thf(950,plain,
! [A: variable > real,B: variable > real,C: set_variable] :
( ( denota1419872369iation @ A @ B @ C )
=> ( denota1419872369iation @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(191,axiom,
! [A: set_variable,B: set_variable,C: variable > real,D: variable > real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( denota1419872369iation @ C @ D @ A )
=> ( denota1419872369iation @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Uvariation__mon) ).
thf(1097,plain,
! [A: set_variable,B: set_variable,C: variable > real,D: variable > real] :
( ( ord_le282106107riable @ A @ B )
=> ( ( denota1419872369iation @ C @ D @ A )
=> ( denota1419872369iation @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(129,axiom,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Uvariation__sym) ).
thf(835,plain,
( denota1419872369iation
= ( ^ [A: variable > real,B: variable > real] : ( denota1419872369iation @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1,conjecture,
( ( uSubst516392818stappt @ sigma @ ua @ theta )
!= none_trm ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( uSubst516392818stappt @ sigma @ ua @ theta )
!= none_trm ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(305,plain,
~ ( ( ( uSubst516392818stappt @ sigma @ ua @ theta )
!= none_trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(90,axiom,
! [A: variable > option_fml > $o,B: variable,C: option_fml] :
( ! [D: variable,E: fml] : ( A @ D @ ( some_fml @ E ) )
=> ( ! [D: variable] : ( A @ D @ none_fml )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Existso_Oinduct) ).
thf(664,plain,
! [A: variable > option_fml > $o,B: variable,C: option_fml] :
( ! [D: variable,E: fml] : ( A @ D @ ( some_fml @ E ) )
=> ( ! [D: variable] : ( A @ D @ none_fml )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(209,axiom,
! [A: trm,B: trm] :
( ( ( some_trm @ A )
= ( some_trm @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_option_Oinject) ).
thf(1165,plain,
! [A: trm,B: trm] :
( ( ( some_trm @ A )
= ( some_trm @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(141,axiom,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_ord__le__eq__subst) ).
thf(886,plain,
! [A: set_variable,B: set_variable,C: set_variable > set_variable,D: set_variable] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_variable,F: set_variable] :
( ( ord_le282106107riable @ E @ F )
=> ( ord_le282106107riable @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le282106107riable @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(292,axiom,
! [A: trm] :
( ( uSubst152838031e_Geqo @ ( some_trm @ A ) @ none_trm )
= none_fml ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Geqo_Osimps_I3_J) ).
thf(1742,plain,
! [A: trm] :
( ( uSubst152838031e_Geqo @ ( some_trm @ A ) @ none_trm )
= none_fml ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(9,axiom,
! [A: char,B: char > $o] :
( ( member_char @ A @ ( collect_char @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(332,plain,
! [A: char,B: char > $o] :
( ( member_char @ A @ ( collect_char @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(233,axiom,
! [A: produc1418842292n_game,B: set_variable,C: trm] :
( ( uSubst516392818stappt @ A @ B @ ( differential @ C ) )
= ( uSubst716837505ntialo
@ ( uSubst516392818stappt @ A
@ ( collect_variable
@ ^ [D: variable] : $true )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_usubstappt_Osimps_I7_J) ).
thf(1261,plain,
! [A: produc1418842292n_game,B: set_variable,C: trm] :
( ( uSubst516392818stappt @ A @ B @ ( differential @ C ) )
= ( uSubst716837505ntialo
@ ( uSubst516392818stappt @ A
@ ( collect_variable
@ ^ [D: variable] : $true )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(235,axiom,
! [A: option_trm] :
( ( A != none_trm )
= ( ? [B: trm] :
( A
= ( some_trm @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_undeft__equiv) ).
thf(1268,plain,
! [A: option_trm] :
( ( A != none_trm )
= ( ? [B: trm] :
( A
= ( some_trm @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(268,axiom,
! [A: char,B: option_trm,C: option_game] :
( ( ( uSubst1827052306e_ODEo @ A @ B )
= C )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( C
!= ( some_game @ ( ode @ A @ D ) ) ) )
=> ~ ( ( B = none_trm )
=> ( C != none_game ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_ODEo_Oelims) ).
thf(1532,plain,
! [A: char,B: option_trm,C: option_game] :
( ( ( uSubst1827052306e_ODEo @ A @ B )
= C )
=> ( ! [D: trm] :
( ( B
= ( some_trm @ D ) )
=> ( C
!= ( some_game @ ( ode @ A @ D ) ) ) )
=> ~ ( ( B = none_trm )
=> ( C != none_game ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(59,axiom,
! [A: option_fml] :
( ( A != none_fml )
= ( ? [B: fml] :
( A
= ( some_fml @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_not__None__eq) ).
thf(528,plain,
! [A: option_fml] :
( ( A != none_fml )
= ( ? [B: fml] :
( A
= ( some_fml @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(259,axiom,
! [A: option_trm] :
( ( A = none_trm )
= ( case_option_o_trm @ $true
@ ^ [B: trm] : $false
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_option_Odisc__eq__case_I1_J) ).
thf(1500,plain,
! [A: option_trm] :
( ( A = none_trm )
= ( case_option_o_trm @ $true
@ ^ [B: trm] : $false
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(126,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm > $o] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ! [D: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ D )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_accp__induct) ).
thf(822,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm,C: produc464795408on_trm > $o] :
( ( accp_P419951815on_trm @ A @ B )
=> ( ! [D: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ D )
=> ( ! [E: produc464795408on_trm] :
( ( A @ E @ D )
=> ( C @ E ) )
=> ( C @ D ) ) )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(249,axiom,
none_trm = none_trm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_undeft__None) ).
thf(1431,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(237,axiom,
! [A: option_game,B: option_game > option_trm > $o,C: option_trm] :
( ( ( A = none_game )
=> ( B @ A @ C ) )
=> ( ( ( C = none_trm )
=> ( B @ A @ C ) )
=> ( ! [D: game,E: trm] :
( ( A
= ( some_game @ D ) )
=> ( ( C
= ( some_trm @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_combine__options__cases) ).
thf(1299,plain,
! [A: option_game,B: option_game > option_trm > $o,C: option_trm] :
( ( ( A = none_game )
=> ( B @ A @ C ) )
=> ( ( ( C = none_trm )
=> ( B @ A @ C ) )
=> ( ! [D: game,E: trm] :
( ( A
= ( some_game @ D ) )
=> ( ( C
= ( some_trm @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(190,axiom,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: fml] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( uSubst516392804stappf @ C @ B @ D )
!= none_fml )
=> ( ( uSubst516392804stappf @ C @ B @ D )
= ( uSubst516392804stappf @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_usubstappf__antimon) ).
thf(1093,plain,
! [A: set_variable,B: set_variable,C: produc1418842292n_game,D: fml] :
( ( ord_le282106107riable @ A @ B )
=> ( ( ( uSubst516392804stappf @ C @ B @ D )
!= none_fml )
=> ( ( uSubst516392804stappf @ C @ B @ D )
= ( uSubst516392804stappf @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(26,axiom,
! [A: char,B: trm,C: trm,D: trm] :
( ( func @ A @ B )
!= ( plus @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_trm_Odistinct_I31_J) ).
thf(395,plain,
! [A: char,B: trm,C: trm,D: trm] :
( ( func @ A @ B )
!= ( plus @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(279,axiom,
( ( uSubst716837505ntialo @ none_trm )
= none_trm ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Differentialo_Osimps_I2_J) ).
thf(1653,plain,
( ( uSubst716837505ntialo @ none_trm )
= none_trm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(167,axiom,
! [A: real,B: real] :
( ( ( number @ A )
= ( number @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_trm_Oinject_I2_J) ).
thf(1009,plain,
! [A: real,B: real] :
( ( ( number @ A )
= ( number @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(147,axiom,
( accp_P394694195on_trm
= ( ^ [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
? [C: produc1024976764on_trm] :
( ( B = C )
& ! [D: produc1024976764on_trm] :
( ( A @ D @ C )
=> ( accp_P394694195on_trm @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_accp_Osimps) ).
thf(923,plain,
( accp_P394694195on_trm
= ( ^ [A: produc1024976764on_trm > produc1024976764on_trm > $o,B: produc1024976764on_trm] :
? [C: produc1024976764on_trm] :
( ( B = C )
& ! [D: produc1024976764on_trm] :
( ( A @ D @ C )
=> ( accp_P394694195on_trm @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(88,axiom,
! [A: set_variable,B: variable > $o,C: variable > $o] :
( ( ord_le282106107riable @ A
@ ( collect_variable
@ ^ [D: variable] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le282106107riable @ A @ ( collect_variable @ B ) )
& ( ord_le282106107riable @ A @ ( collect_variable @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_conj__subset__def) ).
thf(659,plain,
! [A: set_variable,B: variable > $o,C: variable > $o] :
( ( ord_le282106107riable @ A
@ ( collect_variable
@ ^ [D: variable] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le282106107riable @ A @ ( collect_variable @ B ) )
& ( ord_le282106107riable @ A @ ( collect_variable @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(304,axiom,
! [A: option_trm,B: option_trm,C: option_fml] :
( ( ( uSubst152838031e_Geqo @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( C
!= ( some_fml @ ( geq @ D @ E ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( C != none_fml ) )
=> ~ ( ? [D: trm] :
( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( C != none_fml ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Geqo_Oelims) ).
thf(1848,plain,
! [A: option_trm,B: option_trm,C: option_fml] :
( ( ( uSubst152838031e_Geqo @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( C
!= ( some_fml @ ( geq @ D @ E ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( C != none_fml ) )
=> ~ ( ? [D: trm] :
( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( C != none_fml ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(298,axiom,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst918876924Timeso @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( C
!= ( some_trm @ ( times @ D @ E ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( C != none_trm ) )
=> ~ ( ? [D: trm] :
( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( C != none_trm ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Timeso_Oelims) ).
thf(1769,plain,
! [A: option_trm,B: option_trm,C: option_trm] :
( ( ( uSubst918876924Timeso @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some_trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some_trm @ E ) )
=> ( C
!= ( some_trm @ ( times @ D @ E ) ) ) ) )
=> ( ( ( A = none_trm )
=> ( C != none_trm ) )
=> ~ ( ? [D: trm] :
( A
= ( some_trm @ D ) )
=> ( ( B = none_trm )
=> ( C != none_trm ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(189,axiom,
! [A: char,B: option_trm,C: set_Pr943832262on_trm,D: option_trm] :
( ( member694524327on_trm @ ( produc1500300866on_trm @ A @ B ) @ C )
=> ( ( D = B )
=> ( member694524327on_trm @ ( produc1500300866on_trm @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_ssubst__Pair__rhs) ).
thf(1088,plain,
! [A: char,B: option_trm,C: set_Pr943832262on_trm,D: option_trm] :
( ( member694524327on_trm @ ( produc1500300866on_trm @ A @ B ) @ C )
=> ( ( D = B )
=> ( member694524327on_trm @ ( produc1500300866on_trm @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(254,axiom,
! [A: option_trm] :
( ( uSubst152838031e_Geqo @ none_trm @ A )
= none_fml ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Geqo_Osimps_I2_J) ).
thf(1468,plain,
! [A: option_trm] :
( ( uSubst152838031e_Geqo @ none_trm @ A )
= none_fml ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(18,axiom,
! [A: fml,B: fml] :
( ( ( test @ A )
= ( test @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_game_Oinject_I3_J) ).
thf(364,plain,
! [A: fml,B: fml] :
( ( ( test @ A )
= ( test @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(157,axiom,
! [A: option_fml,B: fml] :
( ( A
= ( some_fml @ B ) )
=> ( A != none_fml ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_option_OdiscI) ).
thf(972,plain,
! [A: option_fml,B: fml] :
( ( A
= ( some_fml @ B ) )
=> ( A != none_fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(114,axiom,
! [A: option_fml] :
( ( A != none_fml )
=> ( A
= ( some_fml @ ( the_fml @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_option_Oexhaust__sel) ).
thf(775,plain,
! [A: option_fml] :
( ( A != none_fml )
=> ( A
= ( some_fml @ ( the_fml @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(68,axiom,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ B )
=> ! [C: produc464795408on_trm] :
( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_accp_Ocases) ).
thf(560,plain,
! [A: produc464795408on_trm > produc464795408on_trm > $o,B: produc464795408on_trm] :
( ( accp_P419951815on_trm @ A @ B )
=> ! [C: produc464795408on_trm] :
( ( A @ C @ B )
=> ( accp_P419951815on_trm @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1879,plain,
$false,
inference(e,[status(thm)],[645,1322,1168,1633,479,555,582,1522,308,1073,511,861,1750,977,873,449,1497,385,1655,1137,715,814,945,340,1507,404,1196,898,1782,1650,1601,1475,1254,651,320,565,1055,1264,751,802,1059,1545,1247,416,316,1100,1232,1319,421,870,1115,325,492,1664,443,376,514,1581,353,602,1215,956,1119,411,428,507,380,942,546,925,1199,1153,810,534,1067,1736,1730,1057,894,952,1123,1174,392,424,1238,1021,778,407,693,435,1178,1027,1012,1106,847,484,1143,1064,697,1234,1794,1017,1719,356,857,1397,328,1160,1082,753,1075,637,489,679,1739,537,1150,1451,1131,1799,1002,569,605,1525,622,837,1241,311,765,1035,674,794,633,1779,662,718,1510,1251,430,1103,1747,1548,573,562,843,772,743,579,1403,1503,445,1271,1332,335,919,1224,350,540,611,787,1258,704,979,1194,784,362,1722,1667,477,1471,631,700,1325,1029,964,769,1381,1061,1112,345,367,552,799,1162,726,983,399,959,827,1528,780,1015,608,986,1435,851,912,521,1171,505,438,722,1203,531,617,1181,1551,1134,487,712,1598,1025,1070,1156,414,1230,1400,707,1432,791,441,585,1763,359,1579,1218,1220,840,1785,1085,1658,1766,613,1052,864,1140,1670,1008,446,991,1316,482,671,524,1517,1448,688,903,1326,517,748,390,1629,1745,1244,995,961,1385,433,667,1077,1513,1661,549,832,684,999,1725,818,854,1480,373,950,1097,835,305,664,1165,886,1742,332,1261,1268,1532,528,1500,822,1431,1299,1093,395,1653,1009,923,659,1848,1769,1088,1468,364,972,775,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP200^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 18:09:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.68/1.19 % [INFO] Parsing done (271ms).
% 2.18/1.20 % [INFO] Running in sequential loop mode.
% 2.76/1.41 % [INFO] eprover registered as external prover.
% 2.76/1.41 % [INFO] cvc4 registered as external prover.
% 2.76/1.42 % [INFO] Scanning for conjecture ...
% 3.11/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ...
% 3.39/1.62 % [INFO] Axiom selection finished. Selected 302 axioms (removed 50 axioms).
% 4.06/1.81 % [INFO] Problem is higher-order (TPTP THF).
% 4.20/1.83 % [INFO] Type checking passed.
% 4.20/1.83 % [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 ...
% 15.95/4.87 % External prover 'e' found a proof!
% 15.95/4.87 % [INFO] Killing All external provers ...
% 15.95/4.87 % Time passed: 4355ms (effective reasoning time: 3675ms)
% 15.95/4.87 % 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)>
% 15.95/4.88 % Axioms used in derivation (302): fact_109_combine__options__cases, fact_128_option_Oexhaust, fact_111_combine__options__cases, fact_69_equalityD2, fact_80_Uvariation__sym, fact_78_Uvariation__sym__rel, fact_207_accp__induct, fact_37_dual__order_Oeq__iff, fact_24_fml_Oinject_I2_J, fact_200_accp_Ointros, fact_107_Aterm__Some, fact_48_Collect__mem__eq, fact_155_Greatest__equality, fact_65_Collect__mono, fact_130_option_OdiscI, fact_312_term__sem_Oinduct, fact_219_accp__downward, fact_131_option_OdiscI, fact_339_Assigno__undef, fact_121_split__option__ex, fact_301_trm_Odistinct_I23_J, fact_85_subset__Collect__iff, fact_96_usubstappt_Osimps_I7_J, fact_217_accp__downward, fact_175_option_Ocollapse, fact_151_Geqo_Oelims, fact_141_ODEo_Oinduct, fact_291_usubstappt_Osimps_I1_J, fact_135_option_Odistinct_I1_J, fact_153_Geqo_Osimps_I1_J, fact_201_accp_Ointros, fact_147_Pluso_Osimps_I1_J, fact_241_ssubst__Pair__rhs, fact_10_Differentialo__undef, fact_104_not__None__eq, fact_268_Ando_Ocases, fact_212_accp_Oinducts, fact_240_ssubst__Pair__rhs, fact_58_order__subst2, fact_346_ODEo__undef, fact_345_Assigno_Osimps_I1_J, fact_230_Geqo_Opelims, fact_21_Geqo__undef, fact_186_option_Osel, fact_311_usubstappt_Opsimps_I3_J, fact_289_trm_Odistinct_I1_J, fact_324_Testo_Oelims, fact_165_accp__subset, fact_220_not__accp__down, fact_299_trm_Odistinct_I13_J, fact_16_usubstappf__antimon, fact_4_usubstappt__det, fact_149_usubstappt__differential__conv, fact_158_undeff__equiv, fact_103_not__Some__eq, fact_188_option_Oexhaust__sel, fact_105_not__None__eq, fact_145_Timeso_Osimps_I3_J, fact_211_accp_Oinducts, fact_134_option_Odistinct_I1_J, fact_181_option_Oexpand, fact_332_image2__eqI, fact_113_combine__options__cases, fact_125_option_Oinducts, fact_221_not__accp__down, fact_194_accp_Ocases, fact_309_trm_Oexhaust, fact_8_usubstappt__antimon, fact_334_image2__eqI, fact_270_usubstappt_Opsimps_I6_J, fact_66_subset__refl, fact_29_trm_Odistinct_I37_J, fact_50_Collect__cong, fact_199_accp_Osimps, fact_22_trm_Oinject_I6_J, fact_129_option_Oexhaust, fact_36_dual__order_Oantisym, fact_77_in__mono, fact_197_accp_Osimps, fact_3_undeft__None, fact_329_image2__eqI, fact_30_order__refl, fact_287_trm_Odistinct_I9_J, fact_162_accp__subset, fact_19_usubstappt_Osimps_I6_J, fact_269_usubstappt_Opsimps_I7_J, fact_170_accp__subset__induct, fact_100_trm_Oinject_I7_J, fact_122_split__option__ex, fact_296_trm_Oinject_I3_J, fact_184_option_Osel, fact_203_accp_Ointros, fact_190_accp_Ocases, fact_38_dual__order_Otrans, fact_253_option_Odisc__eq__case_I1_J, fact_216_accp__downward, fact_233_subrelI, fact_2_Geq_Oprems_I1_J, fact_14_Timeso__undef, fact_108_Differentialo_Osimps_I1_J, fact_95_Timeso_Oelims, fact_238_ssubst__Pair__rhs, fact_142_Differentialo_Oelims, fact_52_order_Otrans, fact_213_accp_Oinducts, fact_59_order__subst1, fact_342_Assigno_Opelims, fact_198_accp_Osimps, fact_227_accp__induct__rule, fact_138_Assigno_Oinduct, fact_6_usubstappt__plus__conv, fact_56_ord__le__eq__subst, fact_116_combine__options__cases, fact_114_combine__options__cases, fact_1_usubstappf__geq__conv, fact_140_undeft__equiv, fact_258_Timeso_Ocases, fact_28_subset__antisym, fact_168_accp__subset__induct, fact_252_option_Odisc__eq__case_I1_J, fact_62_set__eq__subset, fact_126_option_Oinducts, fact_298_trm_Odistinct_I5_J, fact_189_option_Oexhaust__sel, fact_177_Composeo_Oinduct, fact_182_option_Oexpand, fact_164_accp__subset, fact_139_Timeso_Oinduct, fact_89_Collect__restrict, fact_210_accp_Oinducts, fact_42_ord__le__eq__trans, fact_46_mem__Collect__eq, fact_283_trm_Odistinct_I17_J, fact_179_Loopo_Oinduct, fact_348_ODEo_Oelims, fact_17_usubstappf__det, fact_132_option_OdiscI, fact_255_option_Odisc__eq__case_I2_J, fact_27_subsetI, fact_15_Geqo_Osimps_I2_J, fact_41_order__class_Oorder_Oantisym, fact_215_accp__downward, fact_263_Pluso_Opelims, fact_159_Testo_Oinduct, fact_202_accp_Ointros, fact_310_term__sem_Ocases, fact_45_antisym__conv, fact_23_trm_Oinject_I5_J, fact_196_accp_Osimps, fact_106_not__None__eq, fact_70_equalityD1, fact_193_accp_Ocases, fact_152_Differentialo_Opelims, fact_161_Ando_Oinduct, fact_75_subsetD, fact_154_GreatestI2__order, fact_254_option_Odisc__eq__case_I1_J, fact_187_option_Oexhaust__sel, fact_336_Testo_Osimps_I1_J, fact_91_prop__restrict, fact_173_usubstappf__geq, fact_304_trm_Odistinct_I25_J, fact_335_image2__eqI, fact_31_Uvariation__univ, fact_169_accp__subset__induct, fact_222_not__accp__down, fact_55_eq__iff, fact_225_accp__induct__rule, fact_272_usubstappt_Opsimps_I1_J, fact_288_trm_Odistinct_I11_J, fact_282_trm_Oinject_I1_J, fact_192_accp_Ocases, fact_347_ODEo_Osimps_I2_J, fact_302_trm_Odistinct_I29_J, fact_115_combine__options__cases, fact_87_subset__CollectI, fact_328_image2__eqI, fact_0_vaouter, fact_94_Pluso_Oelims, fact_245_pred__equals__eq2, fact_226_accp__induct__rule, fact_25_Uvariation__mon, fact_174_option_Ocollapse, fact_265_Assigno_Ocases, fact_205_accp__induct, fact_195_accp_Osimps, fact_72_subset__eq, fact_341_Assigno_Oelims, fact_51_Collect__cong, fact_308_trm_Oinduct, fact_264_ODEo_Ocases, fact_13_Pluso__undef, fact_44_order__class_Oorder_Oeq__iff, fact_43_ord__eq__le__trans, fact_260_case__optionE, fact_12_Timeso_Osimps_I2_J, fact_9_Differentialo_Osimps_I2_J, fact_120_split__option__all, fact_344_game_Odistinct_I15_J, fact_243_pred__equals__eq2, fact_112_combine__options__cases, fact_178_undefg__equiv, fact_257_option_Odisc__eq__case_I2_J, fact_293_Testo_Osimps_I2_J, fact_206_accp__induct, fact_144_trm_Odistinct_I39_J, fact_148_Timeso_Osimps_I1_J, fact_93_conj__subset__def, fact_286_trm_Odistinct_I7_J, fact_150_Geqo_Osimps_I3_J, fact_262_Timeso_Opelims, fact_297_trm_Odistinct_I3_J, fact_49_Collect__mem__eq, fact_340_Assigno_Osimps_I2_J, fact_300_trm_Odistinct_I15_J, fact_325_game_Oinject_I3_J, fact_146_Pluso_Osimps_I3_J, fact_294_Testo__undef, fact_61_Collect__mono__iff, fact_172_usubstappf__geqr, fact_39_dual__order_Orefl, fact_313_usubstappt_Osimps_I3_J, fact_246_pred__equals__eq2, fact_119_split__option__all, fact_101_not__Some__eq, fact_54_antisym, fact_305_trm_Odistinct_I35_J, fact_209_accp__induct, fact_285_trm_Odistinct_I21_J, fact_11_Pluso_Osimps_I2_J, fact_156_Diamondo_Oinduct, fact_40_order__trans, fact_163_accp__subset, fact_133_option_Odistinct_I1_J, fact_79_Uvariation__refl, fact_124_option_Oinducts, fact_261_case__optionE, fact_123_split__option__ex, fact_228_accp__induct__rule, fact_204_accp_Ointros, fact_224_not__accp__down, fact_73_equalityE, fact_267_Existso_Ocases, fact_176_option_Ocollapse, fact_280_in__lex__prod, fact_223_not__accp__down, fact_180_Loopo_Ocases, fact_231_Diamondo_Ocases, fact_259_case__optionE, fact_143_trm_Odistinct_I41_J, fact_7_usubstappt__times__conv, fact_292_usubstappt_Ocases, fact_349_ODEo_Opelims, fact_136_Differentialo_Oinduct, fact_117_combine__options__cases, fact_284_trm_Odistinct_I19_J, fact_81_Uvariation__def, fact_127_option_Oexhaust, fact_110_combine__options__cases, fact_303_trm_Odistinct_I27_J, fact_167_accp__subset__induct, fact_47_mem__Collect__eq, fact_306_trm_Odistinct_I33_J, fact_218_accp__downward, fact_185_option_Osel, fact_57_ord__eq__le__subst, fact_256_option_Odisc__eq__case_I2_J, fact_214_accp_Oinducts, fact_183_option_Oexpand, fact_18_usubstappt_Osimps_I5_J, fact_20_usubstappf_Osimps_I2_J, fact_191_accp_Ocases, fact_98_option_Oinject, fact_248_pred__subset__eq2, fact_102_not__Some__eq, fact_137_Differentialo_Ocases, fact_333_image2__eqI, fact_5_Geq_Oprems_I2_J, fact_229_accp__induct__rule, fact_68_subset__iff, fact_273_usubstappt_Opsimps_I2_J, fact_118_split__option__all, fact_343_game_Oinject_I2_J, fact_290_usubstappt_Osimps_I2_J, fact_281_trm_Oinject_I2_J, fact_307_trm_Odistinct_I31_J, fact_295_trm_Oinject_I4_J, fact_266_Composeo_Ocases, fact_350_game_Oinject_I8_J, fact_277_in__lex__prod, fact_53_eq__refl, fact_33_Collect__subset, fact_63_subset__trans, fact_157_Existso_Oinduct, fact_279_in__lex__prod, fact_271_usubstappt_Opsimps_I5_J, fact_160_Testo_Ocases, fact_99_option_Oinject, fact_208_accp__induct, fact_351_game_Odistinct_I35_J, fact_337_Testo_Opelims, fact_97_option_Oinject
% 15.95/4.88 % No. of inferences in proof: 608
% 15.95/4.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4355 ms resp. 3675 ms w/o parsing
% 16.98/5.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.98/5.09 % [INFO] Killing All external provers ...
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