TSTP Solution File: SWW478^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW478^1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:23:02 EDT 2024
% Result : Theorem 11.68s 3.75s
% Output : Refutation 12.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 168
% Syntax : Number of formulae : 338 ( 185 unt; 0 typ; 0 def)
% Number of atoms : 819 ( 402 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3297 ( 152 ~; 4 |; 46 &;2849 @)
% ( 0 <=>; 246 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 688 ( 688 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 57 usr; 12 con; 0-5 aty)
% Number of variables : 1370 ( 48 ^1302 !; 20 ?;1370 :)
% Comments :
%------------------------------------------------------------------------------
thf(exp_list_char_type,type,
exp_list_char: $tType ).
thf(list_char_type,type,
list_char: $tType ).
thf(list_P1999446415t_char_type,type,
list_P1999446415t_char: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(option_ty_type,type,
option_ty: $tType ).
thf(option_val_type,type,
option_val: $tType ).
thf(option1728594148on_val_type,type,
option1728594148on_val: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val_type,type,
val: $tType ).
thf(produc2090907612on_val_type,type,
produc2090907612on_val: $tType ).
thf(produc1282892786on_val_type,type,
produc1282892786on_val: $tType ).
thf(produc1013743697t_char_type,type,
produc1013743697t_char: $tType ).
thf(produc1746408499on_val_type,type,
produc1746408499on_val: $tType ).
thf(hconf_97414254t_char_type,type,
hconf_97414254t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > $o ).
thf(lconf_496643946t_char_type,type,
lconf_496643946t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_val ) > ( list_char > option_ty ) > $o ).
thf(block_list_char_type,type,
block_list_char: list_char > ty > exp_list_char > exp_list_char ).
thf(lAss_list_char_type,type,
lAss_list_char: list_char > exp_list_char > exp_list_char ).
thf(seq_list_char_type,type,
seq_list_char: exp_list_char > exp_list_char > exp_list_char ).
thf(val_list_char_type,type,
val_list_char: val > exp_list_char ).
thf(fun_up424764369ion_ty_type,type,
fun_up424764369ion_ty: ( list_char > option_ty ) > list_char > option_ty > list_char > option_ty ).
thf(fun_up1149430426on_val_type,type,
fun_up1149430426on_val: ( list_char > option_val ) > list_char > option_val > list_char > option_val ).
thf(wf_J_mdecl_type,type,
wf_J_mdecl: list_P1999446415t_char > list_char > produc1013743697t_char > $o ).
thf(none_ty_type,type,
none_ty: option_ty ).
thf(none_val_type,type,
none_val: option_val ).
thf(some_ty_type,type,
some_ty: ty > option_ty ).
thf(some_val_type,type,
some_val: val > option_val ).
thf(produc755559506on_val_type,type,
produc755559506on_val: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val ).
thf(produc235638504on_val_type,type,
produc235638504on_val: exp_list_char > produc2090907612on_val > produc1282892786on_val ).
thf(produc833389609on_val_type,type,
produc833389609on_val: produc1282892786on_val > produc1282892786on_val > produc1746408499on_val ).
thf(produc575577405_val_o_type,type,
produc575577405_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > produc2090907612on_val > $o ).
thf(produc900512295_val_o_type,type,
produc900512295_val_o: ( exp_list_char > produc2090907612on_val > $o ) > produc1282892786on_val > $o ).
thf(produc2006262054_val_o_type,type,
produc2006262054_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > $o ).
thf(produc146628214_val_o_type,type,
produc146628214_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o ) > produc2090907612on_val > produc2090907612on_val > $o ).
thf(produc74886368_val_o_type,type,
produc74886368_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o ) > produc2090907612on_val > produc1282892786on_val > $o ).
thf(produc252486962_val_o_type,type,
produc252486962_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > produc2090907612on_val > $o ).
thf(produc1016489647on_val_type,type,
produc1016489647on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val ) > produc2090907612on_val > produc1282892786on_val ).
thf(produc1186953840on_val_type,type,
produc1186953840on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val ) > produc2090907612on_val > produc1746408499on_val ).
thf(produc1115879776_val_o_type,type,
produc1115879776_val_o: ( exp_list_char > produc2090907612on_val > produc2090907612on_val > $o ) > produc1282892786on_val > produc2090907612on_val > $o ).
thf(produc68058570_val_o_type,type,
produc68058570_val_o: ( exp_list_char > produc2090907612on_val > produc1282892786on_val > $o ) > produc1282892786on_val > produc1282892786on_val > $o ).
thf(produc1835097372_val_o_type,type,
produc1835097372_val_o: ( exp_list_char > produc2090907612on_val > $o ) > produc1282892786on_val > $o ).
thf(produc69760047on_val_type,type,
produc69760047on_val: ( exp_list_char > produc2090907612on_val > produc2090907612on_val ) > produc1282892786on_val > produc2090907612on_val ).
thf(produc793795679_val_o_type,type,
produc793795679_val_o: ( produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o ) > produc1746408499on_val > produc2090907612on_val > $o ).
thf(produc1798214089_val_o_type,type,
produc1798214089_val_o: ( produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > produc1282892786on_val > $o ).
thf(produc1624062875_val_o_type,type,
produc1624062875_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > $o ).
thf(produc511181936on_val_type,type,
produc511181936on_val: ( produc1282892786on_val > produc1282892786on_val > produc2090907612on_val ) > produc1746408499on_val > produc2090907612on_val ).
thf(assigned_type,type,
assigned: list_char > exp_list_char > $o ).
thf(red_type,type,
red: list_P1999446415t_char > produc1746408499on_val > $o ).
thf(redp_type,type,
redp: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(hp_type,type,
hp: produc2090907612on_val > nat > option1728594148on_val ).
thf(widen_2090681816t_char_type,type,
widen_2090681816t_char: list_P1999446415t_char > ty > ty > $o ).
thf(typeSa1586500134_sconf_type,type,
typeSa1586500134_sconf: list_P1999446415t_char > ( list_char > option_ty ) > produc2090907612on_val > $o ).
thf(unit_type,type,
unit: val ).
thf(wf_pro755087577t_char_type,type,
wf_pro755087577t_char: ( list_P1999446415t_char > list_char > produc1013743697t_char > $o ) > list_P1999446415t_char > $o ).
thf(wTrt_type,type,
wTrt: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > exp_list_char > ty > $o ).
thf(member1846553161on_val_type,type,
member1846553161on_val: produc2090907612on_val > ( produc2090907612on_val > $o ) > $o ).
thf(member1072200031on_val_type,type,
member1072200031on_val: produc1282892786on_val > ( produc1282892786on_val > $o ) > $o ).
thf(member1913460000on_val_type,type,
member1913460000on_val: produc1746408499on_val > ( produc1746408499on_val > $o ) > $o ).
thf(e_type,type,
e: list_char > option_ty ).
thf(p_type,type,
p: list_P1999446415t_char ).
thf(t_type,type,
t: ty ).
thf(t_1_type,type,
t_1: ty ).
thf(v_1_type,type,
v_1: list_char ).
thf(e_a_type,type,
e_a: exp_list_char ).
thf(ea_type,type,
ea: exp_list_char ).
thf(h_a_type,type,
h_a: nat > option1728594148on_val ).
thf(ha_type,type,
ha: nat > option1728594148on_val ).
thf(l_a_type,type,
l_a: list_char > option_val ).
thf(la_type,type,
la: list_char > option_val ).
thf(v_2_type,type,
v_2: val ).
thf(v_type,type,
v: val ).
thf(97,axiom,
! [A: list_char > option_val,B: option_val,C: option_val,D: list_char,E: list_char] :
( ( D != E )
=> ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
= ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_fun__upd__twist) ).
thf(518,plain,
! [A: list_char > option_val,B: option_val,C: option_val,D: list_char,E: list_char] :
( ( D != E )
=> ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
= ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1,conjecture,
member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(170,plain,
~ ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,axiom,
! [A: list_char > option_val,B: list_char,C: option_val] :
( ( fun_up1149430426on_val @ A @ B @ C @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_fun__upd__same) ).
thf(523,plain,
! [A: list_char > option_val,B: list_char,C: option_val] :
( ( fun_up1149430426on_val @ A @ B @ C @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(149,axiom,
! [A: produc1746408499on_val > $o,B: produc1746408499on_val > $o] :
( ( ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ C @ D ) @ B )
= ( member1913460000on_val @ ( produc833389609on_val @ C @ D ) @ A ) ) )
= ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_pred__equals__eq2) ).
thf(683,plain,
! [A: produc1746408499on_val > $o,B: produc1746408499on_val > $o] :
( ( ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ C @ D ) @ B )
= ( member1913460000on_val @ ( produc833389609on_val @ C @ D ) @ A ) ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(166,axiom,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: exp_list_char,D: produc2090907612on_val] :
( A
!= ( produc833389609on_val @ B @ ( produc235638504on_val @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_prod__cases3) ).
thf(741,plain,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: exp_list_char,D: produc2090907612on_val] :
( A
!= ( produc833389609on_val @ B @ ( produc235638504on_val @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(76,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: produc1282892786on_val] :
( ! [C: exp_list_char,D: produc2090907612on_val] :
( ( B
= ( produc235638504on_val @ C @ D ) )
=> ( A @ C @ D ) )
=> ( produc1835097372_val_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_splitI2) ).
thf(440,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: produc1282892786on_val] :
( ! [C: exp_list_char,D: produc2090907612on_val] :
( ( B
= ( produc235638504on_val @ C @ D ) )
=> ( A @ C @ D ) )
=> ( produc1835097372_val_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(95,axiom,
! [A: nat > option1728594148on_val,B: list_char > option_val,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( ( produc755559506on_val @ A @ B )
= ( produc755559506on_val @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Pair__eq) ).
thf(511,plain,
! [A: nat > option1728594148on_val,B: list_char > option_val,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( ( produc755559506on_val @ A @ B )
= ( produc755559506on_val @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(65,axiom,
! [A: list_char > option_val,B: option_val,C: list_char,D: list_char] :
( ( ( D = C )
=> ( ( fun_up1149430426on_val @ A @ C @ B @ D )
= B ) )
& ( ( D != C )
=> ( ( fun_up1149430426on_val @ A @ C @ B @ D )
= ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_fun__upd__def) ).
thf(385,plain,
! [A: list_char > option_val,B: option_val,C: list_char,D: list_char] :
( ( ( D = C )
=> ( ( fun_up1149430426on_val @ A @ C @ B @ D )
= B ) )
& ( ( D != C )
=> ( ( fun_up1149430426on_val @ A @ C @ B @ D )
= ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(50,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: val] :
( ( block_list_char @ A @ B @ C )
!= ( val_list_char @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_exp_Osimps_I83_J) ).
thf(340,plain,
! [A: list_char,B: ty,C: exp_list_char,D: val] :
( ( block_list_char @ A @ B @ C )
!= ( val_list_char @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(144,axiom,
! [A: produc1282892786on_val,B: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,C: exp_list_char,D: produc2090907612on_val] :
( ( member1072200031on_val @ A @ ( B @ C @ D ) )
=> ( member1072200031on_val @ A @ ( produc68058570_val_o @ B @ ( produc235638504on_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mem__splitI) ).
thf(670,plain,
! [A: produc1282892786on_val,B: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,C: exp_list_char,D: produc2090907612on_val] :
( ( member1072200031on_val @ A @ ( B @ C @ D ) )
=> ( member1072200031on_val @ A @ ( produc68058570_val_o @ B @ ( produc235638504on_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(4,axiom,
! [A: list_char > option_ty,B: option_ty,C: option_ty,D: list_char,E: list_char] :
( ( D != E )
=> ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
= ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_fun__upd__twist) ).
thf(174,plain,
! [A: list_char > option_ty,B: option_ty,C: option_ty,D: list_char,E: list_char] :
( ( D != E )
=> ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
= ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(157,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_prod_Osimps_I2_J) ).
thf(709,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(35,axiom,
! [A: produc2090907612on_val,B: produc2090907612on_val > $o] :
( ( member1846553161on_val @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_mem__def) ).
thf(288,plain,
! [A: produc2090907612on_val,B: produc2090907612on_val > $o] :
( ( member1846553161on_val @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: produc2090907612on_val] : ( redp @ A @ ( block_list_char @ B @ C @ ( val_list_char @ D ) ) @ E @ ( val_list_char @ D ) @ E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_redp__redsp_ORedBlock) ).
thf(301,plain,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: produc2090907612on_val] : ( redp @ A @ ( block_list_char @ B @ C @ ( val_list_char @ D ) ) @ E @ ( val_list_char @ D ) @ E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(75,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc2090907612on_val] :
( ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( B
= ( produc755559506on_val @ C @ D ) )
=> ( A @ C @ D ) )
=> ( produc252486962_val_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_splitI2) ).
thf(436,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc2090907612on_val] :
( ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( B
= ( produc755559506on_val @ C @ D ) )
=> ( A @ C @ D ) )
=> ( produc252486962_val_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(116,axiom,
wTrt @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( val_list_char @ v ) ) @ ea ) ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_InitBlockRed_I5_J) ).
thf(570,plain,
wTrt @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( val_list_char @ v ) ) @ ea ) ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(93,axiom,
! [A: produc1282892786on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,C: produc2090907612on_val] :
( ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ( member1072200031on_val @ A @ ( B @ D @ E ) ) )
=> ( member1072200031on_val @ A @ ( produc74886368_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mem__splitI2) ).
thf(504,plain,
! [A: produc1282892786on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,C: produc2090907612on_val] :
( ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ( member1072200031on_val @ A @ ( B @ D @ E ) ) )
=> ( member1072200031on_val @ A @ ( produc74886368_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(51,axiom,
! [A: exp_list_char,B: exp_list_char,C: val] :
( ( seq_list_char @ A @ B )
!= ( val_list_char @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_exp_Osimps_I85_J) ).
thf(344,plain,
! [A: exp_list_char,B: exp_list_char,C: val] :
( ( seq_list_char @ A @ B )
!= ( val_list_char @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(84,axiom,
! [A: produc2090907612on_val,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,C: produc1746408499on_val] :
( ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ( member1846553161on_val @ A @ ( B @ D @ E ) ) )
=> ( member1846553161on_val @ A @ ( produc793795679_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_mem__splitI2) ).
thf(460,plain,
! [A: produc2090907612on_val,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,C: produc1746408499on_val] :
( ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ( member1846553161on_val @ A @ ( B @ D @ E ) ) )
=> ( member1846553161on_val @ A @ ( produc793795679_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(123,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1746408499on_val] :
( ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( B
= ( produc833389609on_val @ C @ D ) )
=> ( A @ C @ D ) )
=> ( produc1624062875_val_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_splitI2) ).
thf(587,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1746408499on_val] :
( ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( B
= ( produc833389609on_val @ C @ D ) )
=> ( A @ C @ D ) )
=> ( produc1624062875_val_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(132,axiom,
! [A: list_char > option_ty,B: ty,C: exp_list_char,D: produc2090907612on_val,E: exp_list_char,F: produc2090907612on_val,G: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ D ) @ ( produc235638504on_val @ E @ F ) ) @ ( red @ G ) )
=> ( ( wTrt @ G @ ( hp @ D ) @ A @ C @ B )
=> ( ( typeSa1586500134_sconf @ G @ A @ D )
=> ( typeSa1586500134_sconf @ G @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_red__preserves__sconf) ).
thf(619,plain,
! [A: list_char > option_ty,B: ty,C: exp_list_char,D: produc2090907612on_val,E: exp_list_char,F: produc2090907612on_val,G: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ D ) @ ( produc235638504on_val @ E @ F ) ) @ ( red @ G ) )
=> ( ( wTrt @ G @ ( hp @ D ) @ A @ C @ B )
=> ( ( typeSa1586500134_sconf @ G @ A @ D )
=> ( typeSa1586500134_sconf @ G @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(9,axiom,
! [A: list_char > option_ty,B: list_char,C: option_ty] :
( ( ( A @ B )
= C )
=> ( ( fun_up424764369ion_ty @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_fun__upd__idem) ).
thf(189,plain,
! [A: list_char > option_ty,B: list_char,C: option_ty] :
( ( ( A @ B )
= C )
=> ( ( fun_up424764369ion_ty @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( lAss_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_exp_Osimps_I142_J) ).
thf(228,plain,
! [A: list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( lAss_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val > $o] :
( ( member1072200031on_val @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_mem__def) ).
thf(261,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val > $o] :
( ( member1072200031on_val @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(124,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ( member1072200031on_val @ A @ ( B @ D @ E ) ) )
=> ( member1072200031on_val @ A @ ( produc1798214089_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_mem__splitI2) ).
thf(591,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ( member1072200031on_val @ A @ ( B @ D @ E ) ) )
=> ( member1072200031on_val @ A @ ( produc1798214089_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(44,axiom,
! [A: val,B: val] :
( ( ( val_list_char @ A )
= ( val_list_char @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_exp_Osimps_I3_J) ).
thf(321,plain,
! [A: val,B: val] :
( ( ( val_list_char @ A )
= ( val_list_char @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(134,axiom,
! [A: produc1282892786on_val,B: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,C: produc1282892786on_val] :
( ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ( member1072200031on_val @ A @ ( B @ D @ E ) ) )
=> ( member1072200031on_val @ A @ ( produc68058570_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_mem__splitI2) ).
thf(623,plain,
! [A: produc1282892786on_val,B: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,C: produc1282892786on_val] :
( ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ( member1072200031on_val @ A @ ( B @ D @ E ) ) )
=> ( member1072200031on_val @ A @ ( produc68058570_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(21,axiom,
! [A: list_P1999446415t_char,B: nat > option1728594148on_val,C: list_char > option_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
( ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( some_ty @ E ) ) @ F @ G )
=> ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_WTrtBlock) ).
thf(238,plain,
! [A: list_P1999446415t_char,B: nat > option1728594148on_val,C: list_char > option_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
( ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( some_ty @ E ) ) @ F @ G )
=> ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(96,axiom,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val] :
( A
!= ( produc833389609on_val @ B @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_prod__cases4) ).
thf(514,plain,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val] :
( A
!= ( produc833389609on_val @ B @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(54,axiom,
! [A: list_P1999446415t_char,B: list_char > option_ty,C: produc2090907612on_val] :
( ( typeSa1586500134_sconf @ A @ B @ C )
= ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( hconf_97414254t_char @ A @ D )
& ( lconf_496643946t_char @ A @ D @ E @ B ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_sconf__def) ).
thf(353,plain,
! [A: list_P1999446415t_char,B: list_char > option_ty,C: produc2090907612on_val] :
( ( typeSa1586500134_sconf @ A @ B @ C )
= ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( hconf_97414254t_char @ A @ D )
& ( lconf_496643946t_char @ A @ D @ E @ B ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(52,axiom,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: val,F: produc2090907612on_val] : ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( val_list_char @ D ) ) @ ( val_list_char @ E ) ) ) @ F @ ( val_list_char @ E ) @ F ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_redp__redsp_ORedInitBlock) ).
thf(348,plain,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: val,F: produc2090907612on_val] : ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( val_list_char @ D ) ) @ ( val_list_char @ E ) ) ) @ F @ ( val_list_char @ E ) @ F ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(118,axiom,
( ( l_a @ v_1 )
= ( some_val @ v_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).
thf(574,plain,
( ( l_a @ v_1 )
= ( some_val @ v_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(127,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_prod_Osimps_I2_J) ).
thf(602,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(140,axiom,
! [A: produc2090907612on_val > $o,B: produc2090907612on_val > $o] :
( ( ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( member1846553161on_val @ ( produc755559506on_val @ C @ D ) @ B )
= ( member1846553161on_val @ ( produc755559506on_val @ C @ D ) @ A ) ) )
= ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_pred__equals__eq2) ).
thf(660,plain,
! [A: produc2090907612on_val > $o,B: produc2090907612on_val > $o] :
( ( ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( member1846553161on_val @ ( produc755559506on_val @ C @ D ) @ B )
= ( member1846553161on_val @ ( produc755559506on_val @ C @ D ) @ A ) ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(73,axiom,
! [A: produc2090907612on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,C: produc2090907612on_val] :
( ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ( member1846553161on_val @ A @ ( B @ D @ E ) ) )
=> ( member1846553161on_val @ A @ ( produc146628214_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mem__splitI2) ).
thf(428,plain,
! [A: produc2090907612on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,C: produc2090907612on_val] :
( ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ( member1846553161on_val @ A @ ( B @ D @ E ) ) )
=> ( member1846553161on_val @ A @ ( produc146628214_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(164,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_prod_Osimps_I2_J) ).
thf(734,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(16,axiom,
! [A: list_char > option_ty,B: list_char,C: ty] :
~ ! [D: list_char] :
( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) @ D )
= none_ty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_map__upd__nonempty) ).
thf(221,plain,
! [A: list_char > option_ty,B: list_char,C: ty] :
~ ! [D: list_char] :
( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) @ D )
= none_ty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc2090907612on_val,C: produc2090907612on_val] :
( ( B = C )
=> ( ( produc252486962_val_o @ A @ B )
= ( produc252486962_val_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_split__weak__cong) ).
thf(307,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc2090907612on_val,C: produc2090907612on_val] :
( ( B = C )
=> ( ( produc252486962_val_o @ A @ B )
= ( produc252486962_val_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(81,axiom,
! [A: produc2090907612on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( member1846553161on_val @ A @ ( B @ C @ D ) )
=> ( member1846553161on_val @ A @ ( produc146628214_val_o @ B @ ( produc755559506on_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_mem__splitI) ).
thf(452,plain,
! [A: produc2090907612on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( member1846553161on_val @ A @ ( B @ C @ D ) )
=> ( member1846553161on_val @ A @ ( produc146628214_val_o @ B @ ( produc755559506on_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( seq_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_exp_Osimps_I197_J) ).
thf(248,plain,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( seq_list_char @ A @ B )
!= ( block_list_char @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(63,axiom,
! [A: produc1746408499on_val,B: produc1746408499on_val > $o] :
( ! [C: produc1282892786on_val,D: exp_list_char,E: produc2090907612on_val] : ( B @ ( produc833389609on_val @ C @ ( produc235638504on_val @ D @ E ) ) )
=> ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_prod__induct3) ).
thf(380,plain,
! [A: produc1746408499on_val,B: produc1746408499on_val > $o] :
( ! [C: produc1282892786on_val,D: exp_list_char,E: produc2090907612on_val] : ( B @ ( produc833389609on_val @ C @ ( produc235638504on_val @ D @ E ) ) )
=> ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(147,axiom,
! [A: list_char,B: ty,C: val,D: produc2090907612on_val,E: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ A @ B @ ( val_list_char @ C ) ) @ D ) @ ( produc235638504on_val @ ( val_list_char @ C ) @ D ) ) @ ( red @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_red__reds_ORedBlock) ).
thf(678,plain,
! [A: list_char,B: ty,C: val,D: produc2090907612on_val,E: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ A @ B @ ( val_list_char @ C ) ) @ D ) @ ( produc235638504on_val @ ( val_list_char @ C ) @ D ) ) @ ( red @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(101,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( A @ B @ C )
=> ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_splitI) ).
thf(529,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( A @ B @ C )
=> ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(11,axiom,
! [A: list_char > option_ty,B: list_char,C: option_ty,D: option_ty] :
( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
= ( fun_up424764369ion_ty @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_fun__upd__upd) ).
thf(201,plain,
! [A: list_char > option_ty,B: list_char,C: option_ty,D: option_ty] :
( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
= ( fun_up424764369ion_ty @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,axiom,
! [A: list_char,B: list_char] :
( ( fun_up1149430426on_val
@ ^ [C: list_char] : none_val
@ A
@ none_val
@ B )
= none_val ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_empty__upd__none) ).
thf(366,plain,
! [A: list_char,B: list_char] :
( ( fun_up1149430426on_val
@ ^ [C: list_char] : none_val
@ A
@ none_val
@ B )
= none_val ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(103,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc575577405_val_o @ A @ ( produc755559506on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_internal__split__conv) ).
thf(534,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc575577405_val_o @ A @ ( produc755559506on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(159,axiom,
! [A: list_char > option_val,B: list_char,C: option_val] :
( ( ( A @ B )
= C )
=> ( ( fun_up1149430426on_val @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_fun__upd__idem) ).
thf(714,plain,
! [A: list_char > option_val,B: list_char,C: option_val] :
( ( ( A @ B )
= C )
=> ( ( fun_up1149430426on_val @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(126,axiom,
! [A: produc1282892786on_val,B: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,C: produc1282892786on_val] :
( ( member1072200031on_val @ A @ ( produc68058570_val_o @ B @ C ) )
=> ~ ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ~ ( member1072200031on_val @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_mem__splitE) ).
thf(598,plain,
! [A: produc1282892786on_val,B: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,C: produc1282892786on_val] :
( ( member1072200031on_val @ A @ ( produc68058570_val_o @ B @ C ) )
=> ~ ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ~ ( member1072200031on_val @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(38,axiom,
! [A: list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( lAss_list_char @ A @ B )
!= ( seq_list_char @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_exp_Osimps_I144_J) ).
thf(297,plain,
! [A: list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( lAss_list_char @ A @ B )
!= ( seq_list_char @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(72,axiom,
! [A: produc2090907612on_val,B: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ( member1846553161on_val @ A @ ( produc1115879776_val_o @ B @ C ) )
=> ~ ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ~ ( member1846553161on_val @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_mem__splitE) ).
thf(424,plain,
! [A: produc2090907612on_val,B: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ( member1846553161on_val @ A @ ( produc1115879776_val_o @ B @ C ) )
=> ~ ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ~ ( member1846553161on_val @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(162,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ( member1072200031on_val @ A @ ( produc1798214089_val_o @ B @ C ) )
=> ~ ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ~ ( member1072200031on_val @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_mem__splitE) ).
thf(729,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ( member1072200031on_val @ A @ ( produc1798214089_val_o @ B @ C ) )
=> ~ ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ~ ( member1072200031on_val @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(153,axiom,
! [A: produc1282892786on_val > $o] :
( ( ? [B: produc1282892786on_val] : ( A @ B ) )
= ( ? [B: exp_list_char,C: produc2090907612on_val] : ( A @ ( produc235638504on_val @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_split__paired__Ex) ).
thf(693,plain,
! [A: produc1282892786on_val > $o] :
( ( ? [B: produc1282892786on_val] : ( A @ B ) )
= ( ? [B: exp_list_char,C: produc2090907612on_val] : ( A @ ( produc235638504on_val @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(136,axiom,
! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: list_char,G: exp_list_char,H: nat > option1728594148on_val,I: list_char > option_val] :
( ( redp @ B @ C @ ( produc755559506on_val @ D @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) @ G @ ( produc755559506on_val @ H @ I ) )
=> ( ( ( I @ F )
= none_val )
=> ( ~ ( assigned @ F @ C )
=> ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( produc755559506on_val @ D @ E ) @ ( block_list_char @ F @ A @ G ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ I @ F @ ( E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_redp__redsp_OBlockRedNone) ).
thf(630,plain,
! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: list_char,G: exp_list_char,H: nat > option1728594148on_val,I: list_char > option_val] :
( ( redp @ B @ C @ ( produc755559506on_val @ D @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) @ G @ ( produc755559506on_val @ H @ I ) )
=> ( ( ( I @ F )
= none_val )
=> ( ~ ( assigned @ F @ C )
=> ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( produc755559506on_val @ D @ E ) @ ( block_list_char @ F @ A @ G ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ I @ F @ ( E @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(86,axiom,
! [A: produc2090907612on_val > $o] :
( ( produc252486962_val_o
@ ^ [B: nat > option1728594148on_val,C: list_char > option_val] : ( A @ ( produc755559506on_val @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_split__eta) ).
thf(467,plain,
! [A: produc2090907612on_val > $o] :
( ( produc252486962_val_o
@ ^ [B: nat > option1728594148on_val,C: list_char > option_val] : ( A @ ( produc755559506on_val @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(115,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: produc1282892786on_val] :
( ( produc1835097372_val_o @ A @ B )
=> ~ ! [C: exp_list_char,D: produc2090907612on_val] :
( ( B
= ( produc235638504on_val @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_splitE) ).
thf(566,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: produc1282892786on_val] :
( ( produc1835097372_val_o @ A @ B )
=> ~ ! [C: exp_list_char,D: produc2090907612on_val] :
( ( B
= ( produc235638504on_val @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(26,axiom,
! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc2090907612on_val,E: exp_list_char,F: produc2090907612on_val] :
( ( redp @ B @ C @ D @ E @ F )
=> ( redp @ B @ ( seq_list_char @ C @ A ) @ D @ ( seq_list_char @ E @ A ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_redp__redsp_OSeqRed) ).
thf(252,plain,
! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc2090907612on_val,E: exp_list_char,F: produc2090907612on_val] :
( ( redp @ B @ C @ D @ E @ F )
=> ( redp @ B @ ( seq_list_char @ C @ A ) @ D @ ( seq_list_char @ E @ A ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(142,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( A @ B @ C )
=> ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_splitI) ).
thf(665,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( A @ B @ C )
=> ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(109,axiom,
! [A: produc1282892786on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( member1072200031on_val @ A @ ( B @ C @ D ) )
=> ( member1072200031on_val @ A @ ( produc74886368_val_o @ B @ ( produc755559506on_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_mem__splitI) ).
thf(551,plain,
! [A: produc1282892786on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( member1072200031on_val @ A @ ( B @ C @ D ) )
=> ( member1072200031on_val @ A @ ( produc74886368_val_o @ B @ ( produc755559506on_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(45,axiom,
! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc2090907612on_val,E: exp_list_char,F: produc2090907612on_val] :
( ( redp @ B @ C @ D @ E @ F )
=> ( redp @ B @ ( lAss_list_char @ A @ C ) @ D @ ( lAss_list_char @ A @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_redp__redsp_OLAssRed) ).
thf(324,plain,
! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc2090907612on_val,E: exp_list_char,F: produc2090907612on_val] :
( ( redp @ B @ C @ D @ E @ F )
=> ( redp @ B @ ( lAss_list_char @ A @ C ) @ D @ ( lAss_list_char @ A @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(120,axiom,
! [A: produc1282892786on_val > $o] :
( ( produc1835097372_val_o
@ ^ [B: exp_list_char,C: produc2090907612on_val] : ( A @ ( produc235638504on_val @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_split__eta) ).
thf(578,plain,
! [A: produc1282892786on_val > $o] :
( ( produc1835097372_val_o
@ ^ [B: exp_list_char,C: produc2090907612on_val] : ( A @ ( produc235638504on_val @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(131,axiom,
! [A: produc2090907612on_val] :
~ ! [B: nat > option1728594148on_val,C: list_char > option_val] :
( A
!= ( produc755559506on_val @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_prod_Oexhaust) ).
thf(615,plain,
! [A: produc2090907612on_val] :
~ ! [B: nat > option1728594148on_val,C: list_char > option_val] :
( A
!= ( produc755559506on_val @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(161,axiom,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: produc1282892786on_val] :
( A
!= ( produc833389609on_val @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_prod_Oexhaust) ).
thf(725,plain,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: produc1282892786on_val] :
( A
!= ( produc833389609on_val @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(55,axiom,
! [A: ty,B: list_P1999446415t_char,C: ty,D: ty] :
( ( widen_2090681816t_char @ B @ C @ D )
=> ( ( widen_2090681816t_char @ B @ D @ A )
=> ( widen_2090681816t_char @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_widen__trans) ).
thf(356,plain,
! [A: ty,B: list_P1999446415t_char,C: ty,D: ty] :
( ( widen_2090681816t_char @ B @ C @ D )
=> ( ( widen_2090681816t_char @ B @ D @ A )
=> ( widen_2090681816t_char @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(71,axiom,
! [A: produc2090907612on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,C: produc2090907612on_val] :
( ( member1846553161on_val @ A @ ( produc146628214_val_o @ B @ C ) )
=> ~ ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ~ ( member1846553161on_val @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_mem__splitE) ).
thf(420,plain,
! [A: produc2090907612on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,C: produc2090907612on_val] :
( ( member1846553161on_val @ A @ ( produc146628214_val_o @ B @ C ) )
=> ~ ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ~ ( member1846553161on_val @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(91,axiom,
! [A: produc1746408499on_val > $o] :
( ( produc1624062875_val_o
@ ^ [B: produc1282892786on_val,C: produc1282892786on_val] : ( A @ ( produc833389609on_val @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_split__eta) ).
thf(499,plain,
! [A: produc1746408499on_val > $o] :
( ( produc1624062875_val_o
@ ^ [B: produc1282892786on_val,C: produc1282892786on_val] : ( A @ ( produc833389609on_val @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(17,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc1016489647on_val @ B @ C ) )
= ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] : ( produc1835097372_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_split__twice) ).
thf(225,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc1016489647on_val @ B @ C ) )
= ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] : ( produc1835097372_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(150,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_splitD) ).
thf(686,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(100,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_split__conv) ).
thf(526,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(13,axiom,
! [A: list_char > option_ty,B: list_char,C: ty,D: list_char > option_ty,E: ty] :
( ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= ( fun_up424764369ion_ty @ D @ B @ ( some_ty @ E ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_map__upd__eqD1) ).
thf(212,plain,
! [A: list_char > option_ty,B: list_char,C: ty,D: list_char > option_ty,E: ty] :
( ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= ( fun_up424764369ion_ty @ D @ B @ ( some_ty @ E ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: list_char > option_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( D = C )
=> ( ( fun_up424764369ion_ty @ A @ C @ B @ D )
= B ) )
& ( ( D != C )
=> ( ( fun_up424764369ion_ty @ A @ C @ B @ D )
= ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_fun__upd__def) ).
thf(193,plain,
! [A: list_char > option_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( D = C )
=> ( ( fun_up424764369ion_ty @ A @ C @ B @ D )
= B ) )
& ( ( D != C )
=> ( ( fun_up424764369ion_ty @ A @ C @ B @ D )
= ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(104,axiom,
! [A: list_char > option_val,B: list_char,C: val] :
~ ! [D: list_char] :
( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) @ D )
= none_val ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_map__upd__nonempty) ).
thf(537,plain,
! [A: list_char > option_val,B: list_char,C: val] :
~ ! [D: list_char] :
( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) @ D )
= none_val ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(66,axiom,
! [A: $o > $o,B: produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ( A @ ( produc1624062875_val_o @ B @ C ) )
=> ~ ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_splitE2) ).
thf(393,plain,
! [A: $o > $o,B: produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ( A @ ( produc1624062875_val_o @ B @ C ) )
=> ~ ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(83,axiom,
! [A: list_char > option_val,B: list_char,C: val] :
( ( ( A @ B )
= ( some_val @ C ) )
=> ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_map__upd__triv) ).
thf(457,plain,
! [A: list_char > option_val,B: list_char,C: val] :
( ( ( A @ B )
= ( some_val @ C ) )
=> ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(128,axiom,
! [A: list_char,B: ty,C: val,D: val,E: produc2090907612on_val,F: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( val_list_char @ C ) ) @ ( val_list_char @ D ) ) ) @ E ) @ ( produc235638504on_val @ ( val_list_char @ D ) @ E ) ) @ ( red @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_red__reds_ORedInitBlock) ).
thf(605,plain,
! [A: list_char,B: ty,C: val,D: val,E: produc2090907612on_val,F: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( val_list_char @ C ) ) @ ( val_list_char @ D ) ) ) @ E ) @ ( produc235638504on_val @ ( val_list_char @ D ) @ E ) ) @ ( red @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(94,axiom,
! [A: produc1746408499on_val > $o] :
( ( ? [B: produc1746408499on_val] : ( A @ B ) )
= ( ? [B: produc1282892786on_val,C: produc1282892786on_val] : ( A @ ( produc833389609on_val @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_split__paired__Ex) ).
thf(508,plain,
! [A: produc1746408499on_val > $o] :
( ( ? [B: produc1746408499on_val] : ( A @ B ) )
= ( ? [B: produc1282892786on_val,C: produc1282892786on_val] : ( A @ ( produc833389609on_val @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(42,axiom,
! [A: $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,C: produc2090907612on_val] :
( ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] :
( A
& ( B @ D @ E ) )
@ C )
= ( A
& ( produc252486962_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_split__part) ).
thf(311,plain,
! [A: $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,C: produc2090907612on_val] :
( ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] :
( A
& ( B @ D @ E ) )
@ C )
= ( A
& ( produc252486962_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(105,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( A @ B @ C )
=> ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_splitI) ).
thf(541,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( A @ B @ C )
=> ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(160,axiom,
! [A: exp_list_char,B: produc2090907612on_val,C: exp_list_char,D: produc2090907612on_val] :
( ( ( produc235638504on_val @ A @ B )
= ( produc235638504on_val @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Pair__inject) ).
thf(718,plain,
! [A: exp_list_char,B: produc2090907612on_val,C: exp_list_char,D: produc2090907612on_val] :
( ( ( produc235638504on_val @ A @ B )
= ( produc235638504on_val @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(137,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( ( produc833389609on_val @ A @ B )
= ( produc833389609on_val @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Pair__inject) ).
thf(633,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( ( produc833389609on_val @ A @ B )
= ( produc833389609on_val @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(57,axiom,
! [A: list_char,B: exp_list_char,C: val] :
( ( lAss_list_char @ A @ B )
!= ( val_list_char @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_exp_Osimps_I75_J) ).
thf(360,plain,
! [A: list_char,B: exp_list_char,C: val] :
( ( lAss_list_char @ A @ B )
!= ( val_list_char @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(68,axiom,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: nat > option1728594148on_val,F: list_char > option_val,G: list_char,H: exp_list_char,I: nat > option1728594148on_val,J: list_char > option_val] :
( ( redp @ C @ D @ ( produc755559506on_val @ E @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) @ H @ ( produc755559506on_val @ I @ J ) )
=> ( ( ( J @ G )
= ( some_val @ B ) )
=> ( ~ ( assigned @ G @ D )
=> ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( produc755559506on_val @ E @ F ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ H ) ) @ ( produc755559506on_val @ I @ ( fun_up1149430426on_val @ J @ G @ ( F @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_redp__redsp_OBlockRedSome) ).
thf(412,plain,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: nat > option1728594148on_val,F: list_char > option_val,G: list_char,H: exp_list_char,I: nat > option1728594148on_val,J: list_char > option_val] :
( ( redp @ C @ D @ ( produc755559506on_val @ E @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) @ H @ ( produc755559506on_val @ I @ J ) )
=> ( ( ( J @ G )
= ( some_val @ B ) )
=> ( ~ ( assigned @ G @ D )
=> ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( produc755559506on_val @ E @ F ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ H ) ) @ ( produc755559506on_val @ I @ ( fun_up1149430426on_val @ J @ G @ ( F @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(169,axiom,
! [A: nat > option1728594148on_val,B: list_char > option_val,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( ( produc755559506on_val @ A @ B )
= ( produc755559506on_val @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Pair__inject) ).
thf(750,plain,
! [A: nat > option1728594148on_val,B: list_char > option_val,C: nat > option1728594148on_val,D: list_char > option_val] :
( ( ( produc755559506on_val @ A @ B )
= ( produc755559506on_val @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(29,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val,C: produc1746408499on_val] :
( ( produc252486962_val_o @ A @ ( produc511181936on_val @ B @ C ) )
= ( produc1624062875_val_o
@ ^ [D: produc1282892786on_val,E: produc1282892786on_val] : ( produc252486962_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_split__twice) ).
thf(264,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val,C: produc1746408499on_val] :
( ( produc252486962_val_o @ A @ ( produc511181936on_val @ B @ C ) )
= ( produc1624062875_val_o
@ ^ [D: produc1282892786on_val,E: produc1282892786on_val] : ( produc252486962_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(167,axiom,
! [A: list_char > option_val,B: list_char,C: option_val,D: option_val] :
( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
= ( fun_up1149430426on_val @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_fun__upd__upd) ).
thf(745,plain,
! [A: list_char > option_val,B: list_char,C: option_val,D: option_val] :
( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
= ( fun_up1149430426on_val @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(6,axiom,
! [A: list_char > option_ty,B: option_ty,C: list_char,D: list_char] :
( ( C != D )
=> ( ( fun_up424764369ion_ty @ A @ D @ B @ C )
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_fun__upd__other) ).
thf(180,plain,
! [A: list_char > option_ty,B: option_ty,C: list_char,D: list_char] :
( ( C != D )
=> ( ( fun_up424764369ion_ty @ A @ D @ B @ C )
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(77,axiom,
member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).
thf(444,plain,
member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(163,axiom,
wf_pro755087577t_char @ wf_J_mdecl @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms) ).
thf(733,plain,
wf_pro755087577t_char @ wf_J_mdecl @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(122,axiom,
! [A: produc1746408499on_val > $o] :
( ( ! [B: produc1746408499on_val] : ( A @ B ) )
= ( ! [B: produc1282892786on_val,C: produc1282892786on_val] : ( A @ ( produc833389609on_val @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_split__paired__All) ).
thf(584,plain,
! [A: produc1746408499on_val > $o] :
( ( ! [B: produc1746408499on_val] : ( A @ B ) )
= ( ! [B: produc1282892786on_val,C: produc1282892786on_val] : ( A @ ( produc833389609on_val @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(34,axiom,
produc900512295_val_o = produc1835097372_val_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_internal__split__def) ).
thf(286,plain,
produc900512295_val_o = produc1835097372_val_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(36,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: ty,F: exp_list_char] :
( ( ( block_list_char @ A @ B @ C )
= ( block_list_char @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_exp_Osimps_I10_J) ).
thf(291,plain,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: ty,F: exp_list_char] :
( ( ( block_list_char @ A @ B @ C )
= ( block_list_char @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
! [A: list_char > option_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( C = D )
=> ( ( fun_up424764369ion_ty @ A @ D @ B @ C )
= B ) )
& ( ( C != D )
=> ( ( fun_up424764369ion_ty @ A @ D @ B @ C )
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_fun__upd__apply) ).
thf(204,plain,
! [A: list_char > option_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( C = D )
=> ( ( fun_up424764369ion_ty @ A @ D @ B @ C )
= B ) )
& ( ( C != D )
=> ( ( fun_up424764369ion_ty @ A @ D @ B @ C )
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(107,axiom,
! [A: produc1746408499on_val,B: produc1746408499on_val > $o] :
( ( member1913460000on_val @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_mem__def) ).
thf(545,plain,
! [A: produc1746408499on_val,B: produc1746408499on_val > $o] :
( ( member1913460000on_val @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(78,axiom,
! [A: list_char,B: val,C: nat > option1728594148on_val,D: list_char > option_val,E: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ A @ ( val_list_char @ B ) ) @ ( produc755559506on_val @ C @ D ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ C @ ( fun_up1149430426on_val @ D @ A @ ( some_val @ B ) ) ) ) ) @ ( red @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_red__reds_ORedLAss) ).
thf(445,plain,
! [A: list_char,B: val,C: nat > option1728594148on_val,D: list_char > option_val,E: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ A @ ( val_list_char @ B ) ) @ ( produc755559506on_val @ C @ D ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ C @ ( fun_up1149430426on_val @ D @ A @ ( some_val @ B ) ) ) ) ) @ ( red @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(64,axiom,
! [A: produc1282892786on_val > $o] :
( ( ! [B: produc1282892786on_val] : ( A @ B ) )
= ( ! [B: exp_list_char,C: produc2090907612on_val] : ( A @ ( produc235638504on_val @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_split__paired__All) ).
thf(382,plain,
! [A: produc1282892786on_val > $o] :
( ( ! [B: produc1282892786on_val] : ( A @ B ) )
= ( ! [B: exp_list_char,C: produc2090907612on_val] : ( A @ ( produc235638504on_val @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(130,axiom,
! [A: produc1282892786on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,C: produc2090907612on_val] :
( ( member1072200031on_val @ A @ ( produc74886368_val_o @ B @ C ) )
=> ~ ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ~ ( member1072200031on_val @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_mem__splitE) ).
thf(611,plain,
! [A: produc1282892786on_val,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,C: produc2090907612on_val] :
( ( member1072200031on_val @ A @ ( produc74886368_val_o @ B @ C ) )
=> ~ ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ~ ( member1072200031on_val @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(155,axiom,
! [A: produc1282892786on_val > $o,B: produc1282892786on_val > $o] :
( ( ! [C: exp_list_char,D: produc2090907612on_val] :
( ( member1072200031on_val @ ( produc235638504on_val @ C @ D ) @ B )
= ( member1072200031on_val @ ( produc235638504on_val @ C @ D ) @ A ) ) )
= ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_pred__equals__eq2) ).
thf(704,plain,
! [A: produc1282892786on_val > $o,B: produc1282892786on_val > $o] :
( ( ! [C: exp_list_char,D: produc2090907612on_val] :
( ( member1072200031on_val @ ( produc235638504on_val @ C @ D ) @ B )
= ( member1072200031on_val @ ( produc235638504on_val @ C @ D ) @ A ) ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(53,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val,C: produc2090907612on_val] :
( ( produc1624062875_val_o @ A @ ( produc1186953840on_val @ B @ C ) )
= ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] : ( produc1624062875_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_split__twice) ).
thf(350,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val,C: produc2090907612on_val] :
( ( produc1624062875_val_o @ A @ ( produc1186953840on_val @ B @ C ) )
= ( produc252486962_val_o
@ ^ [D: nat > option1728594148on_val,E: list_char > option_val] : ( produc1624062875_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(145,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_split__conv) ).
thf(672,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(62,axiom,
! [A: list_char > option_val,B: option_val,C: list_char,D: list_char] :
( ( C != D )
=> ( ( fun_up1149430426on_val @ A @ D @ B @ C )
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_fun__upd__other) ).
thf(377,plain,
! [A: list_char > option_val,B: option_val,C: list_char,D: list_char] :
( ( C != D )
=> ( ( fun_up1149430426on_val @ A @ D @ B @ C )
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(40,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1746408499on_val,C: produc1746408499on_val] :
( ( B = C )
=> ( ( produc1624062875_val_o @ A @ B )
= ( produc1624062875_val_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_split__weak__cong) ).
thf(303,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1746408499on_val,C: produc1746408499on_val] :
( ( B = C )
=> ( ( produc1624062875_val_o @ A @ B )
= ( produc1624062875_val_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(31,axiom,
! [A: $o,B: produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ( produc1624062875_val_o
@ ^ [D: produc1282892786on_val,E: produc1282892786on_val] :
( A
& ( B @ D @ E ) )
@ C )
= ( A
& ( produc1624062875_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_split__part) ).
thf(271,plain,
! [A: $o,B: produc1282892786on_val > produc1282892786on_val > $o,C: produc1746408499on_val] :
( ( produc1624062875_val_o
@ ^ [D: produc1282892786on_val,E: produc1282892786on_val] :
( A
& ( B @ D @ E ) )
@ C )
= ( A
& ( produc1624062875_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(165,axiom,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: produc1282892786on_val] :
( A
!= ( produc833389609on_val @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_PairE) ).
thf(737,plain,
! [A: produc1746408499on_val] :
~ ! [B: produc1282892786on_val,C: produc1282892786on_val] :
( A
!= ( produc833389609on_val @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(43,axiom,
! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( ( seq_list_char @ A @ B )
= ( seq_list_char @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_exp_Osimps_I11_J) ).
thf(318,plain,
! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( ( seq_list_char @ A @ B )
= ( seq_list_char @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(133,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( A @ B @ C )
=> ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_prod__caseI) ).
thf(621,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( A @ B @ C )
=> ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(22,axiom,
produc2006262054_val_o = produc1624062875_val_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_internal__split__def) ).
thf(240,plain,
produc2006262054_val_o = produc1624062875_val_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,axiom,
produc575577405_val_o = produc252486962_val_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_internal__split__def) ).
thf(330,plain,
produc575577405_val_o = produc252486962_val_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(98,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_splitD) ).
thf(521,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(32,axiom,
! [A: val,B: exp_list_char,C: exp_list_char] :
( ( val_list_char @ A )
!= ( seq_list_char @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_exp_Osimps_I84_J) ).
thf(278,plain,
! [A: val,B: exp_list_char,C: exp_list_char] :
( ( val_list_char @ A )
!= ( seq_list_char @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(113,axiom,
typeSa1586500134_sconf @ p @ e @ ( produc755559506on_val @ ha @ la ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_InitBlockRed_I4_J) ).
thf(563,plain,
typeSa1586500134_sconf @ p @ e @ ( produc755559506on_val @ ha @ la ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(30,axiom,
! [A: val,B: list_char,C: ty,D: exp_list_char] :
( ( val_list_char @ A )
!= ( block_list_char @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_exp_Osimps_I82_J) ).
thf(267,plain,
! [A: val,B: list_char,C: ty,D: exp_list_char] :
( ( val_list_char @ A )
!= ( block_list_char @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(146,axiom,
! [A: produc1746408499on_val > $o,B: produc1282892786on_val > produc1282892786on_val > $o] :
( ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( B @ C @ D )
= ( A @ ( produc833389609on_val @ C @ D ) ) )
=> ( ( produc1624062875_val_o @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_cond__split__eta) ).
thf(675,plain,
! [A: produc1746408499on_val > $o,B: produc1282892786on_val > produc1282892786on_val > $o] :
( ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( B @ C @ D )
= ( A @ ( produc833389609on_val @ C @ D ) ) )
=> ( ( produc1624062875_val_o @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(102,axiom,
! [A: ty,B: list_char > option_ty] :
( ( typeSa1586500134_sconf @ p @ B @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) )
=> ( ( wTrt @ p @ ha @ B @ ea @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_a @ C )
& ( widen_2090681816t_char @ p @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_InitBlockRed_I2_J) ).
thf(531,plain,
! [A: ty,B: list_char > option_ty] :
( ( typeSa1586500134_sconf @ p @ B @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) )
=> ( ( wTrt @ p @ ha @ B @ ea @ A )
=> ? [C: ty] :
( ( wTrt @ p @ h_a @ B @ e_a @ C )
& ( widen_2090681816t_char @ p @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(148,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( ( produc833389609on_val @ A @ B )
= ( produc833389609on_val @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Pair__eq) ).
thf(680,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( ( produc833389609on_val @ A @ B )
= ( produc833389609on_val @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(110,axiom,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: nat > option1728594148on_val,F: list_char > option_val,G: list_char,H: val,I: exp_list_char,J: nat > option1728594148on_val,K: list_char > option_val] :
( ( redp @ C @ D @ ( produc755559506on_val @ E @ ( fun_up1149430426on_val @ F @ G @ ( some_val @ H ) ) ) @ I @ ( produc755559506on_val @ J @ K ) )
=> ( ( ( K @ G )
= ( some_val @ B ) )
=> ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ H ) ) @ D ) ) @ ( produc755559506on_val @ E @ F ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ I ) ) @ ( produc755559506on_val @ J @ ( fun_up1149430426on_val @ K @ G @ ( F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_redp__redsp_OInitBlockRed) ).
thf(553,plain,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: nat > option1728594148on_val,F: list_char > option_val,G: list_char,H: val,I: exp_list_char,J: nat > option1728594148on_val,K: list_char > option_val] :
( ( redp @ C @ D @ ( produc755559506on_val @ E @ ( fun_up1149430426on_val @ F @ G @ ( some_val @ H ) ) ) @ I @ ( produc755559506on_val @ J @ K ) )
=> ( ( ( K @ G )
= ( some_val @ B ) )
=> ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ H ) ) @ D ) ) @ ( produc755559506on_val @ E @ F ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( val_list_char @ B ) ) @ I ) ) @ ( produc755559506on_val @ J @ ( fun_up1149430426on_val @ K @ G @ ( F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(141,axiom,
! [A: val,B: exp_list_char,C: produc2090907612on_val,D: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( val_list_char @ A ) @ B ) @ C ) @ ( produc235638504on_val @ B @ C ) ) @ ( red @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_red__reds_ORedSeq) ).
thf(663,plain,
! [A: val,B: exp_list_char,C: produc2090907612on_val,D: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( val_list_char @ A ) @ B ) @ C ) @ ( produc235638504on_val @ B @ C ) ) @ ( red @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(108,axiom,
! [A: list_char > option_val,B: list_char,C: val,D: list_char > option_val,E: val] :
( ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= ( fun_up1149430426on_val @ D @ B @ ( some_val @ E ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_map__upd__eqD1) ).
thf(548,plain,
! [A: list_char > option_val,B: list_char,C: val,D: list_char > option_val,E: val] :
( ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) )
= ( fun_up1149430426on_val @ D @ B @ ( some_val @ E ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(158,axiom,
! [A: produc1746408499on_val,B: produc1746408499on_val > $o] :
( ! [C: produc1282892786on_val,D: exp_list_char,E: nat > option1728594148on_val,F: list_char > option_val] : ( B @ ( produc833389609on_val @ C @ ( produc235638504on_val @ D @ ( produc755559506on_val @ E @ F ) ) ) )
=> ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_prod__induct4) ).
thf(712,plain,
! [A: produc1746408499on_val,B: produc1746408499on_val > $o] :
( ! [C: produc1282892786on_val,D: exp_list_char,E: nat > option1728594148on_val,F: list_char > option_val] : ( B @ ( produc833389609on_val @ C @ ( produc235638504on_val @ D @ ( produc755559506on_val @ E @ F ) ) ) )
=> ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(138,axiom,
! [A: list_char > option_val,B: list_char,C: option_val] :
( ( ( fun_up1149430426on_val @ A @ B @ C )
= A )
= ( ( A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_fun__upd__idem__iff) ).
thf(640,plain,
! [A: list_char > option_val,B: list_char,C: option_val] :
( ( ( fun_up1149430426on_val @ A @ B @ C )
= A )
= ( ( A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(33,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: exp_list_char,E: exp_list_char] :
( ( block_list_char @ A @ B @ C )
!= ( seq_list_char @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_exp_Osimps_I196_J) ).
thf(282,plain,
! [A: list_char,B: ty,C: exp_list_char,D: exp_list_char,E: exp_list_char] :
( ( block_list_char @ A @ B @ C )
!= ( seq_list_char @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(156,axiom,
! [A: produc2090907612on_val,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( member1846553161on_val @ A @ ( B @ C @ D ) )
=> ( member1846553161on_val @ A @ ( produc793795679_val_o @ B @ ( produc833389609on_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_mem__splitI) ).
thf(707,plain,
! [A: produc2090907612on_val,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( member1846553161on_val @ A @ ( B @ C @ D ) )
=> ( member1846553161on_val @ A @ ( produc793795679_val_o @ B @ ( produc833389609on_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(5,axiom,
! [A: list_char > option_ty,B: list_char,C: ty] :
( ( ( A @ B )
= ( some_ty @ C ) )
=> ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_map__upd__triv) ).
thf(177,plain,
! [A: list_char > option_ty,B: list_char,C: ty] :
( ( ( A @ B )
= ( some_ty @ C ) )
=> ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(92,axiom,
! [A: produc2090907612on_val,B: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,C: exp_list_char,D: produc2090907612on_val] :
( ( member1846553161on_val @ A @ ( B @ C @ D ) )
=> ( member1846553161on_val @ A @ ( produc1115879776_val_o @ B @ ( produc235638504on_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_mem__splitI) ).
thf(502,plain,
! [A: produc2090907612on_val,B: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,C: exp_list_char,D: produc2090907612on_val] :
( ( member1846553161on_val @ A @ ( B @ C @ D ) )
=> ( member1846553161on_val @ A @ ( produc1115879776_val_o @ B @ ( produc235638504on_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(139,axiom,
! [A: $o > $o,B: exp_list_char > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ( A @ ( produc1835097372_val_o @ B @ C ) )
=> ~ ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_splitE2) ).
thf(643,plain,
! [A: $o > $o,B: exp_list_char > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ( A @ ( produc1835097372_val_o @ B @ C ) )
=> ~ ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(87,axiom,
! [A: produc1282892786on_val] :
~ ! [B: exp_list_char,C: nat > option1728594148on_val,D: list_char > option_val] :
( A
!= ( produc235638504on_val @ B @ ( produc755559506on_val @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_prod__cases3) ).
thf(470,plain,
! [A: produc1282892786on_val] :
~ ! [B: exp_list_char,C: nat > option1728594148on_val,D: list_char > option_val] :
( A
!= ( produc235638504on_val @ B @ ( produc755559506on_val @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(119,axiom,
! [A: list_char > option_ty,B: ty,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: exp_list_char,G: nat > option1728594148on_val,H: list_char > option_val,I: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ F @ ( produc755559506on_val @ G @ H ) ) ) @ ( red @ I ) )
=> ( ( wTrt @ I @ D @ A @ C @ B )
=> ( ( hconf_97414254t_char @ I @ D )
=> ( hconf_97414254t_char @ I @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_red__preserves__hconf) ).
thf(576,plain,
! [A: list_char > option_ty,B: ty,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: exp_list_char,G: nat > option1728594148on_val,H: list_char > option_val,I: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ F @ ( produc755559506on_val @ G @ H ) ) ) @ ( red @ I ) )
=> ( ( wTrt @ I @ D @ A @ C @ B )
=> ( ( hconf_97414254t_char @ I @ D )
=> ( hconf_97414254t_char @ I @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(49,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( B = C )
=> ( ( produc1835097372_val_o @ A @ B )
= ( produc1835097372_val_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_split__weak__cong) ).
thf(336,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( B = C )
=> ( ( produc1835097372_val_o @ A @ B )
= ( produc1835097372_val_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(117,axiom,
! [A: list_P1999446415t_char,B: exp_list_char,C: produc2090907612on_val,D: exp_list_char,E: produc2090907612on_val] :
( ( redp @ A @ B @ C @ D @ E )
= ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ C ) @ ( produc235638504on_val @ D @ E ) ) @ ( red @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_redp__red__eq) ).
thf(571,plain,
! [A: list_P1999446415t_char,B: exp_list_char,C: produc2090907612on_val,D: exp_list_char,E: produc2090907612on_val] :
( ( redp @ A @ B @ C @ D @ E )
= ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ C ) @ ( produc235638504on_val @ D @ E ) ) @ ( red @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(125,axiom,
! [A: list_char > option_val,B: list_char] :
( ( fun_up1149430426on_val @ A @ B @ ( A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).
thf(595,plain,
! [A: list_char > option_val,B: list_char] :
( ( fun_up1149430426on_val @ A @ B @ ( A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(135,axiom,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_split__conv) ).
thf(627,plain,
! [A: exp_list_char > produc2090907612on_val > $o,B: exp_list_char,C: produc2090907612on_val] :
( ( produc1835097372_val_o @ A @ ( produc235638504on_val @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(80,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_splitD) ).
thf(450,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(111,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc2090907612on_val] :
( ( produc252486962_val_o @ A @ B )
=> ~ ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( B
= ( produc755559506on_val @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_splitE) ).
thf(556,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: produc2090907612on_val] :
( ( produc252486962_val_o @ A @ B )
=> ~ ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( B
= ( produc755559506on_val @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(151,axiom,
! [A: ty,B: val,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: list_char,G: val,H: exp_list_char,I: nat > option1728594148on_val,J: list_char > option_val,K: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ ( fun_up1149430426on_val @ E @ F @ ( some_val @ G ) ) ) ) @ ( produc235638504on_val @ H @ ( produc755559506on_val @ I @ J ) ) ) @ ( red @ K ) )
=> ( ( ( J @ F )
= ( some_val @ B ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ G ) ) @ C ) ) @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ H ) ) @ ( produc755559506on_val @ I @ ( fun_up1149430426on_val @ J @ F @ ( E @ F ) ) ) ) ) @ ( red @ K ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_red__reds_OInitBlockRed) ).
thf(688,plain,
! [A: ty,B: val,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: list_char,G: val,H: exp_list_char,I: nat > option1728594148on_val,J: list_char > option_val,K: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ ( fun_up1149430426on_val @ E @ F @ ( some_val @ G ) ) ) ) @ ( produc235638504on_val @ H @ ( produc755559506on_val @ I @ J ) ) ) @ ( red @ K ) )
=> ( ( ( J @ F )
= ( some_val @ B ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ G ) ) @ C ) ) @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ H ) ) @ ( produc755559506on_val @ I @ ( fun_up1149430426on_val @ J @ F @ ( E @ F ) ) ) ) ) @ ( red @ K ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(121,axiom,
! [A: produc2090907612on_val > $o] :
( ( ! [B: produc2090907612on_val] : ( A @ B ) )
= ( ! [B: nat > option1728594148on_val,C: list_char > option_val] : ( A @ ( produc755559506on_val @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_split__paired__All) ).
thf(581,plain,
! [A: produc2090907612on_val > $o] :
( ( ! [B: produc2090907612on_val] : ( A @ B ) )
= ( ! [B: nat > option1728594148on_val,C: list_char > option_val] : ( A @ ( produc755559506on_val @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(90,axiom,
! [A: produc2090907612on_val,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,C: produc1746408499on_val] :
( ( member1846553161on_val @ A @ ( produc793795679_val_o @ B @ C ) )
=> ~ ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ~ ( member1846553161on_val @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_mem__splitE) ).
thf(495,plain,
! [A: produc2090907612on_val,B: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,C: produc1746408499on_val] :
( ( member1846553161on_val @ A @ ( produc793795679_val_o @ B @ C ) )
=> ~ ! [D: produc1282892786on_val,E: produc1282892786on_val] :
( ( C
= ( produc833389609on_val @ D @ E ) )
=> ~ ( member1846553161on_val @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(15,axiom,
! [A: list_char > option_ty,B: list_char,C: option_ty] :
( ( ( fun_up424764369ion_ty @ A @ B @ C )
= A )
= ( ( A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_fun__upd__idem__iff) ).
thf(218,plain,
! [A: list_char > option_ty,B: list_char,C: option_ty] :
( ( ( fun_up424764369ion_ty @ A @ B @ C )
= A )
= ( ( A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(168,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( A @ B @ C )
=> ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_prod__caseI) ).
thf(748,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1282892786on_val,C: produc1282892786on_val] :
( ( A @ B @ C )
=> ( produc1624062875_val_o @ A @ ( produc833389609on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(8,axiom,
! [A: list_char > option_ty,B: list_char] :
( ( fun_up424764369ion_ty @ A @ B @ ( A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_fun__upd__triv) ).
thf(186,plain,
! [A: list_char > option_ty,B: list_char] :
( ( fun_up424764369ion_ty @ A @ B @ ( A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: list_char,B: list_char] :
( ( fun_up424764369ion_ty
@ ^ [C: list_char] : none_ty
@ A
@ none_ty
@ B )
= none_ty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_empty__upd__none) ).
thf(171,plain,
! [A: list_char,B: list_char] :
( ( fun_up424764369ion_ty
@ ^ [C: list_char] : none_ty
@ A
@ none_ty
@ B )
= none_ty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(70,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val > $o] :
( ! [C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val] : ( B @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) )
=> ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_prod__induct3) ).
thf(418,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val > $o] :
( ! [C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val] : ( B @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) )
=> ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(143,axiom,
! [A: list_char > option_val,B: list_char,C: val,D: list_char,E: val] :
( ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) @ D )
= ( some_val @ E ) )
= ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( A @ D )
= ( some_val @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_map__upd__Some__unfold) ).
thf(667,plain,
! [A: list_char > option_val,B: list_char,C: val,D: list_char,E: val] :
( ( ( fun_up1149430426on_val @ A @ B @ ( some_val @ C ) @ D )
= ( some_val @ E ) )
= ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( A @ D )
= ( some_val @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(89,axiom,
! [A: $o > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,C: produc2090907612on_val] :
( ( A @ ( produc252486962_val_o @ B @ C ) )
=> ~ ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_splitE2) ).
thf(478,plain,
! [A: $o > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,C: produc2090907612on_val] :
( ( A @ ( produc252486962_val_o @ B @ C ) )
=> ~ ! [D: nat > option1728594148on_val,E: list_char > option_val] :
( ( C
= ( produc755559506on_val @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(20,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: exp_list_char > produc2090907612on_val > produc2090907612on_val,C: produc1282892786on_val] :
( ( produc252486962_val_o @ A @ ( produc69760047on_val @ B @ C ) )
= ( produc1835097372_val_o
@ ^ [D: exp_list_char,E: produc2090907612on_val] : ( produc252486962_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_split__twice) ).
thf(235,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: exp_list_char > produc2090907612on_val > produc2090907612on_val,C: produc1282892786on_val] :
( ( produc252486962_val_o @ A @ ( produc69760047on_val @ B @ C ) )
= ( produc1835097372_val_o
@ ^ [D: exp_list_char,E: produc2090907612on_val] : ( produc252486962_val_o @ A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [A: list_P1999446415t_char,B: val,C: exp_list_char,D: produc2090907612on_val] : ( redp @ A @ ( seq_list_char @ ( val_list_char @ B ) @ C ) @ D @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_redp__redsp_ORedSeq) ).
thf(246,plain,
! [A: list_P1999446415t_char,B: val,C: exp_list_char,D: produc2090907612on_val] : ( redp @ A @ ( seq_list_char @ ( val_list_char @ B ) @ C ) @ D @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,axiom,
! [A: exp_list_char,B: produc2090907612on_val,C: exp_list_char,D: produc2090907612on_val] :
( ( ( produc235638504on_val @ A @ B )
= ( produc235638504on_val @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Pair__eq) ).
thf(447,plain,
! [A: exp_list_char,B: produc2090907612on_val,C: exp_list_char,D: produc2090907612on_val] :
( ( ( produc235638504on_val @ A @ B )
= ( produc235638504on_val @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(74,axiom,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1746408499on_val] :
( ( produc1624062875_val_o @ A @ B )
=> ~ ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( B
= ( produc833389609on_val @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_splitE) ).
thf(432,plain,
! [A: produc1282892786on_val > produc1282892786on_val > $o,B: produc1746408499on_val] :
( ( produc1624062875_val_o @ A @ B )
=> ~ ! [C: produc1282892786on_val,D: produc1282892786on_val] :
( ( B
= ( produc833389609on_val @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(67,axiom,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( A @ B @ C )
=> ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_prod__caseI) ).
thf(410,plain,
! [A: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,B: nat > option1728594148on_val,C: list_char > option_val] :
( ( A @ B @ C )
=> ( produc252486962_val_o @ A @ ( produc755559506on_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(7,axiom,
! [A: list_char > option_ty,B: list_char,C: ty,D: list_char,E: ty] :
( ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) @ D )
= ( some_ty @ E ) )
= ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( A @ D )
= ( some_ty @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_map__upd__Some__unfold) ).
thf(183,plain,
! [A: list_char > option_ty,B: list_char,C: ty,D: list_char,E: ty] :
( ( ( fun_up424764369ion_ty @ A @ B @ ( some_ty @ C ) @ D )
= ( some_ty @ E ) )
= ( ( ( D = B )
& ( C = E ) )
| ( ( D != B )
& ( ( A @ D )
= ( some_ty @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,axiom,
! [A: produc2090907612on_val,B: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ( member1846553161on_val @ A @ ( B @ D @ E ) ) )
=> ( member1846553161on_val @ A @ ( produc1115879776_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_mem__splitI2) ).
thf(373,plain,
! [A: produc2090907612on_val,B: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ! [D: exp_list_char,E: produc2090907612on_val] :
( ( C
= ( produc235638504on_val @ D @ E ) )
=> ( member1846553161on_val @ A @ ( B @ D @ E ) ) )
=> ( member1846553161on_val @ A @ ( produc1115879776_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(114,axiom,
! [A: produc1282892786on_val,B: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( member1072200031on_val @ A @ ( B @ C @ D ) )
=> ( member1072200031on_val @ A @ ( produc1798214089_val_o @ B @ ( produc833389609on_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_mem__splitI) ).
thf(564,plain,
! [A: produc1282892786on_val,B: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,C: produc1282892786on_val,D: produc1282892786on_val] :
( ( member1072200031on_val @ A @ ( B @ C @ D ) )
=> ( member1072200031on_val @ A @ ( produc1798214089_val_o @ B @ ( produc833389609on_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(46,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: exp_list_char] :
( ( block_list_char @ A @ B @ C )
!= ( lAss_list_char @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_exp_Osimps_I143_J) ).
thf(326,plain,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: exp_list_char] :
( ( block_list_char @ A @ B @ C )
!= ( lAss_list_char @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(23,axiom,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( seq_list_char @ A @ B )
!= ( lAss_list_char @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_exp_Osimps_I145_J) ).
thf(242,plain,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( seq_list_char @ A @ B )
!= ( lAss_list_char @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(37,axiom,
! [A: list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( ( lAss_list_char @ A @ B )
= ( lAss_list_char @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_exp_Osimps_I6_J) ).
thf(294,plain,
! [A: list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( ( lAss_list_char @ A @ B )
= ( lAss_list_char @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(56,axiom,
! [A: list_P1999446415t_char,B: ty] : ( widen_2090681816t_char @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_widen__refl) ).
thf(358,plain,
! [A: list_P1999446415t_char,B: ty] : ( widen_2090681816t_char @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(88,axiom,
! [A: produc2090907612on_val] :
~ ! [B: nat > option1728594148on_val,C: list_char > option_val] :
( A
!= ( produc755559506on_val @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_PairE) ).
thf(474,plain,
! [A: produc2090907612on_val] :
~ ! [B: nat > option1728594148on_val,C: list_char > option_val] :
( A
!= ( produc755559506on_val @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(154,axiom,
! [A: list_char > option_val,B: option_val,C: list_char,D: list_char] :
( ( ( C = D )
=> ( ( fun_up1149430426on_val @ A @ D @ B @ C )
= B ) )
& ( ( C != D )
=> ( ( fun_up1149430426on_val @ A @ D @ B @ C )
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_fun__upd__apply) ).
thf(696,plain,
! [A: list_char > option_val,B: option_val,C: list_char,D: list_char] :
( ( ( C = D )
=> ( ( fun_up1149430426on_val @ A @ D @ B @ C )
= B ) )
& ( ( C != D )
=> ( ( fun_up1149430426on_val @ A @ D @ B @ C )
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(69,axiom,
! [A: produc2090907612on_val > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( B @ C @ D )
= ( A @ ( produc755559506on_val @ C @ D ) ) )
=> ( ( produc252486962_val_o @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_cond__split__eta) ).
thf(415,plain,
! [A: produc2090907612on_val > $o,B: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ! [C: nat > option1728594148on_val,D: list_char > option_val] :
( ( B @ C @ D )
= ( A @ ( produc755559506on_val @ C @ D ) ) )
=> ( ( produc252486962_val_o @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(85,axiom,
! [A: produc2090907612on_val > $o] :
( ( ? [B: produc2090907612on_val] : ( A @ B ) )
= ( ? [B: nat > option1728594148on_val,C: list_char > option_val] : ( A @ ( produc755559506on_val @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_split__paired__Ex) ).
thf(464,plain,
! [A: produc2090907612on_val > $o] :
( ( ? [B: produc2090907612on_val] : ( A @ B ) )
= ( ? [B: nat > option1728594148on_val,C: list_char > option_val] : ( A @ ( produc755559506on_val @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(48,axiom,
! [A: val,B: list_char,C: exp_list_char] :
( ( val_list_char @ A )
!= ( lAss_list_char @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_exp_Osimps_I74_J) ).
thf(332,plain,
! [A: val,B: list_char,C: exp_list_char] :
( ( val_list_char @ A )
!= ( lAss_list_char @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(152,axiom,
! [A: list_char,B: exp_list_char,C: produc2090907612on_val,D: exp_list_char,E: produc2090907612on_val,F: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ C ) @ ( produc235638504on_val @ D @ E ) ) @ ( red @ F ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ A @ B ) @ C ) @ ( produc235638504on_val @ ( lAss_list_char @ A @ D ) @ E ) ) @ ( red @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_red__reds_OLAssRed) ).
thf(691,plain,
! [A: list_char,B: exp_list_char,C: produc2090907612on_val,D: exp_list_char,E: produc2090907612on_val,F: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ C ) @ ( produc235638504on_val @ D @ E ) ) @ ( red @ F ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ A @ B ) @ C ) @ ( produc235638504on_val @ ( lAss_list_char @ A @ D ) @ E ) ) @ ( red @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(60,axiom,
! [A: produc1282892786on_val] :
~ ! [B: exp_list_char,C: produc2090907612on_val] :
( A
!= ( produc235638504on_val @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_PairE) ).
thf(369,plain,
! [A: produc1282892786on_val] :
~ ! [B: exp_list_char,C: produc2090907612on_val] :
( A
!= ( produc235638504on_val @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(129,axiom,
! [A: produc1282892786on_val] :
~ ! [B: exp_list_char,C: produc2090907612on_val] :
( A
!= ( produc235638504on_val @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_prod_Oexhaust) ).
thf(607,plain,
! [A: produc1282892786on_val] :
~ ! [B: exp_list_char,C: produc2090907612on_val] :
( A
!= ( produc235638504on_val @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(27,axiom,
! [A: $o,B: exp_list_char > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ( produc1835097372_val_o
@ ^ [D: exp_list_char,E: produc2090907612on_val] :
( A
& ( B @ D @ E ) )
@ C )
= ( A
& ( produc1835097372_val_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_split__part) ).
thf(254,plain,
! [A: $o,B: exp_list_char > produc2090907612on_val > $o,C: produc1282892786on_val] :
( ( produc1835097372_val_o
@ ^ [D: exp_list_char,E: produc2090907612on_val] :
( A
& ( B @ D @ E ) )
@ C )
= ( A
& ( produc1835097372_val_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(106,axiom,
! [A: list_char > option_ty,B: ty,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: exp_list_char,G: nat > option1728594148on_val,H: list_char > option_val,I: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ F @ ( produc755559506on_val @ G @ H ) ) ) @ ( red @ I ) )
=> ( ( wTrt @ I @ D @ A @ C @ B )
=> ( ( lconf_496643946t_char @ I @ D @ E @ A )
=> ( lconf_496643946t_char @ I @ G @ H @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_red__preserves__lconf) ).
thf(543,plain,
! [A: list_char > option_ty,B: ty,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: exp_list_char,G: nat > option1728594148on_val,H: list_char > option_val,I: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ F @ ( produc755559506on_val @ G @ H ) ) ) @ ( red @ I ) )
=> ( ( wTrt @ I @ D @ A @ C @ B )
=> ( ( lconf_496643946t_char @ I @ D @ E @ A )
=> ( lconf_496643946t_char @ I @ G @ H @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(14,axiom,
! [A: list_char > option_ty,B: list_char,C: option_ty] :
( ( fun_up424764369ion_ty @ A @ B @ C @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_fun__upd__same) ).
thf(215,plain,
! [A: list_char > option_ty,B: list_char,C: option_ty] :
( ( fun_up424764369ion_ty @ A @ B @ C @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(112,axiom,
! [A: ty,B: val,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: list_char,G: exp_list_char,H: nat > option1728594148on_val,I: list_char > option_val,J: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ ( produc235638504on_val @ G @ ( produc755559506on_val @ H @ I ) ) ) @ ( red @ J ) )
=> ( ( ( I @ F )
= ( some_val @ B ) )
=> ( ~ ( assigned @ F @ C )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ F @ A @ C ) @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ G ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ I @ F @ ( E @ F ) ) ) ) ) @ ( red @ J ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_red__reds_OBlockRedSome) ).
thf(560,plain,
! [A: ty,B: val,C: exp_list_char,D: nat > option1728594148on_val,E: list_char > option_val,F: list_char,G: exp_list_char,H: nat > option1728594148on_val,I: list_char > option_val,J: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C @ ( produc755559506on_val @ D @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ ( produc235638504on_val @ G @ ( produc755559506on_val @ H @ I ) ) ) @ ( red @ J ) )
=> ( ( ( I @ F )
= ( some_val @ B ) )
=> ( ~ ( assigned @ F @ C )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ F @ A @ C ) @ ( produc755559506on_val @ D @ E ) ) @ ( produc235638504on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( val_list_char @ B ) ) @ G ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ I @ F @ ( E @ F ) ) ) ) ) @ ( red @ J ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(82,axiom,
! [A: produc1282892786on_val > $o,B: exp_list_char > produc2090907612on_val > $o] :
( ! [C: exp_list_char,D: produc2090907612on_val] :
( ( B @ C @ D )
= ( A @ ( produc235638504on_val @ C @ D ) ) )
=> ( ( produc1835097372_val_o @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_cond__split__eta) ).
thf(454,plain,
! [A: produc1282892786on_val > $o,B: exp_list_char > produc2090907612on_val > $o] :
( ! [C: exp_list_char,D: produc2090907612on_val] :
( ( B @ C @ D )
= ( A @ ( produc235638504on_val @ C @ D ) ) )
=> ( ( produc1835097372_val_o @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(58,axiom,
! [A: exp_list_char,B: exp_list_char,C: produc2090907612on_val,D: exp_list_char,E: produc2090907612on_val,F: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ C ) @ ( produc235638504on_val @ D @ E ) ) @ ( red @ F ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ B @ A ) @ C ) @ ( produc235638504on_val @ ( seq_list_char @ D @ A ) @ E ) ) @ ( red @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_red__reds_OSeqRed) ).
thf(364,plain,
! [A: exp_list_char,B: exp_list_char,C: produc2090907612on_val,D: exp_list_char,E: produc2090907612on_val,F: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ C ) @ ( produc235638504on_val @ D @ E ) ) @ ( red @ F ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ B @ A ) @ C ) @ ( produc235638504on_val @ ( seq_list_char @ D @ A ) @ E ) ) @ ( red @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19,axiom,
! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: nat > option1728594148on_val,E: list_char > option_ty,F: exp_list_char,G: ty] :
( ( wTrt @ C @ D @ E @ F @ G )
=> ( ( wTrt @ C @ D @ E @ A @ B )
=> ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_WTrtSeq) ).
thf(232,plain,
! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: nat > option1728594148on_val,E: list_char > option_ty,F: exp_list_char,G: ty] :
( ( wTrt @ C @ D @ E @ F @ G )
=> ( ( wTrt @ C @ D @ E @ A @ B )
=> ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(763,plain,
$false,
inference(e,[status(thm)],[518,170,523,683,741,440,511,385,340,670,174,709,288,301,436,570,504,344,460,587,619,189,228,261,591,321,623,238,514,353,348,574,602,660,428,734,221,307,452,248,380,678,529,201,366,534,714,598,297,424,729,693,630,467,566,252,665,551,324,578,615,725,356,420,499,225,686,526,212,193,537,393,457,605,508,311,541,718,633,360,412,750,264,745,180,444,733,584,286,291,204,545,445,382,611,704,350,672,377,303,271,737,318,621,240,330,521,278,563,267,675,531,680,553,663,548,712,640,282,707,177,502,643,470,576,336,571,595,627,450,556,688,581,495,218,748,186,171,418,667,478,235,246,447,432,410,183,373,564,326,242,294,358,474,696,415,464,332,691,369,607,254,543,215,560,454,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW478^1 : TPTP v8.2.0. Released v5.3.0.
% 0.11/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jun 19 08:23:40 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.03/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.18 % [INFO] Parsing done (236ms).
% 1.89/1.19 % [INFO] Running in sequential loop mode.
% 2.48/1.40 % [INFO] eprover registered as external prover.
% 2.48/1.41 % [INFO] Scanning for conjecture ...
% 2.76/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 167 axioms. Running axiom selection ...
% 2.91/1.57 % [INFO] Axiom selection finished. Selected 167 axioms (removed 0 axioms).
% 3.49/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 3.49/1.74 % [INFO] Type checking passed.
% 3.49/1.74 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.68/3.75 % External prover 'e' found a proof!
% 11.68/3.75 % [INFO] Killing All external provers ...
% 11.68/3.75 % Time passed: 3203ms (effective reasoning time: 2556ms)
% 11.68/3.75 % 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)>
% 11.68/3.75 % Axioms used in derivation (167): fact_129_cond__split__eta, fact_100_splitE, fact_111_red__reds_OSeqRed, fact_4_assms, fact_69_splitI, fact_24_fun__upd__def, fact_17_Pair__inject, fact_145_exp_Osimps_I85_J, fact_63_sconf__def, fact_65_prod__caseI, fact_116_mem__splitE, fact_19_Pair__eq, fact_134_exp_Osimps_I143_J, fact_98_splitI2, fact_25_fun__upd__def, fact_5_map__upd__Some__unfold, fact_166_redp__redsp_ORedInitBlock, fact_60_PairE, fact_109_mem__splitI, fact_136_exp_Osimps_I3_J, fact_105_mem__splitI, fact_6_map__upd__Some__unfold, fact_67_splitI, fact_78_internal__split__def, fact_104_mem__splitI, fact_86_prod_Osimps_I2_J, fact_57_split__paired__Ex, fact_7_map__upd__triv, fact_11_InitBlockRed_I2_J, fact_32_fun__upd__apply, fact_139_mem__def, fact_27_fun__upd__idem, fact_23_split__paired__All, fact_54_widen__trans, fact_0_InitBlockRed_I3_J, fact_2_fun__upd__triv, fact_148_exp_Osimps_I83_J, fact_91_split__conv, fact_42_red__preserves__lconf, fact_117_mem__splitE, fact_158_redp__redsp_ORedSeq, fact_33_fun__upd__apply, fact_76_internal__split__def, fact_114_red__reds_ORedBlock, fact_26_fun__upd__idem, fact_130_cond__split__eta, fact_140_mem__def, fact_125_mem__splitI2, fact_137_exp_Osimps_I11_J, fact_102_splitE, fact_39_fun__upd__idem__iff, fact_93_split__eta, fact_66_prod__caseI, fact_46_prod__induct3, fact_28_fun__upd__other, fact_12_prod__induct4, fact_132_splitE2, fact_30_fun__upd__twist, fact_94_split__eta, fact_123_mem__splitI2, fact_53_prod_Oexhaust, fact_152_exp_Osimps_I142_J, fact_151_exp_Osimps_I197_J, fact_126_mem__splitI2, fact_52_prod_Oexhaust, fact_71_splitD, fact_64_prod__caseI, fact_59_PairE, fact_164_redp__redsp_OBlockRedSome, fact_22_split__paired__All, fact_106_mem__splitI, fact_34_fun__upd__same, fact_144_exp_Osimps_I74_J, fact_61_PairE, fact_89_split__conv, fact_142_exp_Osimps_I10_J, fact_9_map__upd__eqD1, fact_103_WTrtBlock, fact_83_split__part, fact_95_red__reds_OInitBlockRed, fact_45_prod__induct3, fact_41_red__preserves__hconf, fact_38_fun__upd__idem__iff, fact_20_Pair__eq, fact_113_red__reds_ORedSeq, fact_118_mem__splitE, fact_13_prod__cases4, fact_121_mem__splitI2, fact_50_pred__equals__eq2, fact_37_fun__upd__upd, fact_138_exp_Osimps_I6_J, fact_56_split__paired__Ex, fact_157_redp__redsp_OBlockRedNone, fact_84_split__part, fact_131_splitE2, fact_29_fun__upd__other, fact_141_mem__def, fact_10_map__upd__eqD1, fact_68_splitI, fact_101_splitE, fact_15_Pair__inject, fact_156_redp__redsp_OLAssRed, fact_143_exp_Osimps_I84_J, fact_35_fun__upd__same, fact_55_InitBlockRed_I5_J, fact_127_red__reds_ORedLAss, fact_110_WTrtSeq, fact_36_fun__upd__upd, fact_154_red__reds_OBlockRedSome, fact_124_mem__splitI2, fact_107_mem__splitI, fact_48_pred__equals__eq2, fact_161_redp__redsp_ORedBlock, fact_88_prod_Osimps_I2_J, fact_155_redp__redsp_OSeqRed, fact_40_widen__refl, fact_92_split__eta, fact_82_split__twice, fact_162_empty__upd__none, fact_51_prod_Oexhaust, fact_43_prod__cases3, fact_16_Pair__inject, fact_165_redp__red__eq, fact_62_internal__split__conv, fact_85_split__part, fact_149_exp_Osimps_I145_J, fact_159_map__upd__nonempty, fact_122_mem__splitI2, fact_163_empty__upd__none, fact_8_map__upd__triv, fact_72_splitD, fact_74_split__weak__cong, fact_18_Pair__eq, fact_99_splitI2, fact_160_map__upd__nonempty, fact_3_fun__upd__triv, fact_1_InitBlockRed_I1_J, fact_58_split__paired__Ex, fact_147_exp_Osimps_I82_J, fact_70_splitD, fact_75_split__weak__cong, fact_120_mem__splitE, fact_49_pred__equals__eq2, fact_119_mem__splitE, fact_21_split__paired__All, fact_44_prod__cases3, fact_150_exp_Osimps_I144_J, fact_81_split__twice, fact_47_red__preserves__sconf, fact_146_exp_Osimps_I75_J, fact_96_red__reds_ORedInitBlock, fact_87_prod_Osimps_I2_J, fact_128_cond__split__eta, fact_97_splitI2, fact_79_split__twice, fact_90_split__conv, fact_133_splitE2, fact_77_internal__split__def, fact_115_mem__splitE, fact_112_red__reds_OLAssRed, fact_73_split__weak__cong, fact_80_split__twice, fact_135_exp_Osimps_I196_J, fact_153_redp__redsp_OInitBlockRed, fact_14_InitBlockRed_I4_J, fact_108_mem__splitI, fact_31_fun__upd__twist
% 11.68/3.75 % No. of inferences in proof: 338
% 11.68/3.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3203 ms resp. 2556 ms w/o parsing
% 12.68/3.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.68/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------