TSTP Solution File: SCT170_3 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SCT170_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:16:57 EDT 2023
% Result : Theorem 1408.31s 130.80s
% Output : CNFRefutation 1408.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 74
% Syntax : Number of formulae : 140 ( 35 unt; 54 typ; 0 def)
% Number of atoms : 310 ( 143 equ)
% Maximal formula atoms : 118 ( 3 avg)
% Number of connectives : 347 ( 123 ~; 168 |; 35 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 54 ( 30 >; 24 *; 0 +; 0 <<)
% Number of predicates : 36 ( 34 usr; 34 prp; 0-2 aty)
% Number of functors : 53 ( 53 usr; 24 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn; 151 !; 0 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_23,type,
arrow_1361987423le_Lin: fun_fu638310559l_bool ).
tff(decl_24,type,
arrow_5070731e_Prof: fun_fu3835832l_bool ).
tff(decl_26,type,
arrow_1525312447_below: fun_fu1287834969t_bool ).
tff(decl_127,type,
cOMBK_1520063231e_indi: fun_fu1868761018l_bool ).
tff(decl_151,type,
pi_Arr959578316t_bool: ( fun_Ar1809396326i_bool * fun_Ar1474557608l_bool ) > fun_fu3835832l_bool ).
tff(decl_192,type,
append1597383892le_alt: fun_li264309018le_alt ).
tff(decl_202,type,
butlas1693249291le_alt: fun_li90789869le_alt ).
tff(decl_211,type,
distin1654625714le_alt: fun_li1109619974t_bool ).
tff(decl_238,type,
hd_Arr1236501138le_alt: list_A114658244le_alt > arrow_1893660431le_alt ).
tff(decl_256,type,
last_A488133080le_alt: list_A114658244le_alt > arrow_1893660431le_alt ).
tff(decl_278,type,
cons_A1647044463le_alt: fun_Ar1448189019le_alt ).
tff(decl_288,type,
nil_Ar557011903le_alt: list_A114658244le_alt ).
tff(decl_319,type,
rotate1753650700le_alt: fun_li90789869le_alt ).
tff(decl_320,type,
set_Ar1995755744le_alt: list_A114658244le_alt > fun_Ar17477381t_bool ).
tff(decl_371,type,
ord_le1609180592i_bool: fun_fu924966107l_bool ).
tff(decl_374,type,
ord_le1099920642l_bool: fun_fu1785284735l_bool ).
tff(decl_382,type,
top_to788185952i_bool: fun_Ar1809396326i_bool ).
tff(decl_390,type,
produc1590937303le_alt: fun_Ar2121501495le_alt ).
tff(decl_461,type,
hAPP_A1058422557t_bool: ( fun_Ar797671557t_bool * arrow_1893660431le_alt ) > fun_Ar1573071255t_bool ).
tff(decl_463,type,
hAPP_A1146194953le_alt: ( fun_Ar2121501495le_alt * arrow_1893660431le_alt ) > fun_Ar245737999le_alt ).
tff(decl_468,type,
hAPP_A436723315le_alt: ( fun_Ar1448189019le_alt * arrow_1893660431le_alt ) > fun_li90789869le_alt ).
tff(decl_471,type,
hAPP_A1501726285l_bool: ( fun_Ar569529141l_bool * arrow_1893660431le_alt ) > fun_fu1618786247l_bool ).
tff(decl_477,type,
hAPP_A1601437999t_bool: ( fun_Ar1573071255t_bool * arrow_1893660431le_alt ) > fun_Pr2067565481t_bool ).
tff(decl_479,type,
hAPP_A1299015393le_alt: ( fun_Ar245737999le_alt * arrow_1893660431le_alt ) > produc472769767le_alt ).
tff(decl_487,type,
hAPP_A1597696899l_bool: ( fun_Ar1047186533l_bool * arrow_856714788e_indi ) > fun_fu844176604l_bool ).
tff(decl_492,type,
hAPP_A1646126530t_bool: ( fun_Ar274636406t_bool * arrow_856714788e_indi ) > fun_Pr2067565481t_bool ).
tff(decl_511,type,
hAPP_l499746980t_bool: ( fun_li1109619974t_bool * list_A114658244le_alt ) > bool ).
tff(decl_512,type,
hAPP_l84111627le_alt: ( fun_li90789869le_alt * list_A114658244le_alt ) > list_A114658244le_alt ).
tff(decl_516,type,
hAPP_l86320102le_alt: ( fun_li264309018le_alt * list_A114658244le_alt ) > fun_li90789869le_alt ).
tff(decl_609,type,
hAPP_f739344229l_bool: ( fun_fu1618786247l_bool * fun_Ar17477381t_bool ) > bool ).
tff(decl_637,type,
hAPP_f584385070l_bool: ( fun_fu844176604l_bool * fun_Ar1809396326i_bool ) > bool ).
tff(decl_639,type,
hAPP_f731870893l_bool: ( fun_fu924966107l_bool * fun_Ar1809396326i_bool ) > fun_fu844176604l_bool ).
tff(decl_662,type,
hAPP_f1225332775l_bool: ( fun_fu361117961l_bool * fun_Ar274636406t_bool ) > fun_fu1370139438l_bool ).
tff(decl_751,type,
hAPP_f73423488l_bool: ( fun_fu1370139438l_bool * fun_fu3835832l_bool ) > bool ).
tff(decl_757,type,
hAPP_f585353809l_bool: ( fun_fu1785284735l_bool * fun_fu3835832l_bool ) > fun_fu1370139438l_bool ).
tff(decl_828,type,
hAPP_f182583295l_bool: ( fun_fu2013733473l_bool * fun_fu638310559l_bool ) > bool ).
tff(decl_830,type,
hAPP_f1717907078l_bool: ( fun_fu1868761018l_bool * fun_fu638310559l_bool ) > fun_Ar1474557608l_bool ).
tff(decl_853,type,
hAPP_f52567537l_bool: ( fun_fu638310559l_bool * fun_Pr2067565481t_bool ) > bool ).
tff(decl_857,type,
hAPP_f1550387441t_bool: ( fun_fu1287834969t_bool * fun_Pr2067565481t_bool ) > fun_Ar797671557t_bool ).
tff(decl_867,type,
hAPP_f1482930381l_bool: ( fun_fu864675765l_bool * fun_Pr2067565481t_bool ) > fun_fu2013733473l_bool ).
tff(decl_933,type,
hAPP_P38525833l_bool: ( fun_Pr1085078251l_bool * produc472769767le_alt ) > fun_fu638310559l_bool ).
tff(decl_971,type,
hBOOL: bool > $o ).
tff(decl_972,type,
member1502664802le_alt: fun_Ar569529141l_bool ).
tff(decl_973,type,
member1479139729e_indi: fun_Ar1047186533l_bool ).
tff(decl_983,type,
member933336803t_bool: fun_fu361117961l_bool ).
tff(decl_1011,type,
member1069471740t_bool: fun_fu864675765l_bool ).
tff(decl_1018,type,
member1333168212le_alt: fun_Pr1085078251l_bool ).
tff(decl_1039,type,
p: fun_Ar274636406t_bool ).
tff(decl_1040,type,
a: arrow_1893660431le_alt ).
tff(decl_1041,type,
b: arrow_1893660431le_alt ).
tff(decl_1042,type,
c: arrow_1893660431le_alt ).
tff(decl_1043,type,
esk1_0: arrow_856714788e_indi ).
tff(decl_1148,type,
esk106_1: list_A114658244le_alt > arrow_1893660431le_alt ).
tff(decl_1149,type,
esk107_1: list_A114658244le_alt > list_A114658244le_alt ).
tff(fact_916_subsetD,axiom,
! [X2445: fun_Ar274636406t_bool,X2446: fun_fu3835832l_bool,X2447: fun_fu3835832l_bool] :
( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X2446),X2447))
=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X2445),X2446))
=> hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X2445),X2447)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_916_subsetD) ).
tff(fact_921_Pi__anti__mono,axiom,
! [X2454: fun_Ar1474557608l_bool,X2455: fun_Ar1809396326i_bool,X2456: fun_Ar1809396326i_bool] :
( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X2455),X2456))
=> hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,pi_Arr959578316t_bool(X2456,X2454)),pi_Arr959578316t_bool(X2455,X2454))) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_921_Pi__anti__mono) ).
tff(fact_989_top__greatest,axiom,
! [X2608: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X2608),top_to788185952i_bool)),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_989_top__greatest) ).
tff(fact_0__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p),arrow_5070731e_Prof)),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_0__096P_A_058_AProf_096) ).
tff(fact_340_Prof__def,axiom,
arrow_5070731e_Prof = pi_Arr959578316t_bool(top_to788185952i_bool,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,arrow_1361987423le_Lin)),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_340_Prof__def) ).
tff(fact_12_in__below,axiom,
! [X3: arrow_1893660431le_alt,X4: arrow_1893660431le_alt,X5: fun_Pr2067565481t_bool,X7: arrow_1893660431le_alt,X8: arrow_1893660431le_alt] :
( ( X7 != X8 )
=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X5),arrow_1361987423le_Lin))
=> ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3),X4)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X5),X7),X8)))
<=> ( ( X3 != X4 )
& ( ( X4 = X7 )
=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3),X8)),X5)) )
& ( ( X4 != X7 )
=> ( ( ( X3 = X7 )
=> ( ( X4 = X8 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X8),X4)),X5)) ) )
& ( ( X3 != X7 )
=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3),X4)),X5)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_12_in__below) ).
tff(conj_0,conjecture,
! [X1: arrow_856714788e_indi] :
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,X1)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,X1)),c),b))) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',conj_0) ).
tff(fact_130_funcset__mem,axiom,
! [X381: arrow_856714788e_indi,X382: fun_Ar274636406t_bool,X383: fun_Ar1809396326i_bool,X384: fun_fu638310559l_bool] :
( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X382),pi_Arr959578316t_bool(X383,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,X384))))
=> ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X381),X383))
=> hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(X382,X381)),X384)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_130_funcset__mem) ).
tff(fact_433_snoc__eq__iff__butlast,axiom,
! [X228: list_A114658244le_alt,X3: arrow_1893660431le_alt,X1146: list_A114658244le_alt] :
( ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X228),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3),nil_Ar557011903le_alt)) = X1146 )
<=> ( ( X1146 != nil_Ar557011903le_alt )
& ( hAPP_l84111627le_alt(butlas1693249291le_alt,X1146) = X228 )
& ( last_A488133080le_alt(X1146) = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_433_snoc__eq__iff__butlast) ).
tff(fact_367_iso__tuple__UNIV__I,axiom,
! [X1119: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X1119),top_to788185952i_bool)),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_367_iso__tuple__UNIV__I) ).
tff(fact_708_distinct_Osimps_I2_J,axiom,
! [X3: arrow_1893660431le_alt,X228: list_A114658244le_alt] :
( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3),X228)))
<=> ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3),set_Ar1995755744le_alt(X228)))
& hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,X228)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_708_distinct_Osimps_I2_J) ).
tff(fact_442_rotate__simps,axiom,
! [X1215: arrow_1893660431le_alt,X1216: list_A114658244le_alt] :
( ( hAPP_l84111627le_alt(rotate1753650700le_alt,nil_Ar557011903le_alt) = nil_Ar557011903le_alt )
& ( hAPP_l84111627le_alt(rotate1753650700le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X1215),X1216)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X1216),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X1215),nil_Ar557011903le_alt)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_442_rotate__simps) ).
tff(fact_88_list_Oexhaust,axiom,
! [X225: list_A114658244le_alt] :
( ( X225 != nil_Ar557011903le_alt )
=> ~ ! [X226: arrow_1893660431le_alt,X227: list_A114658244le_alt] : ( X225 != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X226),X227) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_88_list_Oexhaust) ).
tff(fact_42_list_Oinject,axiom,
! [X7: arrow_1893660431le_alt,X60: list_A114658244le_alt,X61: arrow_1893660431le_alt,X62: list_A114658244le_alt] :
( ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X7),X60) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X61),X62) )
<=> ( ( X7 = X61 )
& ( X60 = X62 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_42_list_Oinject) ).
tff(fact_37_list_Osimps_I2_J,axiom,
! [X52: arrow_1893660431le_alt,X53: list_A114658244le_alt] : ( nil_Ar557011903le_alt != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X52),X53) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_37_list_Osimps_I2_J) ).
tff(fact_689_in__set__butlastD,axiom,
! [X3: arrow_1893660431le_alt,X228: list_A114658244le_alt] :
( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,X228))))
=> hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3),set_Ar1995755744le_alt(X228))) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_689_in__set__butlastD) ).
tff(fact_697_set__rotate1,axiom,
! [X228: list_A114658244le_alt] : ( set_Ar1995755744le_alt(hAPP_l84111627le_alt(rotate1753650700le_alt,X228)) = set_Ar1995755744le_alt(X228) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_697_set__rotate1) ).
tff(fact_4_dist,axiom,
hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,a),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,b),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt))))),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_4_dist) ).
tff(fact_744_hd__in__set,axiom,
! [X228: list_A114658244le_alt] :
( ( X228 != nil_Ar557011903le_alt )
=> hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hd_Arr1236501138le_alt(X228)),set_Ar1995755744le_alt(X228))) ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_744_hd__in__set) ).
tff(fact_583_hd_Osimps,axiom,
! [X1522: arrow_1893660431le_alt,X1523: list_A114658244le_alt] : ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X1522),X1523)) = X1522 ),
file('/export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p',fact_583_hd_Osimps) ).
tff(c_0_20,plain,
! [X4271: fun_Ar274636406t_bool,X4272: fun_fu3835832l_bool,X4273: fun_fu3835832l_bool] :
( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X4272),X4273))
| ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X4271),X4272))
| hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X4271),X4273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_916_subsetD])]) ).
tff(c_0_21,plain,
! [X3609: fun_Ar1474557608l_bool,X3610: fun_Ar1809396326i_bool,X3611: fun_Ar1809396326i_bool] :
( ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X3610),X3611))
| hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,pi_Arr959578316t_bool(X3611,X3609)),pi_Arr959578316t_bool(X3610,X3609))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_921_Pi__anti__mono])]) ).
tff(c_0_22,plain,
! [X4172: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X4172),top_to788185952i_bool)),
inference(variable_rename,[status(thm)],[fact_989_top__greatest]) ).
tcf(c_0_23,plain,
! [X35: fun_Ar274636406t_bool,X163: fun_fu3835832l_bool,X159: fun_fu3835832l_bool] :
( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X35),X163))
| ~ hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X159),X163))
| ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X35),X159)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_24,plain,
hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p),arrow_5070731e_Prof)),
inference(split_conjunct,[status(thm)],[fact_0__096P_A_058_AProf_096]) ).
tcf(c_0_25,plain,
! [X86: fun_Ar1809396326i_bool,X224: fun_Ar1474557608l_bool,X105: fun_Ar1809396326i_bool] :
( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,pi_Arr959578316t_bool(X105,X224)),pi_Arr959578316t_bool(X86,X224)))
| ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X86),X105)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tcf(c_0_26,plain,
arrow_5070731e_Prof = pi_Arr959578316t_bool(top_to788185952i_bool,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,arrow_1361987423le_Lin)),
inference(split_conjunct,[status(thm)],[fact_340_Prof__def]) ).
tcf(c_0_27,plain,
! [X86: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X86),top_to788185952i_bool)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tff(c_0_28,plain,
! [X3035: arrow_1893660431le_alt,X3036: arrow_1893660431le_alt,X3037: fun_Pr2067565481t_bool,X3038: arrow_1893660431le_alt,X3039: arrow_1893660431le_alt] :
( ( ( X3035 != X3036 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3036 != X3038 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ( X3036 = X3039 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3039),X3036)),X3037))
| ( X3036 = X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 = X3038 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ( X3036 = X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3036 != X3038 )
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ( X3035 = X3038 )
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ( X3035 = X3038 )
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ( X3036 != X3039 )
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ( X3036 != X3039 )
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3039),X3036)),X3037))
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3039),X3036)),X3037))
| ( X3036 = X3038 )
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3036 != X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ( X3035 = X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ( X3035 = X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ( X3036 != X3039 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ( X3036 != X3039 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ( X3035 != X3038 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3039),X3036)),X3037))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) )
& ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),X3037))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3039),X3036)),X3037))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3039)),X3037))
| ( X3035 = X3036 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X3035),X3036)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X3037),X3038),X3039)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X3037),arrow_1361987423le_Lin))
| ( X3038 = X3039 ) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_12_in__below])])]) ).
tff(c_0_29,negated_conjecture,
~ ! [X1: arrow_856714788e_indi] :
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,X1)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,X1)),c),b))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_30,plain,
! [X3071: arrow_856714788e_indi,X3072: fun_Ar274636406t_bool,X3073: fun_Ar1809396326i_bool,X3074: fun_fu638310559l_bool] :
( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X3072),pi_Arr959578316t_bool(X3073,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,X3074))))
| ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X3071),X3073))
| hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(X3072,X3071)),X3074)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_130_funcset__mem])]) ).
tcf(c_0_31,plain,
! [X159: fun_fu3835832l_bool] :
( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p),X159))
| ~ hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,arrow_5070731e_Prof),X159)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
tcf(c_0_32,plain,
! [X86: fun_Ar1809396326i_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,arrow_5070731e_Prof),pi_Arr959578316t_bool(X86,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,arrow_1361987423le_Lin)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
tff(c_0_33,plain,
! [X3970: list_A114658244le_alt,X3971: arrow_1893660431le_alt,X3972: list_A114658244le_alt] :
( ( ( X3972 != nil_Ar557011903le_alt )
| ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X3970),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3971),nil_Ar557011903le_alt)) != X3972 ) )
& ( ( hAPP_l84111627le_alt(butlas1693249291le_alt,X3972) = X3970 )
| ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X3970),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3971),nil_Ar557011903le_alt)) != X3972 ) )
& ( ( last_A488133080le_alt(X3972) = X3971 )
| ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X3970),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3971),nil_Ar557011903le_alt)) != X3972 ) )
& ( ( X3972 = nil_Ar557011903le_alt )
| ( hAPP_l84111627le_alt(butlas1693249291le_alt,X3972) != X3970 )
| ( last_A488133080le_alt(X3972) != X3971 )
| ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X3970),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3971),nil_Ar557011903le_alt)) = X3972 ) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_snoc__eq__iff__butlast])])]) ).
tcf(c_0_34,plain,
! [X2: arrow_1893660431le_alt,X4: arrow_1893660431le_alt,X3: arrow_1893660431le_alt,X6: arrow_1893660431le_alt,X5: fun_Pr2067565481t_bool] :
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X6)),X5))
| ( X3 = X6 )
| ( X2 != X3 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X5),X3),X6)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X5),arrow_1361987423le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tff(c_0_35,negated_conjecture,
( ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,esk1_0)))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,esk1_0)),c),b))) )
& ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,esk1_0)))
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,esk1_0)),c),b))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
tcf(c_0_36,plain,
! [X35: fun_Ar274636406t_bool,X1: arrow_856714788e_indi,X179: fun_fu638310559l_bool,X86: fun_Ar1809396326i_bool] :
( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(X35,X1)),X179))
| ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X35),pi_Arr959578316t_bool(X86,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,X179))))
| ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X1),X86)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
tcf(c_0_37,plain,
! [X86: fun_Ar1809396326i_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p),pi_Arr959578316t_bool(X86,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,arrow_1361987423le_Lin)))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
tff(c_0_38,plain,
! [X4166: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X4166),top_to788185952i_bool)),
inference(variable_rename,[status(thm)],[fact_367_iso__tuple__UNIV__I]) ).
tff(c_0_39,plain,
! [X3: arrow_1893660431le_alt,X228: list_A114658244le_alt] :
( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3),X228)))
<=> ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3),set_Ar1995755744le_alt(X228)))
& hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,X228)) ) ),
inference(fof_simplification,[status(thm)],[fact_708_distinct_Osimps_I2_J]) ).
tcf(c_0_40,plain,
! [X2: arrow_1893660431le_alt,X12: list_A114658244le_alt,X11: list_A114658244le_alt] :
( ( hAPP_l84111627le_alt(butlas1693249291le_alt,X11) = X12 )
| ( hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X12),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),nil_Ar557011903le_alt)) != X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
tff(c_0_41,plain,
! [X4121: arrow_1893660431le_alt,X4122: list_A114658244le_alt] :
( ( hAPP_l84111627le_alt(rotate1753650700le_alt,nil_Ar557011903le_alt) = nil_Ar557011903le_alt )
& ( hAPP_l84111627le_alt(rotate1753650700le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X4121),X4122)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X4122),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X4121),nil_Ar557011903le_alt)) ) ),
inference(variable_rename,[status(thm)],[fact_442_rotate__simps]) ).
tcf(c_0_42,plain,
! [X2: arrow_1893660431le_alt,X4: arrow_1893660431le_alt,X3: arrow_1893660431le_alt,X5: fun_Pr2067565481t_bool] :
( ( X2 = X3 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X3)),X5))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X5),X2),X3)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X5),arrow_1361987423le_Lin)) ),
inference(er,[status(thm)],[c_0_34]) ).
tcf(c_0_43,negated_conjecture,
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,esk1_0)))
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,esk1_0)),c),b))) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
tcf(c_0_44,plain,
! [X1: arrow_856714788e_indi,X86: fun_Ar1809396326i_bool] :
( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(p,X1)),arrow_1361987423le_Lin))
| ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X1),X86)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
tcf(c_0_45,plain,
! [X1: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X1),top_to788185952i_bool)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
tff(c_0_46,plain,
! [X3385: arrow_1893660431le_alt,X3386: list_A114658244le_alt] :
( ( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3385),set_Ar1995755744le_alt(X3386)))
| ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3385),X3386))) )
& ( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,X3386))
| ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3385),X3386))) )
& ( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3385),set_Ar1995755744le_alt(X3386)))
| ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,X3386))
| hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3385),X3386))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
tff(c_0_47,plain,
! [X3411: list_A114658244le_alt] :
( ( X3411 = nil_Ar557011903le_alt )
| ( X3411 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,esk106_1(X3411)),esk107_1(X3411)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_list_Oexhaust])])]) ).
tff(c_0_48,plain,
! [X3403: arrow_1893660431le_alt,X3404: list_A114658244le_alt,X3405: arrow_1893660431le_alt,X3406: list_A114658244le_alt] :
( ( ( X3403 = X3405 )
| ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3403),X3404) != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3405),X3406) ) )
& ( ( X3404 = X3406 )
| ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3403),X3404) != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3405),X3406) ) )
& ( ( X3403 != X3405 )
| ( X3404 != X3406 )
| ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3403),X3404) = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3405),X3406) ) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_list_Oinject])])]) ).
tff(c_0_49,plain,
! [X3399: arrow_1893660431le_alt,X3400: list_A114658244le_alt] : ( nil_Ar557011903le_alt != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3399),X3400) ),
inference(variable_rename,[status(thm)],[fact_37_list_Osimps_I2_J]) ).
tff(c_0_50,plain,
! [X3924: arrow_1893660431le_alt,X3925: list_A114658244le_alt] :
( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3924),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,X3925))))
| hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X3924),set_Ar1995755744le_alt(X3925))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_689_in__set__butlastD])]) ).
tcf(c_0_51,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] : hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X11),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),nil_Ar557011903le_alt))) = X11,
inference(er,[status(thm)],[c_0_40]) ).
tcf(c_0_52,plain,
! [X11: list_A114658244le_alt,X2: arrow_1893660431le_alt] : hAPP_l84111627le_alt(rotate1753650700le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11)) = hAPP_l84111627le_alt(hAPP_l86320102le_alt(append1597383892le_alt,X11),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),nil_Ar557011903le_alt)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
tff(c_0_53,plain,
! [X4125: list_A114658244le_alt] : ( set_Ar1995755744le_alt(hAPP_l84111627le_alt(rotate1753650700le_alt,X4125)) = set_Ar1995755744le_alt(X4125) ),
inference(variable_rename,[status(thm)],[fact_697_set__rotate1]) ).
tcf(c_0_54,negated_conjecture,
( ( c = b )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,esk1_0)))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(p,esk1_0)),arrow_1361987423le_Lin)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
tcf(c_0_55,plain,
! [X1: arrow_856714788e_indi] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(p,X1)),arrow_1361987423le_Lin)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
tcf(c_0_56,plain,
! [X2: arrow_1893660431le_alt,X3: arrow_1893660431le_alt,X4: arrow_1893660431le_alt,X6: arrow_1893660431le_alt,X5: fun_Pr2067565481t_bool] :
( ( X4 = X2 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X5),X3),X6)))
| ( X3 = X6 )
| ( X2 != X3 )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X6)),X5))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X5),arrow_1361987423le_Lin)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
tcf(c_0_57,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] :
( hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,X11))
| ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
tcf(c_0_58,plain,
! [X11: list_A114658244le_alt] :
( ( X11 = nil_Ar557011903le_alt )
| ( X11 = hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,esk106_1(X11)),esk107_1(X11)) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
tcf(c_0_59,plain,
! [X2: arrow_1893660431le_alt,X3: arrow_1893660431le_alt,X11: list_A114658244le_alt,X12: list_A114658244le_alt] :
( ( X11 = X12 )
| ( hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11) != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3),X12) ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
tcf(c_0_60,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] : nil_Ar557011903le_alt != hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
tcf(c_0_61,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] :
( ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X2),set_Ar1995755744le_alt(X11)))
| ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
tcf(c_0_62,plain,
hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,a),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,b),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt))))),
inference(split_conjunct,[status(thm)],[fact_4_dist]) ).
tcf(c_0_63,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] :
( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X2),set_Ar1995755744le_alt(X11)))
| ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(butlas1693249291le_alt,X11)))) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
tcf(c_0_64,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] : hAPP_l84111627le_alt(butlas1693249291le_alt,hAPP_l84111627le_alt(rotate1753650700le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11))) = X11,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
tcf(c_0_65,plain,
! [X11: list_A114658244le_alt] : set_Ar1995755744le_alt(hAPP_l84111627le_alt(rotate1753650700le_alt,X11)) = set_Ar1995755744le_alt(X11),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
tcf(c_0_66,negated_conjecture,
( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,esk1_0)))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,esk1_0)),c),b))) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
tcf(c_0_67,negated_conjecture,
( ( c = b )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_A1646126530t_bool(p,esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
tcf(c_0_68,plain,
! [X2: arrow_1893660431le_alt,X3: arrow_1893660431le_alt,X4: arrow_1893660431le_alt,X5: fun_Pr2067565481t_bool] :
( ( X2 = X3 )
| ( X2 = X4 )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,X5),X2),X3)))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X4),X3)),X5))
| ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X5),arrow_1361987423le_Lin)) ),
inference(er,[status(thm)],[c_0_56]) ).
tff(c_0_69,plain,
! [X3930: list_A114658244le_alt] :
( ( X3930 = nil_Ar557011903le_alt )
| hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hd_Arr1236501138le_alt(X3930)),set_Ar1995755744le_alt(X3930))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_744_hd__in__set])]) ).
tff(c_0_70,plain,
! [X4497: arrow_1893660431le_alt,X4498: list_A114658244le_alt] : ( hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X4497),X4498)) = X4497 ),
inference(variable_rename,[status(thm)],[fact_583_hd_Osimps]) ).
tcf(c_0_71,plain,
! [X11: list_A114658244le_alt] :
( ( X11 = nil_Ar557011903le_alt )
| hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,esk107_1(X11)))
| ~ hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,X11)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
tcf(c_0_72,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] : esk107_1(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11)) = X11,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_58])]),c_0_60]) ).
tcf(c_0_73,plain,
~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,a),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,b),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt))))),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
tcf(c_0_74,plain,
! [X2: arrow_1893660431le_alt,X3: arrow_1893660431le_alt,X11: list_A114658244le_alt] :
( hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X3),X11))))
| ~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X2),set_Ar1995755744le_alt(X11))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
tcf(c_0_75,negated_conjecture,
( ( c = b )
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),c)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,esk1_0)),c),b))) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
tcf(c_0_76,negated_conjecture,
! [X2: arrow_1893660431le_alt] :
( ( c = b )
| ( X2 = b )
| ( X2 = a )
| hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),X2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_1525312447_below,hAPP_A1646126530t_bool(p,esk1_0)),X2),b))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_67]),c_0_55])]) ).
tcf(c_0_77,plain,
! [X11: list_A114658244le_alt] :
( ( X11 = nil_Ar557011903le_alt )
| hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,hd_Arr1236501138le_alt(X11)),set_Ar1995755744le_alt(X11))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
tcf(c_0_78,plain,
! [X11: list_A114658244le_alt,X2: arrow_1893660431le_alt] : hd_Arr1236501138le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11)) = X2,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
tcf(c_0_79,plain,
hBOOL(hAPP_l499746980t_bool(distin1654625714le_alt,hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,b),hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt)))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_62]),c_0_72]),c_0_60]) ).
tcf(c_0_80,plain,
~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,a),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt)))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
tcf(c_0_81,negated_conjecture,
( ( c = a )
| ( c = b ) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
tcf(c_0_82,plain,
! [X2: arrow_1893660431le_alt,X11: list_A114658244le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,X2),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,X2),X11)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_60]) ).
tcf(c_0_83,plain,
~ hBOOL(hAPP_f739344229l_bool(hAPP_A1501726285l_bool(member1502664802le_alt,b),set_Ar1995755744le_alt(hAPP_l84111627le_alt(hAPP_A436723315le_alt(cons_A1647044463le_alt,c),nil_Ar557011903le_alt)))),
inference(spm,[status(thm)],[c_0_61,c_0_79]) ).
tcf(c_0_84,negated_conjecture,
c = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.61/0.64 % Problem : SCT170_3 : TPTP v8.1.2. Released v5.3.0.
% 0.61/0.65 % Command : run_E %s %d THM
% 0.64/0.86 % Computer : n011.cluster.edu
% 0.64/0.86 % Model : x86_64 x86_64
% 0.64/0.86 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.64/0.86 % Memory : 8042.1875MB
% 0.64/0.86 % OS : Linux 3.10.0-693.el7.x86_64
% 0.64/0.86 % CPULimit : 2400
% 0.64/0.86 % WCLimit : 300
% 0.64/0.86 % DateTime : Mon Oct 2 11:29:38 EDT 2023
% 0.64/0.86 % CPUTime :
% 1.35/1.52 Running first-order theorem proving
% 1.35/1.52 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.paHfMYK4DW/E---3.1_21046.p
% 1408.31/130.80 # Version: 3.1pre001
% 1408.31/130.80 # Preprocessing class: FMLLSMLLSSSNFFN.
% 1408.31/130.80 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1408.31/130.80 # Starting new_bool_3 with 900s (3) cores
% 1408.31/130.80 # Starting new_bool_1 with 900s (3) cores
% 1408.31/130.80 # Starting sh5l with 300s (1) cores
% 1408.31/130.80 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 1408.31/130.80 # sh5l with pid 21126 completed with status 0
% 1408.31/130.80 # Result found by sh5l
% 1408.31/130.80 # Preprocessing class: FMLLSMLLSSSNFFN.
% 1408.31/130.80 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1408.31/130.80 # Starting new_bool_3 with 900s (3) cores
% 1408.31/130.80 # Starting new_bool_1 with 900s (3) cores
% 1408.31/130.80 # Starting sh5l with 300s (1) cores
% 1408.31/130.80 # SinE strategy is gf500_gu_R04_F100_L20000
% 1408.31/130.80 # Search class: FGHSM-FSLM32-DFFFFFNN
% 1408.31/130.80 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 1408.31/130.80 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 1408.31/130.80 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 21135 completed with status 7
% 1408.31/130.80 # Starting sh5l with 31s (1) cores
% 1408.31/130.80 # sh5l with pid 21139 completed with status 7
% 1408.31/130.80 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 23s (1) cores
% 1408.31/130.80 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 21141 completed with status 7
% 1408.31/130.80 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 23s (1) cores
% 1408.31/130.80 # U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 21150 completed with status 7
% 1408.31/130.80 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 23s (1) cores
% 1408.31/130.80 # G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with pid 21201 completed with status 7
% 1408.31/130.80 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 23s (1) cores
% 1408.31/130.80 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with pid 21205 completed with status 0
% 1408.31/130.80 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 1408.31/130.80 # Preprocessing class: FMLLSMLLSSSNFFN.
% 1408.31/130.80 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1408.31/130.80 # Starting new_bool_3 with 900s (3) cores
% 1408.31/130.80 # Starting new_bool_1 with 900s (3) cores
% 1408.31/130.80 # Starting sh5l with 300s (1) cores
% 1408.31/130.80 # SinE strategy is gf500_gu_R04_F100_L20000
% 1408.31/130.80 # Search class: FGHSM-FSLM32-DFFFFFNN
% 1408.31/130.80 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 1408.31/130.80 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 1408.31/130.80 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 21135 completed with status 7
% 1408.31/130.80 # Starting sh5l with 31s (1) cores
% 1408.31/130.80 # sh5l with pid 21139 completed with status 7
% 1408.31/130.80 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 23s (1) cores
% 1408.31/130.80 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 21141 completed with status 7
% 1408.31/130.80 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 23s (1) cores
% 1408.31/130.80 # U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 21150 completed with status 7
% 1408.31/130.80 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 23s (1) cores
% 1408.31/130.80 # G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with pid 21201 completed with status 7
% 1408.31/130.80 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 23s (1) cores
% 1408.31/130.80 # Preprocessing time : 0.021 s
% 1408.31/130.80 # Presaturation interreduction done
% 1408.31/130.80
% 1408.31/130.80 # Proof found!
% 1408.31/130.80 # SZS status Theorem
% 1408.31/130.80 # SZS output start CNFRefutation
% See solution above
% 1408.31/130.80 # Parsed axioms : 2969
% 1408.31/130.80 # Removed by relevancy pruning/SinE : 2378
% 1408.31/130.80 # Initial clauses : 1002
% 1408.31/130.80 # Removed in clause preprocessing : 18
% 1408.31/130.80 # Initial clauses in saturation : 984
% 1408.31/130.80 # Processed clauses : 23807
% 1408.31/130.80 # ...of these trivial : 121
% 1408.31/130.80 # ...subsumed : 18844
% 1408.31/130.80 # ...remaining for further processing : 4842
% 1408.31/130.80 # Other redundant clauses eliminated : 3046
% 1408.31/130.80 # Clauses deleted for lack of memory : 0
% 1408.31/130.80 # Backward-subsumed : 43
% 1408.31/130.80 # Backward-rewritten : 829
% 1408.31/130.80 # Generated clauses : 142790
% 1408.31/130.80 # ...of the previous two non-redundant : 129519
% 1408.31/130.80 # ...aggressively subsumed : 0
% 1408.31/130.80 # Contextual simplify-reflections : 42
% 1408.31/130.80 # Paramodulations : 139715
% 1408.31/130.80 # Factorizations : 29
% 1408.31/130.80 # NegExts : 0
% 1408.31/130.80 # Equation resolutions : 3068
% 1408.31/130.80 # Total rewrite steps : 33359
% 1408.31/130.80 # Propositional unsat checks : 0
% 1408.31/130.80 # Propositional check models : 0
% 1408.31/130.80 # Propositional check unsatisfiable : 0
% 1408.31/130.80 # Propositional clauses : 0
% 1408.31/130.80 # Propositional clauses after purity: 0
% 1408.31/130.80 # Propositional unsat core size : 0
% 1408.31/130.80 # Propositional preprocessing time : 0.000
% 1408.31/130.80 # Propositional encoding time : 0.000
% 1408.31/130.80 # Propositional solver time : 0.000
% 1408.31/130.80 # Success case prop preproc time : 0.000
% 1408.31/130.80 # Success case prop encoding time : 0.000
% 1408.31/130.80 # Success case prop solver time : 0.000
% 1408.31/130.80 # Current number of processed clauses : 3008
% 1408.31/130.80 # Positive orientable unit clauses : 337
% 1408.31/130.80 # Positive unorientable unit clauses: 4
% 1408.31/130.80 # Negative unit clauses : 158
% 1408.31/130.80 # Non-unit-clauses : 2509
% 1408.31/130.80 # Current number of unprocessed clauses: 107308
% 1408.31/130.80 # ...number of literals in the above : 323078
% 1408.31/130.80 # Current number of archived formulas : 0
% 1408.31/130.80 # Current number of archived clauses : 1690
% 1408.31/130.80 # Clause-clause subsumption calls (NU) : 2028438
% 1408.31/130.80 # Rec. Clause-clause subsumption calls : 1299605
% 1408.31/130.80 # Non-unit clause-clause subsumptions : 14537
% 1408.31/130.80 # Unit Clause-clause subsumption calls : 46596
% 1408.31/130.80 # Rewrite failures with RHS unbound : 230
% 1408.31/130.80 # BW rewrite match attempts : 2076
% 1408.31/130.80 # BW rewrite match successes : 46
% 1408.31/130.80 # Condensation attempts : 0
% 1408.31/130.80 # Condensation successes : 0
% 1408.31/130.80 # Termbank termtop insertions : 2584451
% 1408.31/130.80
% 1408.31/130.80 # -------------------------------------------------
% 1408.31/130.80 # User time : 125.226 s
% 1408.31/130.80 # System time : 2.296 s
% 1408.31/130.80 # Total time : 127.522 s
% 1408.31/130.80 # Maximum resident set size: 11204 pages
% 1408.31/130.80
% 1408.31/130.80 # -------------------------------------------------
% 1408.31/130.80 # User time : 125.325 s
% 1408.31/130.80 # System time : 2.304 s
% 1408.31/130.80 # Total time : 127.629 s
% 1408.31/130.80 # Maximum resident set size: 6588 pages
% 1408.31/130.80 % E---3.1 exiting
% 1408.31/130.81 % E---3.1 exiting
%------------------------------------------------------------------------------