TSTP Solution File: SCT170^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SCT170^2 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 : Tue May 21 02:45:08 EDT 2024
% Result : Theorem 27.97s 4.14s
% Output : CNFRefutation 27.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 70
% Syntax : Number of formulae : 181 ( 56 unt; 37 typ; 0 def)
% Number of atoms : 562 ( 215 equ; 0 cnn)
% Maximal formula atoms : 154 ( 3 avg)
% Number of connectives : 1435 ( 157 ~; 189 |; 41 &;1008 @)
% ( 14 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 7 con; 0-4 aty)
% Number of variables : 224 ( 4 ^ 220 !; 0 ?; 224 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
produc1501160679le_alt: $tType ).
thf(decl_sort2,type,
arrow_1429601828e_indi: $tType ).
thf(decl_sort3,type,
arrow_475358991le_alt: $tType ).
thf(decl_sort4,type,
list_A2115238852le_alt: $tType ).
thf(decl_25,type,
arrow_823908191le_Lin: ( produc1501160679le_alt > $o ) > $o ).
thf(decl_26,type,
arrow_734252939e_Prof: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(decl_28,type,
arrow_2098199487_below: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(decl_60,type,
pi_Arr1929480907_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(decl_76,type,
append179082452le_alt: list_A2115238852le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
thf(decl_85,type,
butlas274947851le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
thf(decl_93,type,
distin236324274le_alt: list_A2115238852le_alt > $o ).
thf(decl_118,type,
hd_Arr1965683346le_alt: list_A2115238852le_alt > arrow_475358991le_alt ).
thf(decl_134,type,
last_A1217315288le_alt: list_A2115238852le_alt > arrow_475358991le_alt ).
thf(decl_154,type,
cons_A228743023le_alt: arrow_475358991le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
thf(decl_163,type,
nil_Ar1286194111le_alt: list_A2115238852le_alt ).
thf(decl_182,type,
rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
thf(decl_186,type,
rotate335349260le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
thf(decl_191,type,
set_Ar577454304le_alt: list_A2115238852le_alt > arrow_475358991le_alt > $o ).
thf(decl_209,type,
tl_Arr465451158le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
thf(decl_225,type,
top_to988227749indi_o: arrow_1429601828e_indi > $o ).
thf(decl_233,type,
produc1347929815le_alt: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt ).
thf(decl_255,type,
collec22405327e_indi: ( arrow_1429601828e_indi > $o ) > arrow_1429601828e_indi > $o ).
thf(decl_281,type,
member526088951_alt_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(decl_283,type,
member377231867_alt_o: ( produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(decl_292,type,
member84363362le_alt: arrow_475358991le_alt > ( arrow_475358991le_alt > $o ) > $o ).
thf(decl_293,type,
member2052026769e_indi: arrow_1429601828e_indi > ( arrow_1429601828e_indi > $o ) > $o ).
thf(decl_299,type,
member214075476le_alt: produc1501160679le_alt > ( produc1501160679le_alt > $o ) > $o ).
thf(decl_314,type,
p: arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(decl_315,type,
a: arrow_475358991le_alt ).
thf(decl_316,type,
b: arrow_475358991le_alt ).
thf(decl_317,type,
c: arrow_475358991le_alt ).
thf(decl_318,type,
esk1_0: arrow_1429601828e_indi ).
thf(decl_422,type,
epred20_0: arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(decl_425,type,
epred23_0: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ).
thf(decl_426,type,
epred24_1: list_A2115238852le_alt > arrow_475358991le_alt > $o ).
thf(decl_430,type,
epred28_0: arrow_1429601828e_indi > $o ).
thf(decl_431,type,
esk86_0: arrow_475358991le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
thf(fact_492_rev__singleton__conv,axiom,
! [X1476: list_A2115238852le_alt,X1477: arrow_475358991le_alt] :
( ( ( rev_Ar1106406943le_alt @ X1476 )
= ( cons_A228743023le_alt @ X1477 @ nil_Ar1286194111le_alt ) )
<=> ( X1476
= ( cons_A228743023le_alt @ X1477 @ nil_Ar1286194111le_alt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_rev__singleton__conv) ).
thf(fact_495_rev_Osimps_I2_J,axiom,
! [X1483: arrow_475358991le_alt,X1484: list_A2115238852le_alt] :
( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X1483 @ X1484 ) )
= ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X1484 ) @ ( cons_A228743023le_alt @ X1483 @ nil_Ar1286194111le_alt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_rev_Osimps_I2_J) ).
thf(fact_344_UNIV__def,axiom,
( top_to988227749indi_o
= ( collec22405327e_indi
@ ^ [X1062: arrow_1429601828e_indi] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_UNIV__def) ).
thf(fact_273_Collect__def,axiom,
! [X941: arrow_1429601828e_indi > $o] :
( ( collec22405327e_indi @ X941 )
= X941 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_Collect__def) ).
thf(fact_464_rotate1__hd__tl,axiom,
! [X1422: list_A2115238852le_alt] :
( ( X1422 != nil_Ar1286194111le_alt )
=> ( ( rotate335349260le_alt @ X1422 )
= ( append179082452le_alt @ ( tl_Arr465451158le_alt @ X1422 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ X1422 ) @ nil_Ar1286194111le_alt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_rotate1__hd__tl) ).
thf(fact_489_rev_Osimps_I1_J,axiom,
( ( rev_Ar1106406943le_alt @ nil_Ar1286194111le_alt )
= nil_Ar1286194111le_alt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_rev_Osimps_I1_J) ).
thf(fact_78_PiE,axiom,
! [X193: arrow_1429601828e_indi,X194: arrow_1429601828e_indi > produc1501160679le_alt > $o,X195: arrow_1429601828e_indi > $o,X196: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ X194 @ ( pi_Arr1929480907_alt_o @ X195 @ X196 ) )
=> ( ~ ( member377231867_alt_o @ ( X194 @ X193 ) @ ( X196 @ X193 ) )
=> ~ ( member2052026769e_indi @ X193 @ X195 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_PiE) ).
thf(fact_289_Prof__def,axiom,
( arrow_734252939e_Prof
= ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
@ ^ [X977: arrow_1429601828e_indi] : arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_Prof__def) ).
thf(fact_316_UNIV__I,axiom,
! [X1032: arrow_1429601828e_indi] : ( member2052026769e_indi @ X1032 @ top_to988227749indi_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_UNIV__I) ).
thf(fact_37_list_Osimps_I2_J,axiom,
! [X53: arrow_475358991le_alt,X54: list_A2115238852le_alt] :
( nil_Ar1286194111le_alt
!= ( cons_A228743023le_alt @ X53 @ X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_list_Osimps_I2_J) ).
thf(fact_12_in__below,axiom,
! [X4: arrow_475358991le_alt,X5: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X9: arrow_475358991le_alt] :
( ( X8 != X9 )
=> ( ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ X4 @ X5 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X9 ) )
<=> ( ( X4 != X5 )
& ( ( X5 = X8 )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ X4 @ X9 ) @ X6 ) )
& ( ( X5 != X8 )
=> ( ( ( X4 = X8 )
=> ( ( X5 = X9 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X9 @ X5 ) @ X6 ) ) )
& ( ( X4 != X8 )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ X4 @ X5 ) @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_in__below) ).
thf(conj_0,conjecture,
! [X1: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ X1 ) )
<=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ X1 ) @ c @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(fact_452_tl_Osimps_I2_J,axiom,
! [X1384: arrow_475358991le_alt,X1385: list_A2115238852le_alt] :
( ( tl_Arr465451158le_alt @ ( cons_A228743023le_alt @ X1384 @ X1385 ) )
= X1385 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_tl_Osimps_I2_J) ).
thf(fact_467_hd_Osimps,axiom,
! [X1434: arrow_475358991le_alt,X1435: list_A2115238852le_alt] :
( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X1434 @ X1435 ) )
= X1434 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_hd_Osimps) ).
thf(fact_365_snoc__eq__iff__butlast,axiom,
! [X1088: list_A2115238852le_alt,X1089: arrow_475358991le_alt,X1090: list_A2115238852le_alt] :
( ( ( append179082452le_alt @ X1088 @ ( cons_A228743023le_alt @ X1089 @ nil_Ar1286194111le_alt ) )
= X1090 )
<=> ( ( X1090 != nil_Ar1286194111le_alt )
& ( ( butlas274947851le_alt @ X1090 )
= X1088 )
& ( ( last_A1217315288le_alt @ X1090 )
= X1089 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_snoc__eq__iff__butlast) ).
thf(fact_556_distinct_Osimps_I2_J,axiom,
! [X1654: arrow_475358991le_alt,X1655: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X1654 @ X1655 ) )
<=> ( ~ ( member84363362le_alt @ X1654 @ ( set_Ar577454304le_alt @ X1655 ) )
& ( distin236324274le_alt @ X1655 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_distinct_Osimps_I2_J) ).
thf(fact_406_distinct1__rotate,axiom,
! [X1214: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( rotate335349260le_alt @ X1214 ) )
<=> ( distin236324274le_alt @ X1214 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_distinct1__rotate) ).
thf(fact_294_last__ConsR,axiom,
! [X991: arrow_475358991le_alt,X992: list_A2115238852le_alt] :
( ( X992 != nil_Ar1286194111le_alt )
=> ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X991 @ X992 ) )
= ( last_A1217315288le_alt @ X992 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_last__ConsR) ).
thf(fact_0__096P_A_058_AProf_096,axiom,
member526088951_alt_o @ p @ arrow_734252939e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096P_A_058_AProf_096) ).
thf(fact_268_mem__def,axiom,
! [X932: produc1501160679le_alt,X933: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ X932 @ X933 )
<=> ( X933 @ X932 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_mem__def) ).
thf(fact_491_distinct__rev,axiom,
! [X1475: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( rev_Ar1106406943le_alt @ X1475 ) )
<=> ( distin236324274le_alt @ X1475 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_distinct__rev) ).
thf(fact_589_hd__in__set,axiom,
! [X1737: list_A2115238852le_alt] :
( ( X1737 != nil_Ar1286194111le_alt )
=> ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X1737 ) @ ( set_Ar577454304le_alt @ X1737 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_hd__in__set) ).
thf(fact_479_hd__rev,axiom,
! [X1456: list_A2115238852le_alt] :
( ( X1456 != nil_Ar1286194111le_alt )
=> ( ( hd_Arr1965683346le_alt @ ( rev_Ar1106406943le_alt @ X1456 ) )
= ( last_A1217315288le_alt @ X1456 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_hd__rev) ).
thf(fact_394_last__snoc,axiom,
! [X1169: list_A2115238852le_alt,X1170: arrow_475358991le_alt] :
( ( last_A1217315288le_alt @ ( append179082452le_alt @ X1169 @ ( cons_A228743023le_alt @ X1170 @ nil_Ar1286194111le_alt ) ) )
= X1170 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_last__snoc) ).
thf(fact_488_Nil__is__rev__conv,axiom,
! [X1471: list_A2115238852le_alt] :
( ( nil_Ar1286194111le_alt
= ( rev_Ar1106406943le_alt @ X1471 ) )
<=> ( X1471 = nil_Ar1286194111le_alt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_Nil__is__rev__conv) ).
thf(fact_572_last__in__set,axiom,
! [X1702: list_A2115238852le_alt] :
( ( X1702 != nil_Ar1286194111le_alt )
=> ( member84363362le_alt @ ( last_A1217315288le_alt @ X1702 ) @ ( set_Ar577454304le_alt @ X1702 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_last__in__set) ).
thf(fact_4_dist,axiom,
distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_dist) ).
thf(c_0_27,plain,
! [X3117: list_A2115238852le_alt,X3118: arrow_475358991le_alt] :
( ( ( ( rev_Ar1106406943le_alt @ X3117 )
!= ( cons_A228743023le_alt @ X3118 @ nil_Ar1286194111le_alt ) )
| ( X3117
= ( cons_A228743023le_alt @ X3118 @ nil_Ar1286194111le_alt ) ) )
& ( ( X3117
!= ( cons_A228743023le_alt @ X3118 @ nil_Ar1286194111le_alt ) )
| ( ( rev_Ar1106406943le_alt @ X3117 )
= ( cons_A228743023le_alt @ X3118 @ nil_Ar1286194111le_alt ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_492_rev__singleton__conv])])]) ).
thf(c_0_28,plain,
! [X2939: arrow_475358991le_alt,X2940: list_A2115238852le_alt] :
( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2939 @ X2940 ) )
= ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X2940 ) @ ( cons_A228743023le_alt @ X2939 @ nil_Ar1286194111le_alt ) ) ),
inference(variable_rename,[status(thm)],[fact_495_rev_Osimps_I2_J]) ).
thf(c_0_29,plain,
! [X3276: list_A2115238852le_alt,X3277: arrow_475358991le_alt] :
( ( esk86_0 @ X3277 @ X3276 )
= ( append179082452le_alt @ X3276 @ ( cons_A228743023le_alt @ X3277 @ nil_Ar1286194111le_alt ) ) ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_30,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( ( rev_Ar1106406943le_alt @ X11 )
= ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) )
| ( X11
!= ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_31,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
= ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X11 ) @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( esk86_0 @ X2 @ X11 )
= ( append179082452le_alt @ X11 @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,plain,
( top_to988227749indi_o
= ( collec22405327e_indi
@ ^ [Z0: arrow_1429601828e_indi] : $true ) ),
inference(fof_simplification,[status(thm)],[fact_344_UNIV__def]) ).
thf(c_0_34,plain,
! [X3257: arrow_1429601828e_indi] :
( ( epred28_0 @ X3257 )
<=> $true ),
introduced(definition) ).
thf(c_0_35,plain,
! [X3194: arrow_1429601828e_indi > $o] :
( ( collec22405327e_indi @ X3194 )
= X3194 ),
inference(variable_rename,[status(thm)],[fact_273_Collect__def]) ).
thf(c_0_36,plain,
! [X1422: list_A2115238852le_alt] :
( ( X1422 != nil_Ar1286194111le_alt )
=> ( ( rotate335349260le_alt @ X1422 )
= ( append179082452le_alt @ ( tl_Arr465451158le_alt @ X1422 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ X1422 ) @ nil_Ar1286194111le_alt ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_464_rotate1__hd__tl]) ).
thf(c_0_37,plain,
! [X2: arrow_475358991le_alt] :
( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) )
= ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ),
inference(er,[status(thm)],[c_0_30]) ).
thf(c_0_38,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
= ( esk86_0 @ X2 @ ( rev_Ar1106406943le_alt @ X11 ) ) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_39,plain,
( ( rev_Ar1106406943le_alt @ nil_Ar1286194111le_alt )
= nil_Ar1286194111le_alt ),
inference(split_conjunct,[status(thm)],[fact_489_rev_Osimps_I1_J]) ).
thf(c_0_40,plain,
! [X193: arrow_1429601828e_indi,X194: arrow_1429601828e_indi > produc1501160679le_alt > $o,X195: arrow_1429601828e_indi > $o,X196: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ X194 @ ( pi_Arr1929480907_alt_o @ X195 @ X196 ) )
=> ( ~ ( member377231867_alt_o @ ( X194 @ X193 ) @ ( X196 @ X193 ) )
=> ~ ( member2052026769e_indi @ X193 @ X195 ) ) ),
inference(fof_simplification,[status(thm)],[fact_78_PiE]) ).
thf(c_0_41,plain,
( arrow_734252939e_Prof
= ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
@ ^ [Z0: arrow_1429601828e_indi] : arrow_823908191le_Lin ) ),
inference(fof_simplification,[status(thm)],[fact_289_Prof__def]) ).
thf(c_0_42,plain,
! [X3239: arrow_1429601828e_indi] :
( ( epred23_0 @ X3239 )
= arrow_823908191le_Lin ),
introduced(definition) ).
thf(c_0_43,plain,
( top_to988227749indi_o
= ( collec22405327e_indi @ epred28_0 ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_33]),c_0_34]) ).
thf(c_0_44,plain,
! [X81: arrow_1429601828e_indi > $o] :
( ( collec22405327e_indi @ X81 )
= X81 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_45,plain,
! [X3072: arrow_1429601828e_indi] : ( member2052026769e_indi @ X3072 @ top_to988227749indi_o ),
inference(variable_rename,[status(thm)],[fact_316_UNIV__I]) ).
thf(c_0_46,plain,
! [X3101: list_A2115238852le_alt] :
( ( X3101 = nil_Ar1286194111le_alt )
| ( ( rotate335349260le_alt @ X3101 )
= ( append179082452le_alt @ ( tl_Arr465451158le_alt @ X3101 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ X3101 ) @ nil_Ar1286194111le_alt ) ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
thf(c_0_47,plain,
! [X2: arrow_475358991le_alt] :
( ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt )
= ( esk86_0 @ X2 @ nil_Ar1286194111le_alt ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
thf(c_0_48,plain,
! [X53: arrow_475358991le_alt,X54: list_A2115238852le_alt] :
( nil_Ar1286194111le_alt
!= ( cons_A228743023le_alt @ X53 @ X54 ) ),
inference(fof_simplification,[status(thm)],[fact_37_list_Osimps_I2_J]) ).
thf(c_0_49,plain,
! [X4: arrow_475358991le_alt,X5: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X9: arrow_475358991le_alt] :
( ( X8 != X9 )
=> ( ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ X4 @ X5 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X9 ) )
<=> ( ( X4 != X5 )
& ( ( X5 = X8 )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ X4 @ X9 ) @ X6 ) )
& ( ( X5 != X8 )
=> ( ( ( X4 = X8 )
=> ( ( X5 = X9 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X9 @ X5 ) @ X6 ) ) )
& ( ( X4 != X8 )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ X4 @ X5 ) @ X6 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_12_in__below]) ).
thf(c_0_50,plain,
! [X3041: arrow_1429601828e_indi,X3042: arrow_1429601828e_indi > produc1501160679le_alt > $o,X3043: arrow_1429601828e_indi > $o,X3044: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ~ ( member526088951_alt_o @ X3042 @ ( pi_Arr1929480907_alt_o @ X3043 @ X3044 ) )
| ( member377231867_alt_o @ ( X3042 @ X3041 ) @ ( X3044 @ X3041 ) )
| ~ ( member2052026769e_indi @ X3041 @ X3043 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
thf(c_0_51,plain,
( arrow_734252939e_Prof
= ( pi_Arr1929480907_alt_o @ top_to988227749indi_o @ epred23_0 ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_41]),c_0_42]) ).
thf(c_0_52,plain,
top_to988227749indi_o = epred28_0,
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_53,plain,
! [X3287: arrow_1429601828e_indi] :
( ( epred23_0 @ X3287 )
= arrow_823908191le_Lin ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_54,plain,
! [X1: arrow_1429601828e_indi] : ( member2052026769e_indi @ X1 @ top_to988227749indi_o ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_55,negated_conjecture,
~ ! [X1: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ X1 ) )
<=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ X1 ) @ c @ b ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_56,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( ( rotate335349260le_alt @ X11 )
= ( append179082452le_alt @ ( tl_Arr465451158le_alt @ X11 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ X11 ) @ nil_Ar1286194111le_alt ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_57,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( append179082452le_alt @ X11 @ ( esk86_0 @ X2 @ nil_Ar1286194111le_alt ) )
= ( esk86_0 @ X2 @ X11 ) ),
inference(rw,[status(thm)],[c_0_32,c_0_47]) ).
thf(c_0_58,plain,
! [X3110: arrow_475358991le_alt,X3111: list_A2115238852le_alt] :
( ( tl_Arr465451158le_alt @ ( cons_A228743023le_alt @ X3110 @ X3111 ) )
= X3111 ),
inference(variable_rename,[status(thm)],[fact_452_tl_Osimps_I2_J]) ).
thf(c_0_59,plain,
! [X3133: arrow_475358991le_alt,X3134: list_A2115238852le_alt] :
( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X3133 @ X3134 ) )
= X3133 ),
inference(variable_rename,[status(thm)],[fact_467_hd_Osimps]) ).
thf(c_0_60,plain,
! [X2742: arrow_475358991le_alt,X2743: list_A2115238852le_alt] :
( nil_Ar1286194111le_alt
!= ( cons_A228743023le_alt @ X2742 @ X2743 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
thf(c_0_61,plain,
! [X1088: list_A2115238852le_alt,X1089: arrow_475358991le_alt,X1090: list_A2115238852le_alt] :
( ( ( append179082452le_alt @ X1088 @ ( cons_A228743023le_alt @ X1089 @ nil_Ar1286194111le_alt ) )
= X1090 )
<=> ( ( X1090 != nil_Ar1286194111le_alt )
& ( ( butlas274947851le_alt @ X1090 )
= X1088 )
& ( ( last_A1217315288le_alt @ X1090 )
= X1089 ) ) ),
inference(fof_simplification,[status(thm)],[fact_365_snoc__eq__iff__butlast]) ).
thf(c_0_62,plain,
! [X2588: arrow_475358991le_alt,X2589: arrow_475358991le_alt,X2590: produc1501160679le_alt > $o,X2591: arrow_475358991le_alt,X2592: arrow_475358991le_alt] :
( ( ( X2588 != X2589 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2589 != X2591 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ( X2589 = X2592 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2592 @ X2589 ) @ X2590 )
| ( X2589 = X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 = X2591 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ( X2589 = X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2589 != X2591 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ( X2588 = X2591 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ( X2588 = X2591 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ( X2589 != X2592 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ( X2589 != X2592 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2592 @ X2589 ) @ X2590 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2592 @ X2589 ) @ X2590 )
| ( X2589 = X2591 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2589 != X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ( X2588 = X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ( X2588 = X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ( X2589 != X2592 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ( X2589 != X2592 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ( X2588 != X2591 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2592 @ X2589 ) @ X2590 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) )
& ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ X2590 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2592 @ X2589 ) @ X2590 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2592 ) @ X2590 )
| ( X2588 = X2589 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2588 @ X2589 ) @ ( arrow_2098199487_below @ X2590 @ X2591 @ X2592 ) )
| ~ ( member377231867_alt_o @ X2590 @ arrow_823908191le_Lin )
| ( X2591 = X2592 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
thf(c_0_63,plain,
! [X38: arrow_1429601828e_indi > produc1501160679le_alt > $o,X1: arrow_1429601828e_indi,X196: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,X81: arrow_1429601828e_indi > $o] :
( ( member377231867_alt_o @ ( X38 @ X1 ) @ ( X196 @ X1 ) )
| ~ ( member526088951_alt_o @ X38 @ ( pi_Arr1929480907_alt_o @ X81 @ X196 ) )
| ~ ( member2052026769e_indi @ X1 @ X81 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_64,plain,
( ( pi_Arr1929480907_alt_o @ epred28_0 @ epred23_0 )
= arrow_734252939e_Prof ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_65,plain,
! [X1: arrow_1429601828e_indi] :
( ( epred23_0 @ X1 )
= arrow_823908191le_Lin ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_66,plain,
! [X1: arrow_1429601828e_indi] : ( member2052026769e_indi @ X1 @ epred28_0 ),
inference(rw,[status(thm)],[c_0_54,c_0_52]) ).
thf(c_0_67,negated_conjecture,
( ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ esk1_0 ) @ c @ b ) ) )
& ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) )
| ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ esk1_0 ) @ c @ b ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
thf(c_0_68,plain,
! [X3291: arrow_1429601828e_indi] :
( ( epred20_0 @ X3291 )
= ( arrow_2098199487_below @ ( p @ X3291 ) @ c @ b ) ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_69,plain,
! [X1654: arrow_475358991le_alt,X1655: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X1654 @ X1655 ) )
<=> ( ~ ( member84363362le_alt @ X1654 @ ( set_Ar577454304le_alt @ X1655 ) )
& ( distin236324274le_alt @ X1655 ) ) ),
inference(fof_simplification,[status(thm)],[fact_556_distinct_Osimps_I2_J]) ).
thf(c_0_70,plain,
! [X2724: list_A2115238852le_alt] :
( ( ~ ( distin236324274le_alt @ ( rotate335349260le_alt @ X2724 ) )
| ( distin236324274le_alt @ X2724 ) )
& ( ~ ( distin236324274le_alt @ X2724 )
| ( distin236324274le_alt @ ( rotate335349260le_alt @ X2724 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_406_distinct1__rotate])])]) ).
thf(c_0_71,plain,
! [X11: list_A2115238852le_alt] :
( ( ( esk86_0 @ ( hd_Arr1965683346le_alt @ X11 ) @ ( tl_Arr465451158le_alt @ X11 ) )
= ( rotate335349260le_alt @ X11 ) )
| ( X11 = nil_Ar1286194111le_alt ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_47]),c_0_57]) ).
thf(c_0_72,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( tl_Arr465451158le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
= X11 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_73,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_74,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( nil_Ar1286194111le_alt
!= ( cons_A228743023le_alt @ X2 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_75,plain,
! [X3285: arrow_475358991le_alt,X3286: list_A2115238852le_alt] :
( ( ~ ( epred24_1 @ X3286 @ X3285 )
| ( X3285
!= ( last_A1217315288le_alt @ X3286 ) ) )
& ( ( X3285
= ( last_A1217315288le_alt @ X3286 ) )
| ( epred24_1 @ X3286 @ X3285 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])]) ).
thf(c_0_76,plain,
! [X991: arrow_475358991le_alt,X992: list_A2115238852le_alt] :
( ( X992 != nil_Ar1286194111le_alt )
=> ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X991 @ X992 ) )
= ( last_A1217315288le_alt @ X992 ) ) ),
inference(fof_simplification,[status(thm)],[fact_294_last__ConsR]) ).
thf(c_0_77,plain,
! [X2881: list_A2115238852le_alt,X2882: arrow_475358991le_alt,X2883: list_A2115238852le_alt] :
( ( ( X2883 != nil_Ar1286194111le_alt )
| ( ( append179082452le_alt @ X2881 @ ( cons_A228743023le_alt @ X2882 @ nil_Ar1286194111le_alt ) )
!= X2883 ) )
& ( ( ( butlas274947851le_alt @ X2883 )
= X2881 )
| ( ( append179082452le_alt @ X2881 @ ( cons_A228743023le_alt @ X2882 @ nil_Ar1286194111le_alt ) )
!= X2883 ) )
& ( ( ( last_A1217315288le_alt @ X2883 )
= X2882 )
| ( ( append179082452le_alt @ X2881 @ ( cons_A228743023le_alt @ X2882 @ nil_Ar1286194111le_alt ) )
!= X2883 ) )
& ( ( X2883 = nil_Ar1286194111le_alt )
| ( ( butlas274947851le_alt @ X2883 )
!= X2881 )
| ( ( last_A1217315288le_alt @ X2883 )
!= X2882 )
| ( ( append179082452le_alt @ X2881 @ ( cons_A228743023le_alt @ X2882 @ nil_Ar1286194111le_alt ) )
= X2883 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
thf(c_0_78,plain,
! [X2: arrow_475358991le_alt,X5: arrow_475358991le_alt,X4: arrow_475358991le_alt,X7: arrow_475358991le_alt,X6: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X7 ) @ X6 )
| ( X4 = X7 )
| ( X2 != X4 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X2 ) @ ( arrow_2098199487_below @ X6 @ X4 @ X7 ) )
| ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_79,plain,
! [X1: arrow_1429601828e_indi,X38: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ ( X38 @ X1 ) @ arrow_823908191le_Lin )
| ~ ( member526088951_alt_o @ X38 @ arrow_734252939e_Prof ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66])]) ).
thf(c_0_80,plain,
member526088951_alt_o @ p @ arrow_734252939e_Prof,
inference(split_conjunct,[status(thm)],[fact_0__096P_A_058_AProf_096]) ).
thf(c_0_81,plain,
! [X2586: produc1501160679le_alt,X2587: produc1501160679le_alt > $o] :
( ( ~ ( member214075476le_alt @ X2586 @ X2587 )
| ( X2587 @ X2586 ) )
& ( ~ ( X2587 @ X2586 )
| ( member214075476le_alt @ X2586 @ X2587 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_268_mem__def])])]) ).
thf(c_0_82,negated_conjecture,
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) )
| ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ esk1_0 ) @ c @ b ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_83,plain,
! [X1: arrow_1429601828e_indi] :
( ( epred20_0 @ X1 )
= ( arrow_2098199487_below @ ( p @ X1 ) @ c @ b ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_84,plain,
! [X2740: arrow_475358991le_alt,X2741: list_A2115238852le_alt] :
( ( ~ ( member84363362le_alt @ X2740 @ ( set_Ar577454304le_alt @ X2741 ) )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2740 @ X2741 ) ) )
& ( ( distin236324274le_alt @ X2741 )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2740 @ X2741 ) ) )
& ( ( member84363362le_alt @ X2740 @ ( set_Ar577454304le_alt @ X2741 ) )
| ~ ( distin236324274le_alt @ X2741 )
| ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2740 @ X2741 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])]) ).
thf(c_0_85,plain,
! [X11: list_A2115238852le_alt] :
( ( distin236324274le_alt @ X11 )
| ~ ( distin236324274le_alt @ ( rotate335349260le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_86,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( rotate335349260le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
= ( esk86_0 @ X2 @ X11 ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]) ).
thf(c_0_87,plain,
! [X2735: list_A2115238852le_alt] :
( ( ~ ( distin236324274le_alt @ ( rev_Ar1106406943le_alt @ X2735 ) )
| ( distin236324274le_alt @ X2735 ) )
& ( ~ ( distin236324274le_alt @ X2735 )
| ( distin236324274le_alt @ ( rev_Ar1106406943le_alt @ X2735 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_491_distinct__rev])])]) ).
thf(c_0_88,plain,
! [X1737: list_A2115238852le_alt] :
( ( X1737 != nil_Ar1286194111le_alt )
=> ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X1737 ) @ ( set_Ar577454304le_alt @ X1737 ) ) ),
inference(fof_simplification,[status(thm)],[fact_589_hd__in__set]) ).
thf(c_0_89,plain,
! [X1456: list_A2115238852le_alt] :
( ( X1456 != nil_Ar1286194111le_alt )
=> ( ( hd_Arr1965683346le_alt @ ( rev_Ar1106406943le_alt @ X1456 ) )
= ( last_A1217315288le_alt @ X1456 ) ) ),
inference(fof_simplification,[status(thm)],[fact_479_hd__rev]) ).
thf(c_0_90,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ~ ( epred24_1 @ X11 @ X2 )
| ( X2
!= ( last_A1217315288le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_91,plain,
! [X3093: arrow_475358991le_alt,X3094: list_A2115238852le_alt] :
( ( X3094 = nil_Ar1286194111le_alt )
| ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X3093 @ X3094 ) )
= ( last_A1217315288le_alt @ X3094 ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])]) ).
thf(c_0_92,plain,
! [X2924: list_A2115238852le_alt,X2925: arrow_475358991le_alt] :
( ( last_A1217315288le_alt @ ( append179082452le_alt @ X2924 @ ( cons_A228743023le_alt @ X2925 @ nil_Ar1286194111le_alt ) ) )
= X2925 ),
inference(variable_rename,[status(thm)],[fact_394_last__snoc]) ).
thf(c_0_93,plain,
! [X2: arrow_475358991le_alt,X12: list_A2115238852le_alt,X11: list_A2115238852le_alt] :
( ( X11 != nil_Ar1286194111le_alt )
| ( ( append179082452le_alt @ X12 @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) )
!= X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_94,plain,
! [X2: arrow_475358991le_alt,X5: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o] :
( ( X2 = X4 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X4 ) @ X6 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X2 ) @ ( arrow_2098199487_below @ X6 @ X2 @ X4 ) )
| ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin ) ),
inference(er,[status(thm)],[c_0_78]) ).
thf(c_0_95,plain,
! [X1: arrow_1429601828e_indi] : ( member377231867_alt_o @ ( p @ X1 ) @ arrow_823908191le_Lin ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_96,plain,
! [X71: produc1501160679le_alt,X6: produc1501160679le_alt > $o] :
( ( X6 @ X71 )
| ~ ( member214075476le_alt @ X71 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_97,negated_conjecture,
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) )
| ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( epred20_0 @ esk1_0 ) ) ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_98,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ~ ( member84363362le_alt @ X2 @ ( set_Ar577454304le_alt @ X11 ) )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_99,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
| ~ ( distin236324274le_alt @ ( esk86_0 @ X2 @ X11 ) ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_100,plain,
! [X11: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( rev_Ar1106406943le_alt @ X11 ) )
| ~ ( distin236324274le_alt @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
thf(c_0_101,plain,
! [X2999: list_A2115238852le_alt] :
( ( X2999 = nil_Ar1286194111le_alt )
| ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X2999 ) @ ( set_Ar577454304le_alt @ X2999 ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])]) ).
thf(c_0_102,plain,
! [X3098: list_A2115238852le_alt] :
( ( X3098 = nil_Ar1286194111le_alt )
| ( ( hd_Arr1965683346le_alt @ ( rev_Ar1106406943le_alt @ X3098 ) )
= ( last_A1217315288le_alt @ X3098 ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])]) ).
thf(c_0_103,plain,
! [X3116: list_A2115238852le_alt] :
( ( ( nil_Ar1286194111le_alt
!= ( rev_Ar1106406943le_alt @ X3116 ) )
| ( X3116 = nil_Ar1286194111le_alt ) )
& ( ( X3116 != nil_Ar1286194111le_alt )
| ( nil_Ar1286194111le_alt
= ( rev_Ar1106406943le_alt @ X3116 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_488_Nil__is__rev__conv])])]) ).
thf(c_0_104,plain,
! [X11: list_A2115238852le_alt] :
~ ( epred24_1 @ X11 @ ( last_A1217315288le_alt @ X11 ) ),
inference(er,[status(thm)],[c_0_90]) ).
thf(c_0_105,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) )
= ( last_A1217315288le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
thf(c_0_106,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( last_A1217315288le_alt @ ( append179082452le_alt @ X11 @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
thf(c_0_107,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( append179082452le_alt @ X11 @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) )
!= nil_Ar1286194111le_alt ),
inference(er,[status(thm)],[c_0_93]) ).
thf(c_0_108,plain,
! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X5: arrow_475358991le_alt,X7: arrow_475358991le_alt,X6: produc1501160679le_alt > $o] :
( ( X5 = X2 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X2 ) @ ( arrow_2098199487_below @ X6 @ X4 @ X7 ) )
| ( X4 = X7 )
| ( X2 != X4 )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X7 ) @ X6 )
| ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_109,plain,
! [X2: arrow_475358991le_alt,X1: arrow_1429601828e_indi] :
( ( b = c )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ b ) @ ( p @ X1 ) )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ c ) @ ( epred20_0 @ X1 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_83]),c_0_95])]) ).
thf(c_0_110,negated_conjecture,
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( epred20_0 @ esk1_0 ) )
| ( p @ esk1_0 @ ( produc1347929815le_alt @ a @ b ) ) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
thf(c_0_111,plain,
! [X6: produc1501160679le_alt > $o,X71: produc1501160679le_alt] :
( ( member214075476le_alt @ X71 @ X6 )
| ~ ( X6 @ X71 ) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_112,negated_conjecture,
( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ esk1_0 ) @ c @ b ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_113,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ~ ( member84363362le_alt @ X2 @ ( set_Ar577454304le_alt @ X11 ) )
| ~ ( distin236324274le_alt @ ( esk86_0 @ X2 @ X11 ) ) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
thf(c_0_114,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( distin236324274le_alt @ ( esk86_0 @ X2 @ ( rev_Ar1106406943le_alt @ X11 ) ) )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) ) ),
inference(spm,[status(thm)],[c_0_100,c_0_38]) ).
thf(c_0_115,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X11 ) @ ( set_Ar577454304le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
thf(c_0_116,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( ( hd_Arr1965683346le_alt @ ( rev_Ar1106406943le_alt @ X11 ) )
= ( last_A1217315288le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
thf(c_0_117,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( nil_Ar1286194111le_alt
!= ( rev_Ar1106406943le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_118,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ~ ( epred24_1 @ ( cons_A228743023le_alt @ X2 @ X11 ) @ ( last_A1217315288le_alt @ X11 ) ) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
thf(c_0_119,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( last_A1217315288le_alt @ ( esk86_0 @ X2 @ X11 ) )
= X2 ),
inference(rw,[status(thm)],[c_0_106,c_0_32]) ).
thf(c_0_120,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( esk86_0 @ X2 @ X11 )
!= nil_Ar1286194111le_alt ),
inference(rw,[status(thm)],[c_0_107,c_0_32]) ).
thf(c_0_121,plain,
! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X5: arrow_475358991le_alt,X6: produc1501160679le_alt > $o] :
( ( X2 = X4 )
| ( X2 = X5 )
| ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X2 ) @ ( arrow_2098199487_below @ X6 @ X2 @ X4 ) )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ X5 @ X4 ) @ X6 )
| ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin ) ),
inference(er,[status(thm)],[c_0_108]) ).
thf(c_0_122,negated_conjecture,
( ( b = c )
| ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]) ).
thf(c_0_123,negated_conjecture,
( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( epred20_0 @ esk1_0 ) )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ esk1_0 ) ) ),
inference(rw,[status(thm)],[c_0_112,c_0_83]) ).
thf(c_0_124,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ~ ( member84363362le_alt @ X2 @ ( set_Ar577454304le_alt @ ( rev_Ar1106406943le_alt @ X11 ) ) )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) ) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
thf(c_0_125,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( member84363362le_alt @ ( last_A1217315288le_alt @ X11 ) @ ( set_Ar577454304le_alt @ ( rev_Ar1106406943le_alt @ X11 ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
thf(c_0_126,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt,X4: arrow_475358991le_alt] :
~ ( epred24_1 @ ( cons_A228743023le_alt @ X2 @ ( esk86_0 @ X4 @ X11 ) ) @ X4 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
thf(c_0_127,plain,
! [X11: list_A2115238852le_alt,X2: arrow_475358991le_alt] :
( ( X2
= ( last_A1217315288le_alt @ X11 ) )
| ( epred24_1 @ X11 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_128,plain,
! [X1702: list_A2115238852le_alt] :
( ( X1702 != nil_Ar1286194111le_alt )
=> ( member84363362le_alt @ ( last_A1217315288le_alt @ X1702 ) @ ( set_Ar577454304le_alt @ X1702 ) ) ),
inference(fof_simplification,[status(thm)],[fact_572_last__in__set]) ).
thf(c_0_129,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
( ( distin236324274le_alt @ X11 )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_130,plain,
distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ),
inference(split_conjunct,[status(thm)],[fact_4_dist]) ).
thf(c_0_131,negated_conjecture,
! [X2: arrow_475358991le_alt] :
( ( b = c )
| ( X2 = b )
| ( X2 = a )
| ( member214075476le_alt @ ( produc1347929815le_alt @ a @ X2 ) @ ( arrow_2098199487_below @ ( p @ esk1_0 ) @ X2 @ b ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_95])]) ).
thf(c_0_132,negated_conjecture,
( ( b = c )
| ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( epred20_0 @ esk1_0 ) ) ),
inference(spm,[status(thm)],[c_0_123,c_0_122]) ).
thf(c_0_133,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ ( last_A1217315288le_alt @ X11 ) @ X11 ) ) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
thf(c_0_134,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt,X4: arrow_475358991le_alt] :
( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X2 @ ( esk86_0 @ X4 @ X11 ) ) )
= X4 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
thf(c_0_135,plain,
! [X2992: list_A2115238852le_alt] :
( ( X2992 = nil_Ar1286194111le_alt )
| ( member84363362le_alt @ ( last_A1217315288le_alt @ X2992 ) @ ( set_Ar577454304le_alt @ X2992 ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])]) ).
thf(c_0_136,plain,
distin236324274le_alt @ ( cons_A228743023le_alt @ b @ ( esk86_0 @ c @ nil_Ar1286194111le_alt ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_47]) ).
thf(c_0_137,plain,
( ( a = c )
| ( b = c ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_83]),c_0_132]) ).
thf(c_0_138,plain,
! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X11: list_A2115238852le_alt] :
~ ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ ( cons_A228743023le_alt @ X4 @ ( esk86_0 @ X2 @ X11 ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_74]) ).
thf(c_0_139,plain,
! [X11: list_A2115238852le_alt] :
( ( X11 = nil_Ar1286194111le_alt )
| ( member84363362le_alt @ ( last_A1217315288le_alt @ X11 ) @ ( set_Ar577454304le_alt @ X11 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
thf(c_0_140,plain,
~ ( member84363362le_alt @ b @ ( set_Ar577454304le_alt @ ( esk86_0 @ c @ nil_Ar1286194111le_alt ) ) ),
inference(spm,[status(thm)],[c_0_98,c_0_136]) ).
thf(c_0_141,plain,
b = c,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_137]),c_0_47]),c_0_138]) ).
thf(c_0_142,plain,
! [X2: arrow_475358991le_alt,X11: list_A2115238852le_alt] : ( member84363362le_alt @ X2 @ ( set_Ar577454304le_alt @ ( esk86_0 @ X2 @ X11 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_119]),c_0_120]) ).
thf(c_0_143,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141]),c_0_142])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SCT170^2 : TPTP v8.2.0. Released v5.3.0.
% 0.09/0.16 % Command : run_E %s %d THM
% 0.17/0.39 % Computer : n024.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun May 19 23:47:07 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.25/0.55 Running higher-order theorem proving
% 0.25/0.55 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.97/4.14 # Version: 3.1.0-ho
% 27.97/4.14 # Preprocessing class: HMLMSMSMSSLNHSA.
% 27.97/4.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.97/4.14 # Starting sh2lt with 1500s (5) cores
% 27.97/4.14 # Starting new_ho_6 with 300s (1) cores
% 27.97/4.14 # Starting almost_fo_2 with 300s (1) cores
% 27.97/4.14 # Starting sh5l with 300s (1) cores
% 27.97/4.14 # sh2lt with pid 15438 completed with status 0
% 27.97/4.14 # Result found by sh2lt
% 27.97/4.14 # Preprocessing class: HMLMSMSMSSLNHSA.
% 27.97/4.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.97/4.14 # Starting sh2lt with 1500s (5) cores
% 27.97/4.14 # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 27.97/4.14 # Search class: HGHSM-FSLM32-DHSFFSBN
% 27.97/4.14 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 27.97/4.14 # Starting full_lambda_3 with 691s (1) cores
% 27.97/4.14 # Starting sh2lt with 151s (1) cores
% 27.97/4.14 # Starting pre_casc_4 with 204s (1) cores
% 27.97/4.14 # Starting lpo5_fix with 136s (1) cores
% 27.97/4.14 # Starting new_bool_12 with 136s (1) cores
% 27.97/4.14 # sh2lt with pid 15445 completed with status 0
% 27.97/4.14 # Result found by sh2lt
% 27.97/4.14 # Preprocessing class: HMLMSMSMSSLNHSA.
% 27.97/4.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.97/4.14 # Starting sh2lt with 1500s (5) cores
% 27.97/4.14 # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 27.97/4.14 # Search class: HGHSM-FSLM32-DHSFFSBN
% 27.97/4.14 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 27.97/4.14 # Starting full_lambda_3 with 691s (1) cores
% 27.97/4.14 # Starting sh2lt with 151s (1) cores
% 27.97/4.14 # Preprocessing time : 0.009 s
% 27.97/4.14 # Presaturation interreduction done
% 27.97/4.14
% 27.97/4.14 # Proof found!
% 27.97/4.14 # SZS status Theorem
% 27.97/4.14 # SZS output start CNFRefutation
% See solution above
% 27.97/4.14 # Parsed axioms : 1031
% 27.97/4.14 # Removed by relevancy pruning/SinE : 798
% 27.97/4.14 # Initial clauses : 447
% 27.97/4.14 # Removed in clause preprocessing : 15
% 27.97/4.14 # Initial clauses in saturation : 432
% 27.97/4.14 # Processed clauses : 12247
% 27.97/4.14 # ...of these trivial : 102
% 27.97/4.14 # ...subsumed : 7936
% 27.97/4.14 # ...remaining for further processing : 4209
% 27.97/4.14 # Other redundant clauses eliminated : 5337
% 27.97/4.14 # Clauses deleted for lack of memory : 0
% 27.97/4.14 # Backward-subsumed : 132
% 27.97/4.14 # Backward-rewritten : 1412
% 27.97/4.14 # Generated clauses : 72152
% 27.97/4.14 # ...of the previous two non-redundant : 63457
% 27.97/4.14 # ...aggressively subsumed : 0
% 27.97/4.14 # Contextual simplify-reflections : 44
% 27.97/4.14 # Paramodulations : 63596
% 27.97/4.14 # Factorizations : 11
% 27.97/4.14 # NegExts : 342
% 27.97/4.14 # Equation resolutions : 5358
% 27.97/4.14 # Disequality decompositions : 0
% 27.97/4.14 # Total rewrite steps : 19280
% 27.97/4.14 # ...of those cached : 16937
% 27.97/4.14 # Propositional unsat checks : 0
% 27.97/4.14 # Propositional check models : 0
% 27.97/4.14 # Propositional check unsatisfiable : 0
% 27.97/4.14 # Propositional clauses : 0
% 27.97/4.14 # Propositional clauses after purity: 0
% 27.97/4.14 # Propositional unsat core size : 0
% 27.97/4.14 # Propositional preprocessing time : 0.000
% 27.97/4.14 # Propositional encoding time : 0.000
% 27.97/4.14 # Propositional solver time : 0.000
% 27.97/4.14 # Success case prop preproc time : 0.000
% 27.97/4.14 # Success case prop encoding time : 0.000
% 27.97/4.14 # Success case prop solver time : 0.000
% 27.97/4.14 # Current number of processed clauses : 2089
% 27.97/4.14 # Positive orientable unit clauses : 281
% 27.97/4.14 # Positive unorientable unit clauses: 0
% 27.97/4.14 # Negative unit clauses : 251
% 27.97/4.14 # Non-unit-clauses : 1557
% 27.97/4.14 # Current number of unprocessed clauses: 50693
% 27.97/4.14 # ...number of literals in the above : 158022
% 27.97/4.14 # Current number of archived formulas : 0
% 27.97/4.14 # Current number of archived clauses : 2061
% 27.97/4.14 # Clause-clause subsumption calls (NU) : 1589852
% 27.97/4.14 # Rec. Clause-clause subsumption calls : 874754
% 27.97/4.14 # Non-unit clause-clause subsumptions : 5051
% 27.97/4.14 # Unit Clause-clause subsumption calls : 108482
% 27.97/4.14 # Rewrite failures with RHS unbound : 0
% 27.97/4.14 # BW rewrite match attempts : 236
% 27.97/4.14 # BW rewrite match successes : 77
% 27.97/4.14 # Condensation attempts : 0
% 27.97/4.14 # Condensation successes : 0
% 27.97/4.14 # Termbank termtop insertions : 2211463
% 27.97/4.14 # Search garbage collected termcells : 15487
% 27.97/4.14
% 27.97/4.14 # -------------------------------------------------
% 27.97/4.14 # User time : 3.419 s
% 27.97/4.14 # System time : 0.054 s
% 27.97/4.14 # Total time : 3.473 s
% 27.97/4.14 # Maximum resident set size: 6336 pages
% 27.97/4.14
% 27.97/4.14 # -------------------------------------------------
% 27.97/4.14 # User time : 16.977 s
% 27.97/4.14 # System time : 0.343 s
% 27.97/4.14 # Total time : 17.319 s
% 27.97/4.14 # Maximum resident set size: 4200 pages
% 27.97/4.14 % E---3.1 exiting
% 27.97/4.15 % E exiting
%------------------------------------------------------------------------------