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
%------------------------------------------------------------------------------