TSTP Solution File: SWW473_1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW473_1 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 18:17:21 EDT 2024

% Result   : Theorem 17.55s 3.14s
% Output   : CNFRefutation 17.55s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
tff(f182,axiom,
    ! [X29: x_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X2))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_subsetD) ).

tff(f195,axiom,
    ! [X5: x_a,X7: fun_a_bool] : ( insert_a(X5,X7) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_insert__compr) ).

tff(f222,axiom,
    ! [X28: x_a,X5: x_a,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X7))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),insert_a(X28,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_insertI2) ).

tff(f231,axiom,
    ! [X2: fun_a_bool,X7: fun_a_bool] :
      ( ( X2 = X7 )
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X2))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_set__eq__subset) ).

tff(f254,axiom,
    ! [X8: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
    <=> hBOOL(hAPP_a_bool(X2,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_mem__def) ).

tff(f255,axiom,
    ! [X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
    <=> hBOOL(hAPP_pname_bool(X2,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_mem__def) ).

tff(f263,axiom,
    ! [X28: x_a,X6: fun_pname_a,X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
     => ( ( hAPP_pname_a(X6,X8) = X28 )
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X28),image_pname_a(X6,X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).

tff(f275,axiom,
    ! [X8: x_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X2)),X7))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_insert__subset) ).

tff(f278,axiom,
    ! [X7: fun_a_bool,X8: x_a,X2: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X8,X7)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_subset__insert) ).

tff(f291,axiom,
    ! [X7: fun_a_bool,X2: fun_a_bool] :
      ( ! [X27: x_a] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X2))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X7)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_subsetI) ).

tff(f299,axiom,
    ! [X8: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X8),X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_order__refl) ).

tff(f312,axiom,
    ! [X15: x_a,X16: x_a] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).

tff(f313,axiom,
    ! [X15: x_a,X16: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).

tff(f318,axiom,
    ! [X41: fun_a_fun_a_bool,X42: x_a,X43: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X41),X42),X43) = hAPP_a_bool(hAPP_a_fun_a_bool(X41,X43),X42) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).

tff(f334,axiom,
    ! [X41: fun_a_1255737515l_bool,X42: fun_a_bool,X43: x_a] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X41),X42),X43) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X41,X43),X42) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).

tff(f363,axiom,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

tff(f366,axiom,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).

tff(f368,conjecture,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).

tff(f369,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(negated_conjecture,[],[f368]) ).

tff(f550,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
    inference(rectify,[],[f182]) ).

tff(f563,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
    inference(rectify,[],[f195]) ).

tff(f590,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2))) ),
    inference(rectify,[],[f222]) ).

tff(f599,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    inference(rectify,[],[f231]) ).

tff(f622,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
    <=> hBOOL(hAPP_a_bool(X1,X0)) ),
    inference(rectify,[],[f254]) ).

tff(f623,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
    <=> hBOOL(hAPP_pname_bool(X1,X0)) ),
    inference(rectify,[],[f255]) ).

tff(f631,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: pname,X3: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
     => ( ( hAPP_pname_a(X1,X2) = X0 )
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3))) ) ),
    inference(rectify,[],[f263]) ).

tff(f643,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
    inference(rectify,[],[f275]) ).

tff(f646,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) ) ),
    inference(rectify,[],[f278]) ).

tff(f659,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ! [X2: x_a] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ),
    inference(rectify,[],[f291]) ).

tff(f667,plain,
    ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
    inference(rectify,[],[f299]) ).

tff(f680,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ),
    inference(rectify,[],[f312]) ).

tff(f681,plain,
    ! [X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f313]) ).

tff(f686,plain,
    ! [X0: fun_a_fun_a_bool,X1: x_a,X2: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
    inference(rectify,[],[f318]) ).

tff(f702,plain,
    ! [X0: fun_a_1255737515l_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
    inference(rectify,[],[f334]) ).

tff(f730,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(flattening,[],[f369]) ).

tff(f933,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f550]) ).

tff(f934,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(flattening,[],[f933]) ).

tff(f954,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(ennf_transformation,[],[f590]) ).

tff(f992,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: pname,X3: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
      | ( hAPP_pname_a(X1,X2) != X0 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
    inference(ennf_transformation,[],[f631]) ).

tff(f993,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: pname,X3: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
      | ( hAPP_pname_a(X1,X2) != X0 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
    inference(flattening,[],[f992]) ).

tff(f996,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(ennf_transformation,[],[f646]) ).

tff(f1007,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ? [X2: x_a] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) ),
    inference(ennf_transformation,[],[f659]) ).

tff(f1070,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( ( X0 = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f599]) ).

tff(f1071,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( ( X0 = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
        | ( X0 != X1 ) ) ),
    inference(flattening,[],[f1070]) ).

tff(f1073,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
        | ~ hBOOL(hAPP_a_bool(X1,X0)) )
      & ( hBOOL(hAPP_a_bool(X1,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
    inference(nnf_transformation,[],[f622]) ).

tff(f1074,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_pname_bool(X1,X0)) )
      & ( hBOOL(hAPP_pname_bool(X1,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
    inference(nnf_transformation,[],[f623]) ).

tff(f1083,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
    inference(nnf_transformation,[],[f643]) ).

tff(f1084,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2)) ) ),
    inference(flattening,[],[f1083]) ).

tff(f1087,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(nnf_transformation,[],[f996]) ).

tff(f1096,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ? [X2: x_a] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0,X1)),X0))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1097,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0,X1)),X0))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0,X1)),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f1007,f1096]) ).

tff(f1332,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f934]) ).

tff(f1348,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( insert_a(X0,X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
    inference(cnf_transformation,[],[f563]) ).

tff(f1390,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X0,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f954]) ).

tff(f1405,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f1071]) ).

tff(f1432,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_a_bool(X1,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(cnf_transformation,[],[f1073]) ).

tff(f1433,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_a_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f1073]) ).

tff(f1434,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_pname_bool(X1,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(cnf_transformation,[],[f1074]) ).

tff(f1435,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_pname_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f1074]) ).

tff(f1445,plain,
    ! [X2: pname,X3: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X3)))
      | ( hAPP_pname_a(X1,X2) != X0 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
    inference(cnf_transformation,[],[f993]) ).

tff(f1463,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X0,X1)),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
    inference(cnf_transformation,[],[f1084]) ).

tff(f1468,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),insert_a(X1,X0)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f1087]) ).

tff(f1486,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f1097]) ).

tff(f1487,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f1097]) ).

tff(f1498,plain,
    ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
    inference(cnf_transformation,[],[f667]) ).

tff(f1513,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ),
    inference(cnf_transformation,[],[f680]) ).

tff(f1514,plain,
    ! [X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f681]) ).

tff(f1519,plain,
    ! [X2: x_a,X0: fun_a_fun_a_bool,X1: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f686]) ).

tff(f1535,plain,
    ! [X2: x_a,X0: fun_a_1255737515l_bool,X1: fun_a_bool] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f702]) ).

tff(f1564,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[],[f363]) ).

tff(f1567,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(cnf_transformation,[],[f366]) ).

tff(f1569,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[],[f730]) ).

tff(f1662,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(definition_unfolding,[],[f1390,f1348]) ).

tff(f1681,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
    inference(definition_unfolding,[],[f1463,f1348]) ).

tff(f1689,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)))))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(definition_unfolding,[],[f1468,f1348]) ).

tff(f1698,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
    inference(definition_unfolding,[],[f1569,f1348]) ).

tff(f1735,plain,
    ! [X2: pname,X3: fun_pname_bool,X1: fun_pname_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
    inference(equality_resolution,[],[f1445]) ).

tff(f1737,plain,
    ! [X1: x_a] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
    inference(equality_resolution,[],[f1514]) ).

cnf(c_269,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X1_19)) ),
    inference(cnf_transformation,[],[f1332]) ).

cnf(c_321,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0_19))))) ),
    inference(cnf_transformation,[],[f1662]) ).

cnf(c_334,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),X0_19))
    | X0_19 = X1_19 ),
    inference(cnf_transformation,[],[f1405]) ).

cnf(c_363,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(cnf_transformation,[],[f1433]) ).

cnf(c_364,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(cnf_transformation,[],[f1432]) ).

cnf(c_365,plain,
    ( ~ hBOOL(hAPP_pname_bool(X0_27,X0_14))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_14),X0_27)) ),
    inference(cnf_transformation,[],[f1435]) ).

cnf(c_366,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_14),X0_27))
    | hBOOL(hAPP_pname_bool(X0_27,X0_14)) ),
    inference(cnf_transformation,[],[f1434]) ).

cnf(c_376,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0_14),X0_27))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_25,X0_14)),image_pname_a(X0_25,X0_27))) ),
    inference(cnf_transformation,[],[f1735]) ).

cnf(c_386,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1_19)))),X0_19)) ),
    inference(cnf_transformation,[],[f1681]) ).

cnf(c_394,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1_19)))))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19)) ),
    inference(cnf_transformation,[],[f1689]) ).

cnf(c_411,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0_19,X1_19)),X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),X0_19)) ),
    inference(cnf_transformation,[],[f1487]) ).

cnf(c_412,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK10(X0_19,X1_19)),X1_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),X0_19)) ),
    inference(cnf_transformation,[],[f1486]) ).

cnf(c_423,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X0_19)),
    inference(cnf_transformation,[],[f1498]) ).

cnf(c_438,plain,
    ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0_13),X1_13))
    | X0_13 = X1_13 ),
    inference(cnf_transformation,[],[f1513]) ).

cnf(c_439,plain,
    hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0_13),X0_13)),
    inference(cnf_transformation,[],[f1737]) ).

cnf(c_444,plain,
    hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0_21),X0_13),X1_13) = hAPP_a_bool(hAPP_a_fun_a_bool(X0_21,X1_13),X0_13),
    inference(cnf_transformation,[],[f1519]) ).

cnf(c_460,plain,
    hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0_24),X0_19),X0_13) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0_24,X0_13),X0_19),
    inference(cnf_transformation,[],[f1535]) ).

cnf(c_489,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[],[f1564]) ).

cnf(c_492,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(cnf_transformation,[],[f1567]) ).

cnf(c_494,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[],[f1698]) ).

cnf(c_821,plain,
    ( hBOOL(hAPP_a_bool(X0_19,X0_13))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(prop_impl_just,[status(thm)],[c_364]) ).

cnf(c_822,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(renaming,[status(thm)],[c_821]) ).

cnf(c_823,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(prop_impl_just,[status(thm)],[c_363]) ).

cnf(c_1143,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0_19)))))
    | ~ hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(prop_impl_just,[status(thm)],[c_363,c_321]) ).

cnf(c_1144,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0_19))))) ),
    inference(renaming,[status(thm)],[c_1143]) ).

cnf(c_1153,plain,
    ( ~ hBOOL(hAPP_pname_bool(X0_27,X0_14))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_25,X0_14)),image_pname_a(X0_25,X0_27))) ),
    inference(prop_impl_just,[status(thm)],[c_365,c_376]) ).

cnf(c_1976,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X1_19)) ),
    inference(bin_hyper_res,[status(thm)],[c_269,c_823]) ).

cnf(c_1986,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | ~ hBOOL(hAPP_a_bool(X1_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0_19)))),X1_19)) ),
    inference(bin_hyper_res,[status(thm)],[c_386,c_823]) ).

cnf(c_1989,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1_19)))))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(bin_hyper_res,[status(thm)],[c_394,c_822]) ).

cnf(c_5628,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0_19)))))
    | ~ hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(prop_impl_just,[status(thm)],[c_1144]) ).

cnf(c_5629,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1_13)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0_19))))) ),
    inference(renaming,[status(thm)],[c_5628]) ).

cnf(c_5636,plain,
    ( ~ hBOOL(hAPP_pname_bool(X0_27,X0_14))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0_25,X0_14)),image_pname_a(X0_25,X0_27))) ),
    inference(prop_impl_just,[status(thm)],[c_1153]) ).

cnf(c_9181,plain,
    cOMBC_a_a_bool(fequal_a) = sP0_iProver_def,
    definition ).

cnf(c_9182,plain,
    hAPP_pname_a(mgt_call,pn) = sP1_iProver_def,
    definition ).

cnf(c_9183,plain,
    hAPP_a_fun_a_bool(sP0_iProver_def,sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_9184,plain,
    cOMBB_1972296269bool_a(fdisj,sP2_iProver_def) = sP3_iProver_def,
    definition ).

cnf(c_9185,plain,
    cOMBC_1355376034l_bool(member_a) = sP4_iProver_def,
    definition ).

cnf(c_9186,plain,
    hAPP_f2050579477a_bool(sP4_iProver_def,g) = sP5_iProver_def,
    definition ).

cnf(c_9187,plain,
    cOMBS_a_bool_bool(sP3_iProver_def,sP5_iProver_def) = sP6_iProver_def,
    definition ).

cnf(c_9188,plain,
    collect_a(sP6_iProver_def) = sP7_iProver_def,
    definition ).

cnf(c_9189,plain,
    hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP7_iProver_def) = sP8_iProver_def,
    definition ).

cnf(c_9190,plain,
    image_pname_a(mgt_call,u) = sP9_iProver_def,
    definition ).

cnf(c_9191,plain,
    hAPP_fun_a_bool_bool(sP8_iProver_def,sP9_iProver_def) = sP10_iProver_def,
    definition ).

cnf(c_9192,negated_conjecture,
    ~ hBOOL(sP10_iProver_def),
    inference(demodulation,[status(thm)],[c_494,c_9190,c_9185,c_9186,c_9182,c_9181,c_9183,c_9184,c_9187,c_9188,c_9189,c_9191]) ).

cnf(c_12915,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | ~ hBOOL(hAPP_a_bool(X1_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X0_19)))),X1_19)) ),
    inference(light_normalisation,[status(thm)],[c_1986,c_9181,c_9185]) ).

cnf(c_12925,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | ~ hBOOL(hAPP_a_bool(X1_19,sP1_iProver_def))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,sP2_iProver_def),hAPP_f2050579477a_bool(sP4_iProver_def,X0_19)))),X1_19)) ),
    inference(superposition,[status(thm)],[c_9183,c_12915]) ).

cnf(c_12927,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | ~ hBOOL(hAPP_a_bool(X1_19,sP1_iProver_def))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(sP3_iProver_def,hAPP_f2050579477a_bool(sP4_iProver_def,X0_19)))),X1_19)) ),
    inference(light_normalisation,[status(thm)],[c_12925,c_9184]) ).

cnf(c_12942,plain,
    ( ~ hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13))
    | ~ hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(superposition,[status(thm)],[c_9189,c_1976]) ).

cnf(c_12956,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),sP9_iProver_def)),
    inference(light_normalisation,[status(thm)],[c_489,c_9190]) ).

cnf(c_12957,plain,
    ( ~ hBOOL(hAPP_a_bool(g,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12956,c_1976]) ).

cnf(c_12969,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X1_19)))))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(light_normalisation,[status(thm)],[c_1989,c_9181,c_9185]) ).

cnf(c_13216,plain,
    hBOOL(hAPP_pname_bool(u,pn)),
    inference(superposition,[status(thm)],[c_492,c_366]) ).

cnf(c_13259,plain,
    ( ~ hBOOL(hAPP_a_bool(g,X0_13))
    | hBOOL(hAPP_a_bool(sP9_iProver_def,X0_13)) ),
    inference(superposition,[status(thm)],[c_12957,c_364]) ).

cnf(c_13781,plain,
    hAPP_a_bool(hAPP_f2050579477a_bool(sP4_iProver_def,X0_19),X0_13) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19),
    inference(superposition,[status(thm)],[c_9185,c_460]) ).

cnf(c_13801,plain,
    hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),g) = hAPP_a_bool(sP5_iProver_def,X0_13),
    inference(superposition,[status(thm)],[c_9186,c_13781]) ).

cnf(c_13804,plain,
    ( ~ hBOOL(hAPP_a_bool(sP5_iProver_def,X0_13))
    | hBOOL(hAPP_a_bool(g,X0_13)) ),
    inference(superposition,[status(thm)],[c_13801,c_364]) ).

cnf(c_13970,plain,
    ( hBOOL(hAPP_a_bool(sP5_iProver_def,sK10(X0_19,g)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),X0_19)) ),
    inference(superposition,[status(thm)],[c_13801,c_412]) ).

cnf(c_13971,plain,
    ( hBOOL(hAPP_a_bool(X0_19,sK10(X1_19,X0_19)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19)) ),
    inference(superposition,[status(thm)],[c_412,c_364]) ).

cnf(c_14050,plain,
    ( hBOOL(hAPP_a_bool(g,sK10(X0_19,sP5_iProver_def)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),X0_19)) ),
    inference(superposition,[status(thm)],[c_13971,c_13804]) ).

cnf(c_14093,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X1_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X0_19))))) ),
    inference(light_normalisation,[status(thm)],[c_5629,c_9181,c_9185]) ).

cnf(c_14102,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X1_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X0_19))),X0_13)) ),
    inference(superposition,[status(thm)],[c_14093,c_364]) ).

cnf(c_14219,plain,
    ( hBOOL(hAPP_a_bool(sP9_iProver_def,sK10(X0_19,sP5_iProver_def)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),X0_19)) ),
    inference(superposition,[status(thm)],[c_14050,c_13259]) ).

cnf(c_14266,plain,
    ( ~ hBOOL(hAPP_pname_bool(X0_27,pn))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sP1_iProver_def),image_pname_a(mgt_call,X0_27))) ),
    inference(superposition,[status(thm)],[c_9182,c_5636]) ).

cnf(c_14504,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X1_19)))))
    | ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X1_19))),sP1_iProver_def))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(sP3_iProver_def,hAPP_f2050579477a_bool(sP4_iProver_def,X0_19)))),X1_19))
    | hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(sP3_iProver_def,hAPP_f2050579477a_bool(sP4_iProver_def,X0_19))),X0_13)) ),
    inference(superposition,[status(thm)],[c_12927,c_12969]) ).

cnf(c_14539,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,sK10(X0_19,X1_19)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),X0_19)) ),
    inference(superposition,[status(thm)],[c_363,c_411]) ).

cnf(c_14542,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,sK10(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X0_19))),X1_19)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X0_19))))) ),
    inference(superposition,[status(thm)],[c_14093,c_411]) ).

cnf(c_14609,plain,
    ( ~ hBOOL(hAPP_pname_bool(u,pn))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sP1_iProver_def),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_9190,c_14266]) ).

cnf(c_14613,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sP1_iProver_def),sP9_iProver_def)),
    inference(forward_subsumption_resolution,[status(thm)],[c_14609,c_13216]) ).

cnf(c_14641,plain,
    hBOOL(hAPP_a_bool(sP9_iProver_def,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_14613,c_364]) ).

cnf(c_14835,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),sP5_iProver_def)),
    inference(superposition,[status(thm)],[c_13970,c_14539]) ).

cnf(c_14838,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),g)),
    inference(superposition,[status(thm)],[c_14050,c_14539]) ).

cnf(c_17147,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),g))
    | g = sP5_iProver_def ),
    inference(superposition,[status(thm)],[c_14835,c_334]) ).

cnf(c_17170,plain,
    g = sP5_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_17147,c_14838]) ).

cnf(c_17242,plain,
    hAPP_f2050579477a_bool(sP4_iProver_def,sP5_iProver_def) = sP5_iProver_def,
    inference(demodulation,[status(thm)],[c_9186,c_17170]) ).

cnf(c_20991,plain,
    hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,sP7_iProver_def)),
    inference(superposition,[status(thm)],[c_9189,c_423]) ).

cnf(c_20992,plain,
    ( ~ hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13))
    | ~ hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(superposition,[status(thm)],[c_9189,c_1976]) ).

cnf(c_21005,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),sP9_iProver_def)),
    inference(light_normalisation,[status(thm)],[c_489,c_9190]) ).

cnf(c_21006,plain,
    ( ~ hBOOL(hAPP_a_bool(g,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_21005,c_1976]) ).

cnf(c_21017,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,X1_19)))))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(light_normalisation,[status(thm)],[c_1989,c_9181,c_9185]) ).

cnf(c_21031,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),sP5_iProver_def))))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),g))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(superposition,[status(thm)],[c_9186,c_21017]) ).

cnf(c_21274,plain,
    hBOOL(hAPP_pname_bool(u,pn)),
    inference(superposition,[status(thm)],[c_492,c_366]) ).

cnf(c_21321,plain,
    ( ~ hBOOL(hAPP_a_bool(g,X0_13))
    | hBOOL(hAPP_a_bool(sP9_iProver_def,X0_13)) ),
    inference(superposition,[status(thm)],[c_21006,c_364]) ).

cnf(c_23778,plain,
    hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0_13),X1_13) = hAPP_a_bool(hAPP_a_fun_a_bool(sP0_iProver_def,X1_13),X0_13),
    inference(superposition,[status(thm)],[c_9181,c_444]) ).

cnf(c_23779,plain,
    hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(sP0_iProver_def,X0_13),X0_13)),
    inference(demodulation,[status(thm)],[c_439,c_23778]) ).

cnf(c_23907,plain,
    hAPP_a_bool(hAPP_f2050579477a_bool(sP4_iProver_def,X0_19),X0_13) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19),
    inference(superposition,[status(thm)],[c_9185,c_460]) ).

cnf(c_23908,plain,
    ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(sP0_iProver_def,X0_13),X1_13))
    | X0_13 = X1_13 ),
    inference(superposition,[status(thm)],[c_23778,c_438]) ).

cnf(c_23937,plain,
    hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),g) = hAPP_a_bool(sP5_iProver_def,X0_13),
    inference(superposition,[status(thm)],[c_9186,c_23907]) ).

cnf(c_24000,plain,
    ( ~ hBOOL(hAPP_a_bool(sP5_iProver_def,X0_13))
    | hBOOL(hAPP_a_bool(g,X0_13)) ),
    inference(superposition,[status(thm)],[c_23937,c_364]) ).

cnf(c_24599,plain,
    ( hBOOL(hAPP_a_bool(X0_19,sK10(X1_19,X0_19)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),X1_19)) ),
    inference(superposition,[status(thm)],[c_412,c_364]) ).

cnf(c_25001,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,sP9_iProver_def))))),
    inference(superposition,[status(thm)],[c_14219,c_14542]) ).

cnf(c_25112,plain,
    ( hBOOL(hAPP_a_bool(g,sK10(X0_19,sP5_iProver_def)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),X0_19)) ),
    inference(superposition,[status(thm)],[c_24599,c_24000]) ).

cnf(c_26346,plain,
    ( hBOOL(hAPP_a_bool(sP9_iProver_def,sK10(X0_19,sP5_iProver_def)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),X0_19)) ),
    inference(superposition,[status(thm)],[c_25112,c_21321]) ).

cnf(c_26523,plain,
    ( ~ hBOOL(hAPP_pname_bool(X0_27,pn))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sP1_iProver_def),image_pname_a(mgt_call,X0_27))) ),
    inference(superposition,[status(thm)],[c_9182,c_5636]) ).

cnf(c_27102,plain,
    ( ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,sP9_iProver_def))),sP1_iProver_def))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(sP3_iProver_def,hAPP_f2050579477a_bool(sP4_iProver_def,sP5_iProver_def)))),sP9_iProver_def))
    | hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(sP3_iProver_def,hAPP_f2050579477a_bool(sP4_iProver_def,sP5_iProver_def))),X0_13)) ),
    inference(superposition,[status(thm)],[c_25001,c_14504]) ).

cnf(c_27113,plain,
    ( ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,sP9_iProver_def))),sP1_iProver_def))
    | hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13))
    | hBOOL(sP10_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_27102,c_9187,c_9188,c_9189,c_9191,c_17242]) ).

cnf(c_27114,plain,
    ( ~ hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(sP0_iProver_def,X0_13)),hAPP_f2050579477a_bool(sP4_iProver_def,sP9_iProver_def))),sP1_iProver_def))
    | hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_27113,c_9192]) ).

cnf(c_27149,plain,
    ( ~ hBOOL(hAPP_a_bool(sP9_iProver_def,sP1_iProver_def))
    | hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13)) ),
    inference(superposition,[status(thm)],[c_14102,c_27114]) ).

cnf(c_27151,plain,
    hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13)),
    inference(forward_subsumption_resolution,[status(thm)],[c_27149,c_14641]) ).

cnf(c_27153,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_12942,c_27151]) ).

cnf(c_28423,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,sK10(X0_19,X1_19)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1_19),X0_19)) ),
    inference(superposition,[status(thm)],[c_363,c_411]) ).

cnf(c_28627,plain,
    ( ~ hBOOL(hAPP_pname_bool(u,pn))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sP1_iProver_def),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_9190,c_26523]) ).

cnf(c_28631,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sP1_iProver_def),sP9_iProver_def)),
    inference(forward_subsumption_resolution,[status(thm)],[c_28627,c_21274]) ).

cnf(c_28651,plain,
    hBOOL(hAPP_a_bool(sP9_iProver_def,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_28631,c_364]) ).

cnf(c_29040,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,X0_19))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),X0_19)) ),
    inference(global_subsumption_just,[status(thm)],[c_20992,c_27153]) ).

cnf(c_29047,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,X0_19))
    | hBOOL(hAPP_a_bool(X0_19,X0_13)) ),
    inference(superposition,[status(thm)],[c_29040,c_364]) ).

cnf(c_29426,plain,
    hBOOL(hAPP_a_bool(sP7_iProver_def,X0_13)),
    inference(superposition,[status(thm)],[c_20991,c_29047]) ).

cnf(c_29846,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),sP7_iProver_def)),
    inference(superposition,[status(thm)],[c_29426,c_28423]) ).

cnf(c_29856,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP5_iProver_def),sP9_iProver_def)),
    inference(superposition,[status(thm)],[c_26346,c_28423]) ).

cnf(c_30228,plain,
    ( ~ hBOOL(hAPP_a_bool(sP5_iProver_def,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_29856,c_1976]) ).

cnf(c_30757,plain,
    ( ~ hBOOL(hAPP_a_bool(sP5_iProver_def,sK10(sP9_iProver_def,X0_19)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_30228,c_411]) ).

cnf(c_31061,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,sP2_iProver_def),sP5_iProver_def))))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),g))
    | hBOOL(hAPP_a_bool(X0_19,sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_9183,c_21031]) ).

cnf(c_31062,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),sP7_iProver_def))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),g))
    | hBOOL(hAPP_a_bool(X0_19,sP1_iProver_def)) ),
    inference(light_normalisation,[status(thm)],[c_31061,c_9184,c_9187,c_9188]) ).

cnf(c_31063,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),g))
    | hBOOL(hAPP_a_bool(X0_19,sP1_iProver_def)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31062,c_29846]) ).

cnf(c_31187,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0_13),g))
    | hBOOL(hAPP_a_bool(X0_19,sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_31063,c_1976]) ).

cnf(c_31190,plain,
    ( ~ hBOOL(hAPP_a_bool(X0_19,X0_13))
    | hBOOL(hAPP_a_bool(X0_19,sP1_iProver_def))
    | hBOOL(hAPP_a_bool(sP5_iProver_def,X0_13)) ),
    inference(light_normalisation,[status(thm)],[c_31187,c_23937]) ).

cnf(c_31523,plain,
    ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(sP0_iProver_def,X0_13),sP1_iProver_def))
    | hBOOL(hAPP_a_bool(sP5_iProver_def,X0_13)) ),
    inference(superposition,[status(thm)],[c_23779,c_31190]) ).

cnf(c_31775,plain,
    ( X0_13 = sP1_iProver_def
    | hBOOL(hAPP_a_bool(sP5_iProver_def,X0_13)) ),
    inference(superposition,[status(thm)],[c_31523,c_23908]) ).

cnf(c_31794,plain,
    ( sK10(sP9_iProver_def,X0_19) = sP1_iProver_def
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0_19),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_31775,c_30757]) ).

cnf(c_32827,plain,
    ( sK10(sP9_iProver_def,sP7_iProver_def) = sP1_iProver_def
    | hBOOL(hAPP_fun_a_bool_bool(sP8_iProver_def,sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_9189,c_31794]) ).

cnf(c_32830,plain,
    ( sK10(sP9_iProver_def,sP7_iProver_def) = sP1_iProver_def
    | hBOOL(sP10_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_32827,c_9191]) ).

cnf(c_32831,plain,
    sK10(sP9_iProver_def,sP7_iProver_def) = sP1_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_32830,c_9192]) ).

cnf(c_32837,plain,
    ( ~ hBOOL(hAPP_a_bool(sP9_iProver_def,sP1_iProver_def))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sP7_iProver_def),sP9_iProver_def)) ),
    inference(superposition,[status(thm)],[c_32831,c_28423]) ).

cnf(c_32844,plain,
    ( ~ hBOOL(hAPP_a_bool(sP9_iProver_def,sP1_iProver_def))
    | hBOOL(sP10_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_32837,c_9189,c_9191]) ).

cnf(c_32845,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_32844,c_9192,c_28651]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem  : SWW473_1 : TPTP v8.2.0. Released v5.3.0.
% 0.02/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Wed Jun 19 09:47:09 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.55/3.14  % SZS status Started for theBenchmark.p
% 17.55/3.14  % SZS status Theorem for theBenchmark.p
% 17.55/3.14  
% 17.55/3.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.55/3.14  
% 17.55/3.14  ------  iProver source info
% 17.55/3.14  
% 17.55/3.14  git: date: 2024-06-12 09:56:46 +0000
% 17.55/3.14  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 17.55/3.14  git: non_committed_changes: false
% 17.55/3.14  
% 17.55/3.14  ------ Parsing...
% 17.55/3.14  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  ------ Preprocessing... sup_sim: 135  pe_s  pe_e  sup_sim: 0  pe_s  pe_e 
% 17.55/3.14  
% 17.55/3.14  ------ Preprocessing...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 17.55/3.14   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e ------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  ------ Preprocessing...
% 17.55/3.14  ------ Proving...
% 17.55/3.14  ------ Problem Properties 
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  clauses                                 371
% 17.55/3.14  conjectures                             1
% 17.55/3.14  EPR                                     1
% 17.55/3.14  Horn                                    339
% 17.55/3.14  unary                                   101
% 17.55/3.14  binary                                  188
% 17.55/3.14  lits                                    734
% 17.55/3.14  lits eq                                 130
% 17.55/3.14  fd_pure                                 0
% 17.55/3.14  fd_pseudo                               0
% 17.55/3.14  fd_cond                                 0
% 17.55/3.14  fd_pseudo_cond                          28
% 17.55/3.14  AC symbols                              0
% 17.55/3.14  
% 17.55/3.14  ------ Schedule dynamic 5 is on 
% 17.55/3.14  
% 17.55/3.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  ------ 
% 17.55/3.14  Current options:
% 17.55/3.14  ------ 
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  ------ Proving...
% 17.55/3.14  
% 17.55/3.14  
% 17.55/3.14  % SZS status Theorem for theBenchmark.p
% 17.55/3.14  
% 17.55/3.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.55/3.14  
% 17.55/3.15  
%------------------------------------------------------------------------------