TSTP Solution File: SWW470_3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW470_3 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 18:17:17 EDT 2024

% Result   : Theorem 72.48s 10.64s
% Output   : CNFRefutation 72.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   64 (  35 unt;   0 typ;   0 def)
%            Number of atoms       :  574 (  28 equ)
%            Maximal formula atoms :    4 (   8 avg)
%            Number of connectives :   91 (  36   ~;  32   |;   9   &)
%                                         (   2 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  455 ( 455 fml;   0 var)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   60 (  58 usr;  32 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  160 (  31 sgn  88   !;   9   ?;  97   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f5,axiom,
    ! [X0: fun_Ho882550911a_bool,X10: fun_a_fun_state_bool,X11: com,X12: fun_a_fun_state_bool,X13: bool] :
      ( ( hBOOL(X13)
       => hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X10,X11,X12)),bot_bo214064617a_bool))) )
     => hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X10))),X13),X11,X12)),bot_bo214064617a_bool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_constant) ).

tff(f8,axiom,
    ! [X10: fun_a_fun_state_bool,X0: fun_Ho882550911a_bool,X17: fun_a_fun_state_bool,X11: com,X12: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X17,X11,X12)),bot_bo214064617a_bool)))
     => ( ! [X14: x_a,X15: state] :
            ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X10,X14),X15))
           => hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X17,X14),X15)) )
       => hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X10,X11,X12)),bot_bo214064617a_bool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_conseq1) ).

tff(f20,axiom,
    ! [X20: hoare_2076525193iple_a] : ( hAPP_f642208769a_bool(collec977865374iple_a,hAPP_H2077279219a_bool(fequal1589671816iple_a,X20)) = hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,X20),bot_bo214064617a_bool) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_singleton__conv2) ).

tff(f46,axiom,
    ! [X22: fun_Ho882550911a_bool] :
      ( ! [X24: hoare_2076525193iple_a] : ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X24),X22))
    <=> ( bot_bo214064617a_bool = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_all__not__in__conv) ).

tff(f200,axiom,
    ! [X10: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,X10) = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Collect__def) ).

tff(f1207,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

tff(f1229,axiom,
    ! [X288: bool,X289: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X288),X289) = X288 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).

tff(f1252,axiom,
    ! [X288: fun_state_bool,X289: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X288),X289) = X288 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).

tff(f1364,conjecture,
    hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f1365,negated_conjecture,
    ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
    inference(negated_conjecture,[],[f1364]) ).

tff(f1369,plain,
    ! [X0: fun_Ho882550911a_bool,X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool,X4: bool] :
      ( ( hBOOL(X4)
       => hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X1,X2,X3)),bot_bo214064617a_bool))) )
     => hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X1))),X4),X2,X3)),bot_bo214064617a_bool))) ),
    inference(rectify,[],[f5]) ).

tff(f1372,plain,
    ! [X0: fun_a_fun_state_bool,X1: fun_Ho882550911a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X2,X3,X4)),bot_bo214064617a_bool)))
     => ( ! [X5: x_a,X6: state] :
            ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6))
           => hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6)) )
       => hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X0,X3,X4)),bot_bo214064617a_bool))) ) ),
    inference(rectify,[],[f8]) ).

tff(f1384,plain,
    ! [X0: hoare_2076525193iple_a] : ( hAPP_f642208769a_bool(collec977865374iple_a,hAPP_H2077279219a_bool(fequal1589671816iple_a,X0)) = hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,X0),bot_bo214064617a_bool) ),
    inference(rectify,[],[f20]) ).

tff(f1410,plain,
    ! [X0: fun_Ho882550911a_bool] :
      ( ! [X1: hoare_2076525193iple_a] : ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),X0))
    <=> ( bot_bo214064617a_bool = X0 ) ),
    inference(rectify,[],[f46]) ).

tff(f1561,plain,
    ! [X0: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,X0) = X0 ),
    inference(rectify,[],[f200]) ).

tff(f2572,plain,
    ! [X0: bool,X1: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0),X1) = X0 ),
    inference(rectify,[],[f1229]) ).

tff(f2595,plain,
    ! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X0),X1) = X0 ),
    inference(rectify,[],[f1252]) ).

tff(f2707,plain,
    ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
    inference(flattening,[],[f1365]) ).

tff(f2712,plain,
    ! [X0: fun_Ho882550911a_bool,X1: fun_a_fun_state_bool,X2: com,X3: fun_a_fun_state_bool,X4: bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X1))),X4),X2,X3)),bot_bo214064617a_bool)))
      | ( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X1,X2,X3)),bot_bo214064617a_bool)))
        & hBOOL(X4) ) ),
    inference(ennf_transformation,[],[f1369]) ).

tff(f2716,plain,
    ! [X0: fun_a_fun_state_bool,X1: fun_Ho882550911a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X0,X3,X4)),bot_bo214064617a_bool)))
      | ? [X5: x_a,X6: state] :
          ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6))
          & hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
      | ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X2,X3,X4)),bot_bo214064617a_bool))) ),
    inference(ennf_transformation,[],[f1372]) ).

tff(f2717,plain,
    ! [X0: fun_a_fun_state_bool,X1: fun_Ho882550911a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X0,X3,X4)),bot_bo214064617a_bool)))
      | ? [X5: x_a,X6: state] :
          ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6))
          & hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
      | ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X2,X3,X4)),bot_bo214064617a_bool))) ),
    inference(flattening,[],[f2716]) ).

tff(f3788,plain,
    ! [X0: fun_a_fun_state_bool,X2: fun_a_fun_state_bool] :
      ( ? [X5: x_a,X6: state] :
          ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,X5),X6))
          & hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,X5),X6)) )
     => ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK8(X0,X2)),sK9(X0,X2)))
        & hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK8(X0,X2)),sK9(X0,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3789,plain,
    ! [X0: fun_a_fun_state_bool,X1: fun_Ho882550911a_bool,X2: fun_a_fun_state_bool,X3: com,X4: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X0,X3,X4)),bot_bo214064617a_bool)))
      | ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2,sK8(X0,X2)),sK9(X0,X2)))
        & hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK8(X0,X2)),sK9(X0,X2))) )
      | ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X2,X3,X4)),bot_bo214064617a_bool))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f2717,f3788]) ).

tff(f3829,plain,
    ! [X0: fun_Ho882550911a_bool] :
      ( ( ! [X1: hoare_2076525193iple_a] : ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),X0))
        | ( bot_bo214064617a_bool != X0 ) )
      & ( ( bot_bo214064617a_bool = X0 )
        | ? [X1: hoare_2076525193iple_a] : hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1410]) ).

tff(f3830,plain,
    ! [X0: fun_Ho882550911a_bool] :
      ( ( ! [X1: hoare_2076525193iple_a] : ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),X0))
        | ( bot_bo214064617a_bool != X0 ) )
      & ( ( bot_bo214064617a_bool = X0 )
        | ? [X2: hoare_2076525193iple_a] : hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X2),X0)) ) ),
    inference(rectify,[],[f3829]) ).

tff(f3831,plain,
    ! [X0: fun_Ho882550911a_bool] :
      ( ? [X2: hoare_2076525193iple_a] : hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X2),X0))
     => hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,sK22(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3832,plain,
    ! [X0: fun_Ho882550911a_bool] :
      ( ( ! [X1: hoare_2076525193iple_a] : ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),X0))
        | ( bot_bo214064617a_bool != X0 ) )
      & ( ( bot_bo214064617a_bool = X0 )
        | hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,sK22(X0)),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f3830,f3831]) ).

tff(f4437,plain,
    ! [X2: com,X3: fun_a_fun_state_bool,X0: fun_Ho882550911a_bool,X1: fun_a_fun_state_bool,X4: bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X1))),X4),X2,X3)),bot_bo214064617a_bool)))
      | hBOOL(X4) ),
    inference(cnf_transformation,[],[f2712]) ).

tff(f4443,plain,
    ! [X2: fun_a_fun_state_bool,X3: com,X0: fun_a_fun_state_bool,X1: fun_Ho882550911a_bool,X4: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X0,X3,X4)),bot_bo214064617a_bool)))
      | hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0,sK8(X0,X2)),sK9(X0,X2)))
      | ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X1),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X2,X3,X4)),bot_bo214064617a_bool))) ),
    inference(cnf_transformation,[],[f3789]) ).

tff(f4461,plain,
    ! [X0: hoare_2076525193iple_a] : ( hAPP_f642208769a_bool(collec977865374iple_a,hAPP_H2077279219a_bool(fequal1589671816iple_a,X0)) = hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,X0),bot_bo214064617a_bool) ),
    inference(cnf_transformation,[],[f1384]) ).

tff(f4503,plain,
    ! [X0: fun_Ho882550911a_bool,X1: hoare_2076525193iple_a] :
      ( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),X0))
      | ( bot_bo214064617a_bool != X0 ) ),
    inference(cnf_transformation,[],[f3832]) ).

tff(f4739,plain,
    ! [X0: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,X0) = X0 ),
    inference(cnf_transformation,[],[f1561]) ).

tff(f6174,plain,
    ~ hBOOL(fFalse),
    inference(cnf_transformation,[],[f1207]) ).

tff(f6196,plain,
    ! [X0: bool,X1: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0),X1) = X0 ),
    inference(cnf_transformation,[],[f2572]) ).

tff(f6219,plain,
    ! [X0: fun_state_bool,X1: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X0),X1) = X0 ),
    inference(cnf_transformation,[],[f2595]) ).

tff(f6331,plain,
    ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
    inference(cnf_transformation,[],[f2707]) ).

tff(f6344,plain,
    ! [X1: hoare_2076525193iple_a] : ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X1),bot_bo214064617a_bool)),
    inference(equality_resolution,[],[f4503]) ).

cnf(c_56,plain,
    ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17),X0_14,X1_21)),bot_bo214064617a_bool)))
    | hBOOL(X0_17) ),
    inference(cnf_transformation,[],[f4437]) ).

cnf(c_62,plain,
    ( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X0_21,X0_14,X1_21)),bot_bo214064617a_bool)))
    | hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(X2_21,X0_14,X1_21)),bot_bo214064617a_bool)))
    | hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2_21,sK8(X2_21,X0_21)),sK9(X2_21,X0_21))) ),
    inference(cnf_transformation,[],[f4443]) ).

cnf(c_79,plain,
    hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,X0_18),bot_bo214064617a_bool) = hAPP_f642208769a_bool(collec977865374iple_a,hAPP_H2077279219a_bool(fequal1589671816iple_a,X0_18)),
    inference(cnf_transformation,[],[f4461]) ).

cnf(c_120,plain,
    ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X0_18),bot_bo214064617a_bool)),
    inference(cnf_transformation,[],[f6344]) ).

cnf(c_352,plain,
    hAPP_f642208769a_bool(collec977865374iple_a,X0_42) = X0_42,
    inference(cnf_transformation,[],[f4739]) ).

cnf(c_1747,plain,
    ~ hBOOL(fFalse),
    inference(cnf_transformation,[],[f6174]) ).

cnf(c_1769,plain,
    hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0_17),X0_15) = X0_17,
    inference(cnf_transformation,[],[f6196]) ).

cnf(c_1792,plain,
    hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X0_27),X0_13) = X0_27,
    inference(cnf_transformation,[],[f6219]) ).

cnf(c_1904,negated_conjecture,
    ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
    inference(cnf_transformation,[],[f6331]) ).

cnf(c_3440,plain,
    ( hBOOL(X0_17)
    | hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17),X0_14,X1_21)),bot_bo214064617a_bool))) ),
    inference(prop_impl_just,[status(thm)],[c_56]) ).

cnf(c_3441,plain,
    ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17),X0_14,X1_21)),bot_bo214064617a_bool)))
    | hBOOL(X0_17) ),
    inference(renaming,[status(thm)],[c_3440]) ).

cnf(c_13286,plain,
    hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,X0_18),bot_bo214064617a_bool) = hAPP_H2077279219a_bool(fequal1589671816iple_a,X0_18),
    inference(demodulation,[status(thm)],[c_79,c_352]) ).

cnf(c_15274,plain,
    ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17),X0_14,X1_21))))
    | hBOOL(X0_17) ),
    inference(demodulation,[status(thm)],[c_3441,c_13286]) ).

cnf(c_16010,plain,
    ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))),
    inference(demodulation,[status(thm)],[c_1904,c_13286]) ).

cnf(c_16063,plain,
    ( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(X0_21,X0_14,X1_21))))
    | hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2_21,sK8(X2_21,X0_21)),sK9(X2_21,X0_21)))
    | hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(X2_21,X0_14,X1_21)))) ),
    inference(demodulation,[status(thm)],[c_62,c_13286]) ).

cnf(c_17498,plain,
    ( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(X0_21,X0_14,X1_21))))
    | hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X2_21,sK8(X2_21,X0_21)),sK9(X2_21,X0_21)))
    | hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(X2_21,X0_14,X1_21)))) ),
    inference(subtyping,[status(esa)],[c_16063]) ).

cnf(c_17505,plain,
    ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))),
    inference(subtyping,[status(esa)],[c_16010]) ).

cnf(c_17569,plain,
    ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17),X0_14,X1_21))))
    | hBOOL(X0_17) ),
    inference(subtyping,[status(esa)],[c_15274]) ).

cnf(c_17932,plain,
    hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X0_27),X0_327) = X0_27,
    inference(subtyping,[status(esa)],[c_1792]) ).

cnf(c_17955,plain,
    hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X0_17),X0_15) = X0_17,
    inference(subtyping,[status(esa)],[c_1769]) ).

cnf(c_17976,plain,
    ~ hBOOL(fFalse),
    inference(subtyping,[status(esa)],[c_1747]) ).

cnf(c_18837,plain,
    ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X0_18),bot_bo214064617a_bool)),
    inference(subtyping,[status(esa)],[c_120]) ).

cnf(c_32737,plain,
    ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X0_21,sK8(X0_21,hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X1_21))),X0_17))),sK9(X0_21,hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X1_21))),X0_17))))
    | hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(X0_42),hAPP_H2077279219a_bool(fequal1589671816iple_a,hoare_1876769875iple_a(X0_21,X0_14,X2_21))))
    | hBOOL(X0_17) ),
    inference(superposition,[status(thm)],[c_17569,c_17498]) ).

cnf(c_34546,plain,
    ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),sK8(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17))),sK9(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(hAPP_f1006724181e_bool(cOMBB_1348041619bool_a,cOMBC_231445413l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),X0_21))),X0_17))))
    | hBOOL(X0_17) ),
    inference(superposition,[status(thm)],[c_32737,c_17505]) ).

cnf(c_34552,plain,
    ( hBOOL(X0_17)
    | hBOOL(fFalse) ),
    inference(demodulation,[status(thm)],[c_34546,c_17955,c_17932]) ).

cnf(c_34553,plain,
    hBOOL(X0_17),
    inference(forward_subsumption_resolution,[status(thm)],[c_34552,c_17976]) ).

cnf(c_34627,plain,
    $false,
    inference(superposition,[status(thm)],[c_34553,c_18837]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SWW470_3 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.30  % Computer : n021.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Wed Jun 19 06:29:39 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 72.48/10.64  % SZS status Started for theBenchmark.p
% 72.48/10.64  % SZS status Theorem for theBenchmark.p
% 72.48/10.64  
% 72.48/10.64  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 72.48/10.64  
% 72.48/10.64  ------  iProver source info
% 72.48/10.64  
% 72.48/10.64  git: date: 2024-06-12 09:56:46 +0000
% 72.48/10.64  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 72.48/10.64  git: non_committed_changes: false
% 72.48/10.64  
% 72.48/10.64  ------ Parsing...
% 72.48/10.64  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 72.48/10.64  
% 72.48/10.64  ------ Preprocessing... sup_sim: 280  sf_s  rm: 7 0s  sf_e  pe_s  pe_e 
% 72.48/10.64  
% 72.48/10.64  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 72.48/10.64  
% 72.48/10.64  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 72.48/10.64  ------ Proving...
% 72.48/10.64  ------ Problem Properties 
% 72.48/10.64  
% 72.48/10.64  
% 72.48/10.64  clauses                                 1409
% 72.48/10.64  conjectures                             0
% 72.48/10.64  EPR                                     6
% 72.48/10.64  Horn                                    1095
% 72.48/10.64  unary                                   425
% 72.48/10.64  binary                                  512
% 72.48/10.64  lits                                    3073
% 72.48/10.64  lits eq                                 976
% 72.48/10.64  fd_pure                                 1
% 72.48/10.64  fd_pseudo                               0
% 72.48/10.64  fd_cond                                 88
% 72.48/10.64  fd_pseudo_cond                          101
% 72.48/10.64  AC symbols                              0
% 72.48/10.64  
% 72.48/10.64  ------ Input Options Time Limit: Unbounded
% 72.48/10.64  
% 72.48/10.64  
% 72.48/10.64  ------ 
% 72.48/10.64  Current options:
% 72.48/10.64  ------ 
% 72.48/10.64  
% 72.48/10.64  
% 72.48/10.64  
% 72.48/10.64  
% 72.48/10.64  ------ Proving...
% 72.48/10.64  
% 72.48/10.64  
% 72.48/10.64  % SZS status Theorem for theBenchmark.p
% 72.48/10.64  
% 72.48/10.64  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.48/10.64  
% 72.48/10.64  
%------------------------------------------------------------------------------