TSTP Solution File: SWW470_2 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWW470_2 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 06:45:44 EDT 2024

% Result   : Theorem 62.02s 8.32s
% Output   : CNFRefutation 62.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   86
% Syntax   : Number of formulae    :  121 (  28 unt;  75 typ;   0 def)
%            Number of atoms       :   81 (  25 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :   58 (  23   ~;  21   |;   6   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :   30 (  29 usr)
%            Number of type conns  :   57 (  26   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   45 (  45 usr;  20 con; 0-6 aty)
%            Number of variables   :   73 (   0 sgn  71   !;   2   ?;  73   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    fun_fu1631777789e_bool: $tType ).

tff(decl_sort2,type,
    bool: $tType ).

tff(decl_sort3,type,
    fun_fu88048803e_bool: $tType ).

tff(decl_sort4,type,
    fun_fu1873708859l_bool: $tType ).

tff(decl_sort5,type,
    fun_fu1340893257l_bool: $tType ).

tff(decl_sort6,type,
    fun_fu734682033e_bool: $tType ).

tff(decl_sort7,type,
    fun_bo1936561970e_bool: $tType ).

tff(decl_sort8,type,
    fun_bo873159128a_bool: $tType ).

tff(decl_sort9,type,
    fun_fu281355805e_bool: $tType ).

tff(decl_sort10,type,
    fun_fu1047394976e_bool: $tType ).

tff(decl_sort11,type,
    com: $tType ).

tff(decl_sort12,type,
    fun_Ho611385006a_bool: $tType ).

tff(decl_sort13,type,
    fun_fu1441721944l_bool: $tType ).

tff(decl_sort14,type,
    fun_Ho287446294a_bool: $tType ).

tff(decl_sort15,type,
    hoare_1544627872iple_a: $tType ).

tff(decl_sort16,type,
    fun_fu410471825a_bool: $tType ).

tff(decl_sort17,type,
    fun_a_fun_state_bool: $tType ).

tff(decl_sort18,type,
    fun_bo1549164019l_bool: $tType ).

tff(decl_sort19,type,
    state: $tType ).

tff(decl_sort20,type,
    fun_bool_bool: $tType ).

tff(decl_sort21,type,
    x_a: $tType ).

tff(decl_sort22,type,
    fun_state_bool: $tType ).

tff(decl_sort23,type,
    fun_a_1632297036l_bool: $tType ).

tff(decl_sort24,type,
    fun_fu373216837e_bool: $tType ).

tff(decl_sort25,type,
    fun_a_2117018159e_bool: $tType ).

tff(decl_sort26,type,
    fun_Ho448013557l_bool: $tType ).

tff(decl_sort27,type,
    fun_fu2118559873l_bool: $tType ).

tff(decl_sort28,type,
    fun_fu2008829792e_bool: $tType ).

tff(decl_sort29,type,
    fun_fu1658206819l_bool: $tType ).

tff(decl_25,type,
    cOMBB_160679318_state: fun_fu88048803e_bool ).

tff(decl_30,type,
    cOMBB_188601460_state: fun_fu1873708859l_bool ).

tff(decl_38,type,
    cOMBB_1355796797bool_a: fun_fu1340893257l_bool ).

tff(decl_44,type,
    cOMBB_145932198bool_a: fun_fu1631777789e_bool ).

tff(decl_53,type,
    cOMBC_892787026e_bool: fun_fu734682033e_bool ).

tff(decl_77,type,
    cOMBK_bool_state: fun_bo1936561970e_bool ).

tff(decl_78,type,
    cOMBK_329760839iple_a: fun_bo873159128a_bool ).

tff(decl_90,type,
    cOMBK_1458035955bool_a: fun_fu281355805e_bool ).

tff(decl_92,type,
    cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).

tff(decl_141,type,
    hoare_1546678894rivs_a: fun_Ho287446294a_bool > fun_fu1441721944l_bool ).

tff(decl_143,type,
    hoare_196563068iple_a: ( fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > hoare_1544627872iple_a ).

tff(decl_161,type,
    bot_bot_bool: bool ).

tff(decl_163,type,
    bot_bo1766443648a_bool: fun_Ho287446294a_bool ).

tff(decl_175,type,
    collec445968053iple_a: fun_Ho287446294a_bool > fun_Ho287446294a_bool ).

tff(decl_188,type,
    insert1051021594iple_a: fun_Ho611385006a_bool ).

tff(decl_195,type,
    fFalse: bool ).

tff(decl_196,type,
    fNot: fun_bool_bool ).

tff(decl_198,type,
    fconj: fun_bo1549164019l_bool ).

tff(decl_208,type,
    hAPP_a2036067514e_bool: ( fun_a_fun_state_bool * x_a ) > fun_state_bool ).

tff(decl_214,type,
    hAPP_state_bool: ( fun_state_bool * state ) > bool ).

tff(decl_227,type,
    hAPP_b2019457360e_bool: ( fun_bo1936561970e_bool * bool ) > fun_state_bool ).

tff(decl_230,type,
    hAPP_b704538998a_bool: ( fun_bo873159128a_bool * bool ) > fun_Ho287446294a_bool ).

tff(decl_234,type,
    hAPP_H2006434664a_bool: ( fun_Ho287446294a_bool * hoare_1544627872iple_a ) > bool ).

tff(decl_243,type,
    hAPP_H736103437l_bool: ( fun_Ho448013557l_bool * hoare_1544627872iple_a ) > fun_fu1441721944l_bool ).

tff(decl_244,type,
    hAPP_H762155206a_bool: ( fun_Ho611385006a_bool * hoare_1544627872iple_a ) > fun_fu410471825a_bool ).

tff(decl_269,type,
    hAPP_f1509969235l_bool: ( fun_fu2118559873l_bool * fun_a_fun_state_bool ) > fun_a_1632297036l_bool ).

tff(decl_272,type,
    hAPP_f963367678e_bool: ( fun_fu2008829792e_bool * fun_a_1632297036l_bool ) > fun_a_2117018159e_bool ).

tff(decl_275,type,
    hAPP_f1261923407e_bool: ( fun_fu734682033e_bool * fun_a_2117018159e_bool ) > fun_fu281355805e_bool ).

tff(decl_279,type,
    hAPP_f762886889e_bool: ( fun_fu281355805e_bool * fun_state_bool ) > fun_a_fun_state_bool ).

tff(decl_280,type,
    hAPP_f1759915619e_bool: ( fun_fu373216837e_bool * fun_state_bool ) > fun_state_bool ).

tff(decl_296,type,
    hAPP_f2073279419e_bool: ( fun_fu88048803e_bool * fun_bool_bool ) > fun_fu373216837e_bool ).

tff(decl_301,type,
    hAPP_f1561913689l_bool: ( fun_fu1873708859l_bool * fun_bo1549164019l_bool ) > fun_fu1658206819l_bool ).

tff(decl_306,type,
    hAPP_f2063540982l_bool: ( fun_fu1441721944l_bool * fun_Ho287446294a_bool ) > bool ).

tff(decl_308,type,
    hAPP_f909437487a_bool: ( fun_fu410471825a_bool * fun_Ho287446294a_bool ) > fun_Ho287446294a_bool ).

tff(decl_352,type,
    hAPP_f1178339559l_bool: ( fun_fu1340893257l_bool * fun_fu1658206819l_bool ) > fun_fu2118559873l_bool ).

tff(decl_358,type,
    hAPP_f375255701e_bool: ( fun_fu1631777789e_bool * fun_fu1047394976e_bool ) > fun_fu2008829792e_bool ).

tff(decl_374,type,
    hBOOL: bool > $o ).

tff(decl_375,type,
    member1891733107iple_a: fun_Ho448013557l_bool ).

tff(decl_379,type,
    g: fun_Ho287446294a_bool ).

tff(decl_380,type,
    p: fun_a_fun_state_bool ).

tff(decl_381,type,
    b: fun_state_bool ).

tff(decl_382,type,
    c: com ).

tff(decl_407,type,
    esk25_1: fun_Ho287446294a_bool > hoare_1544627872iple_a ).

tff(decl_424,type,
    esk42_4: ( fun_a_fun_state_bool * fun_Ho287446294a_bool * com * fun_a_fun_state_bool ) > x_a ).

tff(decl_425,type,
    esk43_4: ( fun_a_fun_state_bool * fun_Ho287446294a_bool * com * fun_a_fun_state_bool ) > state ).

tff(decl_426,type,
    esk44_6: ( fun_a_fun_state_bool * fun_Ho287446294a_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).

tff(fact_54_empty__Collect__eq,axiom,
    ! [X110: fun_Ho287446294a_bool] :
      ( ( bot_bo1766443648a_bool = collec445968053iple_a(X110) )
    <=> ! [X111: hoare_1544627872iple_a] : ~ hBOOL(hAPP_H2006434664a_bool(X110,X111)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_empty__Collect__eq) ).

tff(fact_24_emptyE,axiom,
    ! [X56: hoare_1544627872iple_a] : ~ hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X56),bot_bo1766443648a_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_emptyE) ).

tff(fact_232_Collect__def,axiom,
    ! [X437: fun_Ho287446294a_bool] : ( collec445968053iple_a(X437) = X437 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Collect__def) ).

tff(fact_156_bot__empty__eq,axiom,
    ! [X281: hoare_1544627872iple_a] :
      ( hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X281))
    <=> hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X281),bot_bo1766443648a_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_bot__empty__eq) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____xlrqixeqwe__,axiom,
    ! [X1353: bool,X1419: hoare_1544627872iple_a] : ( hAPP_H2006434664a_bool(hAPP_b704538998a_bool(cOMBK_329760839iple_a,X1353),X1419) = X1353 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____xlrqixeqwe__) ).

tff(fact_64_empty__def,axiom,
    bot_bo1766443648a_bool = collec445968053iple_a(hAPP_b704538998a_bool(cOMBK_329760839iple_a,fFalse)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_empty__def) ).

tff(fact_145_conseq,axiom,
    ! [X24: fun_a_fun_state_bool,X1: fun_Ho287446294a_bool,X23: com,X22: fun_a_fun_state_bool] :
      ( ! [X29: x_a,X30: state] :
          ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X22,X29),X30))
         => ? [X257: fun_a_fun_state_bool,X258: fun_a_fun_state_bool] :
              ( hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X257,X23,X258)),bot_bo1766443648a_bool)))
              & ! [X47: state] :
                  ( ! [X48: x_a] :
                      ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X257,X48),X30))
                     => hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X258,X48),X47)) )
                 => hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X24,X29),X47)) ) ) )
     => hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X22,X23,X24)),bot_bo1766443648a_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_conseq) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U,axiom,
    ! [X1378: fun_state_bool,X1379: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X1378),X1379) = X1378 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).

tff(fact_124_bot__apply,axiom,
    ! [X134: hoare_1544627872iple_a] :
      ( hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X134))
    <=> hBOOL(bot_bot_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_bot__apply) ).

tff(conj_0,conjecture,
    hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(g),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_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_bo1766443648a_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U,axiom,
    ! [X1353: bool,X1366: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X1353),X1366) = X1353 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).

tff(c_0_11,plain,
    ! [X110: fun_Ho287446294a_bool] :
      ( ( bot_bo1766443648a_bool = collec445968053iple_a(X110) )
    <=> ! [X111: hoare_1544627872iple_a] : ~ hBOOL(hAPP_H2006434664a_bool(X110,X111)) ),
    inference(fof_simplification,[status(thm)],[fact_54_empty__Collect__eq]) ).

tff(c_0_12,plain,
    ! [X56: hoare_1544627872iple_a] : ~ hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X56),bot_bo1766443648a_bool)),
    inference(fof_simplification,[status(thm)],[fact_24_emptyE]) ).

tff(c_0_13,plain,
    ! [X1752: fun_Ho287446294a_bool,X1753: hoare_1544627872iple_a,X1754: fun_Ho287446294a_bool] :
      ( ( ( bot_bo1766443648a_bool != collec445968053iple_a(X1752) )
        | ~ hBOOL(hAPP_H2006434664a_bool(X1752,X1753)) )
      & ( hBOOL(hAPP_H2006434664a_bool(X1754,esk25_1(X1754)))
        | ( bot_bo1766443648a_bool = collec445968053iple_a(X1754) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])]) ).

tff(c_0_14,plain,
    ! [X2467: fun_Ho287446294a_bool] : ( collec445968053iple_a(X2467) = X2467 ),
    inference(variable_rename,[status(thm)],[fact_232_Collect__def]) ).

tff(c_0_15,plain,
    ! [X1665: hoare_1544627872iple_a] :
      ( ( ~ hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X1665))
        | hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X1665),bot_bo1766443648a_bool)) )
      & ( ~ hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X1665),bot_bo1766443648a_bool))
        | hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X1665)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_bot__empty__eq])])]) ).

tff(c_0_16,plain,
    ! [X1579: hoare_1544627872iple_a] : ~ hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X1579),bot_bo1766443648a_bool)),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).

tcf(c_0_17,plain,
    ! [X1: fun_Ho287446294a_bool] :
      ( hBOOL(hAPP_H2006434664a_bool(X1,esk25_1(X1)))
      | ( bot_bo1766443648a_bool = collec445968053iple_a(X1) ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_18,plain,
    ! [X1: fun_Ho287446294a_bool] : collec445968053iple_a(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

tff(c_0_19,plain,
    ! [X3205: bool,X3206: hoare_1544627872iple_a] : ( hAPP_H2006434664a_bool(hAPP_b704538998a_bool(cOMBK_329760839iple_a,X3205),X3206) = X3205 ),
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____xlrqixeqwe__]) ).

tcf(c_0_20,plain,
    bot_bo1766443648a_bool = collec445968053iple_a(hAPP_b704538998a_bool(cOMBK_329760839iple_a,fFalse)),
    inference(split_conjunct,[status(thm)],[fact_64_empty__def]) ).

tff(c_0_21,plain,
    ! [X1889: fun_a_fun_state_bool,X1890: fun_Ho287446294a_bool,X1891: com,X1892: fun_a_fun_state_bool,X1895: fun_a_fun_state_bool,X1896: fun_a_fun_state_bool,X1898: x_a] :
      ( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1892,esk42_4(X1889,X1890,X1891,X1892)),esk43_4(X1889,X1890,X1891,X1892)))
        | hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1890),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X1892,X1891,X1889)),bot_bo1766443648a_bool))) )
      & ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1895,X1898),esk43_4(X1889,X1890,X1891,X1892)))
        | hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1896,X1898),esk44_6(X1889,X1890,X1891,X1892,X1895,X1896)))
        | ~ hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1890),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X1895,X1891,X1896)),bot_bo1766443648a_bool)))
        | hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1890),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X1892,X1891,X1889)),bot_bo1766443648a_bool))) )
      & ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X1889,esk42_4(X1889,X1890,X1891,X1892)),esk44_6(X1889,X1890,X1891,X1892,X1895,X1896)))
        | ~ hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1890),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X1895,X1891,X1896)),bot_bo1766443648a_bool)))
        | hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1890),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X1892,X1891,X1889)),bot_bo1766443648a_bool))) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_conseq])])])])])]) ).

tff(c_0_22,plain,
    ! [X1903: fun_state_bool,X1904: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X1903),X1904) = X1903 ),
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U]) ).

tff(c_0_23,plain,
    ! [X2309: hoare_1544627872iple_a] :
      ( ( ~ hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X2309))
        | hBOOL(bot_bot_bool) )
      & ( ~ hBOOL(bot_bot_bool)
        | hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X2309)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_124_bot__apply])])]) ).

tcf(c_0_24,plain,
    ! [X18: hoare_1544627872iple_a] :
      ( hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X18),bot_bo1766443648a_bool))
      | ~ hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X18)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

tcf(c_0_25,plain,
    ! [X18: hoare_1544627872iple_a] : ~ hBOOL(hAPP_f2063540982l_bool(hAPP_H736103437l_bool(member1891733107iple_a,X18),bot_bo1766443648a_bool)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

tcf(c_0_26,plain,
    ! [X1: fun_Ho287446294a_bool] :
      ( ( bot_bo1766443648a_bool = X1 )
      | hBOOL(hAPP_H2006434664a_bool(X1,esk25_1(X1))) ),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

tcf(c_0_27,plain,
    ! [X18: hoare_1544627872iple_a,X25: bool] : hAPP_H2006434664a_bool(hAPP_b704538998a_bool(cOMBK_329760839iple_a,X25),X18) = X25,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

tcf(c_0_28,plain,
    bot_bo1766443648a_bool = hAPP_b704538998a_bool(cOMBK_329760839iple_a,fFalse),
    inference(rw,[status(thm)],[c_0_20,c_0_18]) ).

tff(c_0_29,negated_conjecture,
    ~ hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(g),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_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_bo1766443648a_bool))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

tcf(c_0_30,plain,
    ! [X1: fun_Ho287446294a_bool,X4: com,X9: fun_a_fun_state_bool,X10: fun_a_fun_state_bool] :
      ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(X9,esk42_4(X10,X1,X4,X9)),esk43_4(X10,X1,X4,X9)))
      | hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(X9,X4,X10)),bot_bo1766443648a_bool))) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

tcf(c_0_31,plain,
    ! [X29: x_a,X1378: fun_state_bool] : hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X1378),X29) = X1378,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

tff(c_0_32,plain,
    ! [X2004: bool,X2005: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X2004),X2005) = X2004 ),
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U]) ).

tcf(c_0_33,plain,
    ! [X18: hoare_1544627872iple_a] :
      ( hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X18))
      | ~ hBOOL(bot_bot_bool) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

tcf(c_0_34,plain,
    ! [X18: hoare_1544627872iple_a] : ~ hBOOL(hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X18)),
    inference(sr,[status(thm)],[c_0_24,c_0_25]) ).

tcf(c_0_35,plain,
    ! [X25: bool] :
      ( ( hAPP_b704538998a_bool(cOMBK_329760839iple_a,X25) = bot_bo1766443648a_bool )
      | hBOOL(X25) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

tcf(c_0_36,plain,
    ! [X18: hoare_1544627872iple_a] : hAPP_H2006434664a_bool(bot_bo1766443648a_bool,X18) = fFalse,
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

tff(c_0_37,negated_conjecture,
    ~ hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(g),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_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_bo1766443648a_bool))),
    inference(fof_nnf,[status(thm)],[c_0_29]) ).

tcf(c_0_38,plain,
    ! [X1: fun_Ho287446294a_bool,X4: com,X9: fun_a_fun_state_bool,X1378: fun_state_bool] :
      ( hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X1378),X4,X9)),bot_bo1766443648a_bool)))
      | hBOOL(hAPP_state_bool(X1378,esk43_4(X9,X1,X4,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,X1378)))) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

tcf(c_0_39,plain,
    ! [X30: state,X25: bool] : hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,X25),X30) = X25,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

tcf(c_0_40,plain,
    ~ hBOOL(bot_bot_bool),
    inference(sr,[status(thm)],[c_0_33,c_0_34]) ).

tcf(c_0_41,plain,
    ! [X25: bool] :
      ( ( fFalse = X25 )
      | hBOOL(X25) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_36]) ).

tcf(c_0_42,negated_conjecture,
    ~ hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(g),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_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_bo1766443648a_bool))),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

tcf(c_0_43,plain,
    ! [X1: fun_Ho287446294a_bool,X4: com,X9: fun_a_fun_state_bool,X25: bool] :
      ( hBOOL(hAPP_f2063540982l_bool(hoare_1546678894rivs_a(X1),hAPP_f909437487a_bool(hAPP_H762155206a_bool(insert1051021594iple_a,hoare_196563068iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,X25)),X4,X9)),bot_bo1766443648a_bool)))
      | hBOOL(X25) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

tcf(c_0_44,plain,
    fFalse = bot_bot_bool,
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : SWW470_2 : TPTP v8.2.0. Released v5.3.0.
% 0.02/0.10  % Command    : run_E %s %d THM
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Sat May 18 20:12:07 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.14/0.41  Running first-order model finding
% 0.14/0.41  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.02/8.32  # Version: 3.1.0
% 62.02/8.32  # Preprocessing class: FMLMSMSLSSSNFFN.
% 62.02/8.32  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 62.02/8.32  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 62.02/8.32  # Starting new_bool_3 with 600s (2) cores
% 62.02/8.32  # Starting new_bool_1 with 600s (2) cores
% 62.02/8.32  # Starting sh5l with 300s (1) cores
% 62.02/8.32  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 22219 completed with status 0
% 62.02/8.32  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 62.02/8.32  # Preprocessing class: FMLMSMSLSSSNFFN.
% 62.02/8.32  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 62.02/8.32  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 62.02/8.32  # SinE strategy is gf600_h_gu_R05_F100_L20000
% 62.02/8.32  # Search class: FGHSM-SSLM32-DFFFFFNN
% 62.02/8.32  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 62.02/8.32  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 68s (1) cores
% 62.02/8.32  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 62.02/8.32  # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 68s (1) cores
% 62.02/8.32  # G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with pid 22228 completed with status 0
% 62.02/8.32  # Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN
% 62.02/8.32  # Preprocessing class: FMLMSMSLSSSNFFN.
% 62.02/8.32  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 62.02/8.32  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 62.02/8.32  # SinE strategy is gf600_h_gu_R05_F100_L20000
% 62.02/8.32  # Search class: FGHSM-SSLM32-DFFFFFNN
% 62.02/8.32  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 62.02/8.32  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 68s (1) cores
% 62.02/8.32  # Preprocessing time       : 0.017 s
% 62.02/8.32  # Presaturation interreduction done
% 62.02/8.32  
% 62.02/8.32  # Proof found!
% 62.02/8.32  # SZS status Theorem
% 62.02/8.32  # SZS output start CNFRefutation
% See solution above
% 62.02/8.32  # Parsed axioms                        : 1339
% 62.02/8.32  # Removed by relevancy pruning/SinE    : 614
% 62.02/8.32  # Initial clauses                      : 1084
% 62.02/8.32  # Removed in clause preprocessing      : 33
% 62.02/8.32  # Initial clauses in saturation        : 1051
% 62.02/8.32  # Processed clauses                    : 27021
% 62.02/8.32  # ...of these trivial                  : 306
% 62.02/8.32  # ...subsumed                          : 20791
% 62.02/8.32  # ...remaining for further processing  : 5924
% 62.02/8.32  # Other redundant clauses eliminated   : 734
% 62.02/8.32  # Clauses deleted for lack of memory   : 0
% 62.02/8.32  # Backward-subsumed                    : 107
% 62.02/8.32  # Backward-rewritten                   : 332
% 62.02/8.32  # Generated clauses                    : 220307
% 62.02/8.32  # ...of the previous two non-redundant : 199530
% 62.02/8.32  # ...aggressively subsumed             : 0
% 62.02/8.32  # Contextual simplify-reflections      : 30
% 62.02/8.32  # Paramodulations                      : 219508
% 62.02/8.32  # Factorizations                       : 39
% 62.02/8.32  # NegExts                              : 0
% 62.02/8.32  # Equation resolutions                 : 768
% 62.02/8.32  # Disequality decompositions           : 0
% 62.02/8.32  # Total rewrite steps                  : 61938
% 62.02/8.32  # ...of those cached                   : 56472
% 62.02/8.32  # Propositional unsat checks           : 1
% 62.02/8.32  #    Propositional check models        : 0
% 62.02/8.32  #    Propositional check unsatisfiable : 0
% 62.02/8.32  #    Propositional clauses             : 0
% 62.02/8.32  #    Propositional clauses after purity: 0
% 62.02/8.32  #    Propositional unsat core size     : 0
% 62.02/8.32  #    Propositional preprocessing time  : 0.000
% 62.02/8.32  #    Propositional encoding time       : 0.446
% 62.02/8.32  #    Propositional solver time         : 0.212
% 62.02/8.32  #    Success case prop preproc time    : 0.000
% 62.02/8.32  #    Success case prop encoding time   : 0.000
% 62.02/8.32  #    Success case prop solver time     : 0.000
% 62.02/8.32  # Current number of processed clauses  : 4607
% 62.02/8.32  #    Positive orientable unit clauses  : 446
% 62.02/8.32  #    Positive unorientable unit clauses: 40
% 62.02/8.32  #    Negative unit clauses             : 236
% 62.02/8.32  #    Non-unit-clauses                  : 3885
% 62.02/8.32  # Current number of unprocessed clauses: 172795
% 62.02/8.32  # ...number of literals in the above   : 532494
% 62.02/8.32  # Current number of archived formulas  : 0
% 62.02/8.32  # Current number of archived clauses   : 1235
% 62.02/8.32  # Clause-clause subsumption calls (NU) : 3263370
% 62.02/8.32  # Rec. Clause-clause subsumption calls : 1618092
% 62.02/8.32  # Non-unit clause-clause subsumptions  : 11213
% 62.02/8.32  # Unit Clause-clause subsumption calls : 39879
% 62.02/8.32  # Rewrite failures with RHS unbound    : 0
% 62.02/8.32  # BW rewrite match attempts            : 4916
% 62.02/8.32  # BW rewrite match successes           : 304
% 62.02/8.32  # Condensation attempts                : 0
% 62.02/8.32  # Condensation successes               : 0
% 62.02/8.32  # Termbank termtop insertions          : 7622188
% 62.02/8.32  # Search garbage collected termcells   : 15579
% 62.02/8.32  
% 62.02/8.32  # -------------------------------------------------
% 62.02/8.32  # User time                : 7.513 s
% 62.02/8.32  # System time              : 0.208 s
% 62.02/8.32  # Total time               : 7.721 s
% 62.02/8.32  # Maximum resident set size: 8576 pages
% 62.02/8.32  
% 62.02/8.32  # -------------------------------------------------
% 62.02/8.32  # User time                : 22.184 s
% 62.02/8.32  # System time              : 0.621 s
% 62.02/8.32  # Total time               : 22.804 s
% 62.02/8.32  # Maximum resident set size: 4072 pages
% 62.02/8.32  % E---3.1 exiting
%------------------------------------------------------------------------------