TSTP Solution File: ITP204^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP204^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 : Sat May  4 08:07:19 EDT 2024

% Result   : Theorem 0.45s 0.72s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   48 (   8 unt;  30 typ;   0 def)
%            Number of atoms       :   39 (  38 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  341 (  15   ~;   8   |;   5   &; 305   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :   10 (  10 usr)
%            Number of type conns  :  141 ( 141   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;   7 con; 0-3 aty)
%            Number of variables   :   92 (  88   ^   4   !;   0   ?;  92   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    option_fml: $tType ).

thf(decl_sort2,type,
    option_trm: $tType ).

thf(decl_sort3,type,
    set_variable: $tType ).

thf(decl_sort4,type,
    option_game: $tType ).

thf(decl_sort5,type,
    fml: $tType ).

thf(decl_sort6,type,
    trm: $tType ).

thf(decl_sort7,type,
    char: $tType ).

thf(decl_sort8,type,
    produc799602994n_game: $tType ).

thf(decl_sort9,type,
    produc62062515n_game: $tType ).

thf(decl_sort10,type,
    produc1418842292n_game: $tType ).

thf(decl_26,type,
    inf_inf_set_variable: set_variable > set_variable > set_variable ).

thf(decl_27,type,
    none_fml: option_fml ).

thf(decl_39,type,
    the_fml: option_fml > fml ).

thf(decl_41,type,
    the_trm: option_trm > trm ).

thf(decl_43,type,
    bot_bot_set_variable: set_variable ).

thf(decl_57,type,
    produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).

thf(decl_61,type,
    produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).

thf(decl_65,type,
    produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).

thf(decl_70,type,
    static_FVF: fml > set_variable ).

thf(decl_73,type,
    pred: char > trm > fml ).

thf(decl_77,type,
    uSubst1408967625substt: trm > produc1418842292n_game ).

thf(decl_79,type,
    uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).

thf(decl_80,type,
    uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).

thf(decl_83,type,
    va: set_variable ).

thf(decl_84,type,
    sigma: produc1418842292n_game ).

thf(decl_85,type,
    theta: trm ).

thf(decl_86,type,
    p: char ).

thf(decl_221,type,
    esk132_0: ( char > option_fml ) > ( char > option_game ) > char > option_fml ).

thf(decl_222,type,
    esk133_0: ( char > option_trm ) > produc799602994n_game > char > option_fml ).

thf(decl_223,type,
    esk134_0: ( char > option_trm ) > produc62062515n_game > char > option_fml ).

thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,axiom,
    ( ~ ( ( ( ( inf_inf_set_variable
              @ ( static_FVF
                @ ( the_fml
                  @ ( produc1250175341on_fml
                    @ ^ [X5: char > option_trm] :
                        ( produc1615133358on_fml
                        @ ^ [X6: char > option_trm] :
                            ( produc1420172399on_fml
                            @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
                    @ sigma
                    @ p ) ) )
              @ va )
            = bot_bot_set_variable )
         => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
              @ ( the_fml
                @ ( produc1250175341on_fml
                  @ ^ [X5: char > option_trm] :
                      ( produc1615133358on_fml
                      @ ^ [X6: char > option_trm] :
                          ( produc1420172399on_fml
                          @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
                  @ sigma
                  @ p ) ) )
            = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
        & ( ( ( inf_inf_set_variable
              @ ( static_FVF
                @ ( the_fml
                  @ ( produc1250175341on_fml
                    @ ^ [X5: char > option_trm] :
                        ( produc1615133358on_fml
                        @ ^ [X6: char > option_trm] :
                            ( produc1420172399on_fml
                            @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
                    @ sigma
                    @ p ) ) )
              @ va )
           != bot_bot_set_variable )
         => ( none_fml
            = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
   => ( ( produc1250175341on_fml
        @ ^ [X5: char > option_trm] :
            ( produc1615133358on_fml
            @ ^ [X6: char > option_trm] :
                ( produc1420172399on_fml
                @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
        @ sigma
        @ p )
      = none_fml ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9KcTFzypL5/E---3.1_7088.p',fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062) ).

thf(conj_0,conjecture,
    ( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
     != none_fml )
    | ( ( produc1250175341on_fml
        @ ^ [X5: char > option_trm] :
            ( produc1615133358on_fml
            @ ^ [X6: char > option_trm] :
                ( produc1420172399on_fml
                @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
        @ sigma
        @ p )
      = none_fml ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9KcTFzypL5/E---3.1_7088.p',conj_0) ).

thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,axiom,
    ~ ( ( ( inf_inf_set_variable
          @ ( static_FVF
            @ ( the_fml
              @ ( produc1250175341on_fml
                @ ^ [X5: char > option_trm] :
                    ( produc1615133358on_fml
                    @ ^ [X6: char > option_trm] :
                        ( produc1420172399on_fml
                        @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
                @ sigma
                @ p ) ) )
          @ va )
        = bot_bot_set_variable )
     => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
          @ ( the_fml
            @ ( produc1250175341on_fml
              @ ^ [X5: char > option_trm] :
                  ( produc1615133358on_fml
                  @ ^ [X6: char > option_trm] :
                      ( produc1420172399on_fml
                      @ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
              @ sigma
              @ p ) ) )
        = none_fml ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9KcTFzypL5/E---3.1_7088.p',fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062) ).

thf(c_0_3,plain,
    ( ~ ( ( ( ( inf_inf_set_variable
              @ ( static_FVF
                @ ( the_fml
                  @ ( produc1250175341on_fml
                    @ ^ [Z0: char > option_trm] :
                        ( produc1615133358on_fml
                        @ ^ [Z1: char > option_trm] :
                            ( produc1420172399on_fml
                            @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
                    @ sigma
                    @ p ) ) )
              @ va )
            = bot_bot_set_variable )
         => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
              @ ( the_fml
                @ ( produc1250175341on_fml
                  @ ^ [Z0: char > option_trm] :
                      ( produc1615133358on_fml
                      @ ^ [Z1: char > option_trm] :
                          ( produc1420172399on_fml
                          @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
                  @ sigma
                  @ p ) ) )
            = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
        & ( ( ( inf_inf_set_variable
              @ ( static_FVF
                @ ( the_fml
                  @ ( produc1250175341on_fml
                    @ ^ [Z0: char > option_trm] :
                        ( produc1615133358on_fml
                        @ ^ [Z1: char > option_trm] :
                            ( produc1420172399on_fml
                            @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
                    @ sigma
                    @ p ) ) )
              @ va )
           != bot_bot_set_variable )
         => ( none_fml
            = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
   => ( ( produc1250175341on_fml
        @ ^ [Z0: char > option_trm] :
            ( produc1615133358on_fml
            @ ^ [Z1: char > option_trm] :
                ( produc1420172399on_fml
                @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
        @ sigma
        @ p )
      = none_fml ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062])]) ).

thf(c_0_4,negated_conjecture,
    ~ ( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
       != none_fml )
      | ( ( produc1250175341on_fml
          @ ^ [Z0: char > option_trm] :
              ( produc1615133358on_fml
              @ ^ [Z1: char > option_trm] :
                  ( produc1420172399on_fml
                  @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
          @ sigma
          @ p )
        = none_fml ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])]) ).

thf(c_0_5,plain,
    ~ ( ( ( inf_inf_set_variable
          @ ( static_FVF
            @ ( the_fml
              @ ( produc1250175341on_fml
                @ ^ [Z0: char > option_trm] :
                    ( produc1615133358on_fml
                    @ ^ [Z1: char > option_trm] :
                        ( produc1420172399on_fml
                        @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
                @ sigma
                @ p ) ) )
          @ va )
        = bot_bot_set_variable )
     => ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
          @ ( the_fml
            @ ( produc1250175341on_fml
              @ ^ [Z0: char > option_trm] :
                  ( produc1615133358on_fml
                  @ ^ [Z1: char > option_trm] :
                      ( produc1420172399on_fml
                      @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
              @ sigma
              @ p ) ) )
        = none_fml ) ),
    inference(fof_simplification,[status(thm)],[fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062]) ).

thf(c_0_6,plain,
    ( ( ( ( inf_inf_set_variable
          @ ( static_FVF
            @ ( the_fml
              @ ( produc1250175341on_fml
                @ ^ [Z0: char > option_trm] :
                    ( produc1615133358on_fml
                    @ ^ [Z1: char > option_trm] :
                        ( produc1420172399on_fml
                        @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
                @ sigma
                @ p ) ) )
          @ va )
       != bot_bot_set_variable )
      | ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
          @ ( the_fml
            @ ( produc1250175341on_fml
              @ ^ [Z0: char > option_trm] :
                  ( produc1615133358on_fml
                  @ ^ [Z1: char > option_trm] :
                      ( produc1420172399on_fml
                      @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
              @ sigma
              @ p ) ) )
        = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) )
      | ( ( produc1250175341on_fml
          @ ^ [Z0: char > option_trm] :
              ( produc1615133358on_fml
              @ ^ [Z1: char > option_trm] :
                  ( produc1420172399on_fml
                  @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
          @ sigma
          @ p )
        = none_fml ) )
    & ( ( ( inf_inf_set_variable
          @ ( static_FVF
            @ ( the_fml
              @ ( produc1250175341on_fml
                @ ^ [Z0: char > option_trm] :
                    ( produc1615133358on_fml
                    @ ^ [Z1: char > option_trm] :
                        ( produc1420172399on_fml
                        @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
                @ sigma
                @ p ) ) )
          @ va )
        = bot_bot_set_variable )
      | ( none_fml
        = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) )
      | ( ( produc1250175341on_fml
          @ ^ [Z0: char > option_trm] :
              ( produc1615133358on_fml
              @ ^ [Z1: char > option_trm] :
                  ( produc1420172399on_fml
                  @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
          @ sigma
          @ p )
        = none_fml ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

thf(c_0_7,plain,
    ! [X2713: char > option_trm] :
      ( ( esk134_0 @ X2713 )
      = ( produc1615133358on_fml @ esk133_0 ) ),
    introduced(definition) ).

thf(c_0_8,plain,
    ! [X2712: char > option_trm] :
      ( ( esk133_0 @ X2712 )
      = ( produc1420172399on_fml @ esk132_0 ) ),
    introduced(definition) ).

thf(c_0_9,plain,
    ! [X2711: char > option_game,X2710: char > option_fml] :
      ( ( esk132_0 @ X2710 @ X2711 )
      = X2710 ),
    introduced(definition) ).

thf(c_0_10,negated_conjecture,
    ( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
      = none_fml )
    & ( ( produc1250175341on_fml
        @ ^ [Z0: char > option_trm] :
            ( produc1615133358on_fml
            @ ^ [Z1: char > option_trm] :
                ( produc1420172399on_fml
                @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
        @ sigma
        @ p )
     != none_fml ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

thf(c_0_11,plain,
    ( ( ( inf_inf_set_variable
        @ ( static_FVF
          @ ( the_fml
            @ ( produc1250175341on_fml
              @ ^ [Z0: char > option_trm] :
                  ( produc1615133358on_fml
                  @ ^ [Z1: char > option_trm] :
                      ( produc1420172399on_fml
                      @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
              @ sigma
              @ p ) ) )
        @ va )
      = bot_bot_set_variable )
    & ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
        @ ( the_fml
          @ ( produc1250175341on_fml
            @ ^ [Z0: char > option_trm] :
                ( produc1615133358on_fml
                @ ^ [Z1: char > option_trm] :
                    ( produc1420172399on_fml
                    @ ^ [Z2: char > option_fml,Z3: char > option_game] : Z2 ) )
            @ sigma
            @ p ) ) )
     != none_fml ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).

thf(c_0_12,plain,
    ( ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ ( the_fml @ ( produc1250175341on_fml @ esk134_0 @ sigma @ p ) ) )
      = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) )
    | ( ( produc1250175341on_fml @ esk134_0 @ sigma @ p )
      = none_fml )
    | ( ( inf_inf_set_variable @ ( static_FVF @ ( the_fml @ ( produc1250175341on_fml @ esk134_0 @ sigma @ p ) ) ) @ va )
     != bot_bot_set_variable ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6]),c_0_7]),c_0_8]),c_0_9]),c_0_7]),c_0_8]),c_0_9]),c_0_7]),c_0_8]),c_0_9]) ).

thf(c_0_13,negated_conjecture,
    ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
    = none_fml ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_14,plain,
    ( ( inf_inf_set_variable @ ( static_FVF @ ( the_fml @ ( produc1250175341on_fml @ esk134_0 @ sigma @ p ) ) ) @ va )
    = bot_bot_set_variable ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11]),c_0_7]),c_0_8]),c_0_9]) ).

thf(c_0_15,plain,
    ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ ( the_fml @ ( produc1250175341on_fml @ esk134_0 @ sigma @ p ) ) )
   != none_fml ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11]),c_0_7]),c_0_8]),c_0_9]) ).

thf(c_0_16,negated_conjecture,
    ( ( produc1250175341on_fml @ esk134_0 @ sigma @ p )
   != none_fml ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10]),c_0_7]),c_0_8]),c_0_9]) ).

thf(c_0_17,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_15]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.18  % Problem    : ITP204^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.19  % Command    : run_E %s %d THM
% 0.19/0.40  % Computer : n013.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit   : 300
% 0.19/0.40  % WCLimit    : 300
% 0.19/0.40  % DateTime   : Fri May  3 12:26:04 EDT 2024
% 0.25/0.40  % CPUTime    : 
% 0.26/0.60  Running higher-order theorem proving
% 0.26/0.60  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.9KcTFzypL5/E---3.1_7088.p
% 0.45/0.72  # Version: 3.1.0-ho
% 0.45/0.72  # Preprocessing class: HSLSSMSMSSLNHHA.
% 0.45/0.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.72  # Starting new_ho_10 with 1500s (5) cores
% 0.45/0.72  # Starting new_bool_2 with 300s (1) cores
% 0.45/0.72  # Starting lpo1_def_fix with 300s (1) cores
% 0.45/0.72  # Starting new_bool_3 with 300s (1) cores
% 0.45/0.72  # new_ho_10 with pid 7233 completed with status 0
% 0.45/0.72  # Result found by new_ho_10
% 0.45/0.72  # Preprocessing class: HSLSSMSMSSLNHHA.
% 0.45/0.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.72  # Starting new_ho_10 with 1500s (5) cores
% 0.45/0.72  # No SInE strategy applied
% 0.45/0.72  # Search class: HGHSM-FSLM31-MHHFFSBN
% 0.45/0.72  # partial match(1): HGHSM-FSLM31-MHFFFSBN
% 0.45/0.72  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.45/0.72  # Starting new_ho_10 with 901s (1) cores
% 0.45/0.72  # Starting pre_casc_8 with 151s (1) cores
% 0.45/0.72  # Starting additional_ho_6 with 151s (1) cores
% 0.45/0.72  # Starting full_lambda_10 with 151s (1) cores
% 0.45/0.72  # Starting new_ho_3 with 146s (1) cores
% 0.45/0.72  # new_ho_10 with pid 7258 completed with status 0
% 0.45/0.72  # Result found by new_ho_10
% 0.45/0.72  # Preprocessing class: HSLSSMSMSSLNHHA.
% 0.45/0.72  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.72  # Starting new_ho_10 with 1500s (5) cores
% 0.45/0.72  # No SInE strategy applied
% 0.45/0.72  # Search class: HGHSM-FSLM31-MHHFFSBN
% 0.45/0.72  # partial match(1): HGHSM-FSLM31-MHFFFSBN
% 0.45/0.72  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.45/0.72  # Starting new_ho_10 with 901s (1) cores
% 0.45/0.72  # Preprocessing time       : 0.012 s
% 0.45/0.72  # Presaturation interreduction done
% 0.45/0.72  
% 0.45/0.72  # Proof found!
% 0.45/0.72  # SZS status Theorem
% 0.45/0.72  # SZS output start CNFRefutation
% See solution above
% 0.45/0.72  # Parsed axioms                        : 438
% 0.45/0.72  # Removed by relevancy pruning/SinE    : 0
% 0.45/0.72  # Initial clauses                      : 955
% 0.45/0.72  # Removed in clause preprocessing      : 239
% 0.45/0.72  # Initial clauses in saturation        : 716
% 0.45/0.72  # Processed clauses                    : 85
% 0.45/0.72  # ...of these trivial                  : 3
% 0.45/0.72  # ...subsumed                          : 18
% 0.45/0.72  # ...remaining for further processing  : 63
% 0.45/0.72  # Other redundant clauses eliminated   : 17
% 0.45/0.72  # Clauses deleted for lack of memory   : 0
% 0.45/0.72  # Backward-subsumed                    : 0
% 0.45/0.72  # Backward-rewritten                   : 1
% 0.45/0.72  # Generated clauses                    : 17
% 0.45/0.72  # ...of the previous two non-redundant : 18
% 0.45/0.72  # ...aggressively subsumed             : 0
% 0.45/0.72  # Contextual simplify-reflections      : 0
% 0.45/0.72  # Paramodulations                      : 0
% 0.45/0.72  # Factorizations                       : 0
% 0.45/0.72  # NegExts                              : 0
% 0.45/0.72  # Equation resolutions                 : 17
% 0.45/0.72  # Disequality decompositions           : 0
% 0.45/0.72  # Total rewrite steps                  : 9
% 0.45/0.72  # ...of those cached                   : 6
% 0.45/0.72  # Propositional unsat checks           : 0
% 0.45/0.72  #    Propositional check models        : 0
% 0.45/0.72  #    Propositional check unsatisfiable : 0
% 0.45/0.72  #    Propositional clauses             : 0
% 0.45/0.72  #    Propositional clauses after purity: 0
% 0.45/0.72  #    Propositional unsat core size     : 0
% 0.45/0.72  #    Propositional preprocessing time  : 0.000
% 0.45/0.72  #    Propositional encoding time       : 0.000
% 0.45/0.72  #    Propositional solver time         : 0.000
% 0.45/0.72  #    Success case prop preproc time    : 0.000
% 0.45/0.72  #    Success case prop encoding time   : 0.000
% 0.45/0.72  #    Success case prop solver time     : 0.000
% 0.45/0.72  # Current number of processed clauses  : 45
% 0.45/0.72  #    Positive orientable unit clauses  : 23
% 0.45/0.72  #    Positive unorientable unit clauses: 1
% 0.45/0.72  #    Negative unit clauses             : 18
% 0.45/0.72  #    Non-unit-clauses                  : 3
% 0.45/0.72  # Current number of unprocessed clauses: 649
% 0.45/0.72  # ...number of literals in the above   : 1549
% 0.45/0.72  # Current number of archived formulas  : 0
% 0.45/0.72  # Current number of archived clauses   : 1
% 0.45/0.72  # Clause-clause subsumption calls (NU) : 3
% 0.45/0.72  # Rec. Clause-clause subsumption calls : 3
% 0.45/0.72  # Non-unit clause-clause subsumptions  : 1
% 0.45/0.72  # Unit Clause-clause subsumption calls : 40
% 0.45/0.72  # Rewrite failures with RHS unbound    : 0
% 0.45/0.72  # BW rewrite match attempts            : 2
% 0.45/0.72  # BW rewrite match successes           : 1
% 0.45/0.72  # Condensation attempts                : 85
% 0.45/0.72  # Condensation successes               : 0
% 0.45/0.72  # Termbank termtop insertions          : 61813
% 0.45/0.72  # Search garbage collected termcells   : 15986
% 0.45/0.72  
% 0.45/0.72  # -------------------------------------------------
% 0.45/0.72  # User time                : 0.069 s
% 0.45/0.72  # System time              : 0.015 s
% 0.45/0.72  # Total time               : 0.085 s
% 0.45/0.72  # Maximum resident set size: 6380 pages
% 0.45/0.72  
% 0.45/0.72  # -------------------------------------------------
% 0.45/0.72  # User time                : 0.143 s
% 0.45/0.72  # System time              : 0.044 s
% 0.45/0.72  # Total time               : 0.187 s
% 0.45/0.72  # Maximum resident set size: 2780 pages
% 0.45/0.72  % E---3.1 exiting
% 0.45/0.72  % E exiting
%------------------------------------------------------------------------------