TSTP Solution File: SEU461^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU461^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 03:27:29 EDT 2024

% Result   : Theorem 0.13s 0.47s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   61 (  17 unt;  18 typ;   0 def)
%            Number of atoms       :  113 (   7 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  617 (  34   ~;  75   |;  28   &; 459   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  110 ( 110   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18 usr;   4 con; 0-3 aty)
%            Number of variables   :   90 (  15   ^  75   !;   0   ?;  90   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf(decl_34,type,
    trans: ( $i > $i > $o ) > $o ).

thf(decl_35,type,
    tc: ( $i > $i > $o ) > $i > $i > $o ).

thf(decl_51,type,
    epred1_0: $i > $i > $o ).

thf(decl_52,type,
    esk1_0: $i ).

thf(decl_53,type,
    esk2_0: $i ).

thf(decl_54,type,
    esk3_0: $i ).

thf(decl_55,type,
    esk4_1: ( $i > $i > $o ) > $i ).

thf(decl_56,type,
    esk5_1: ( $i > $i > $o ) > $i ).

thf(decl_57,type,
    esk6_1: ( $i > $i > $o ) > $i ).

thf(decl_58,type,
    esk7_1: ( $i > $i > $o ) > $i ).

thf(decl_59,type,
    esk8_1: ( $i > $i > $o ) > $i ).

thf(decl_60,type,
    esk9_1: ( $i > $i > $o ) > $i ).

thf(decl_61,type,
    esk10_1: ( $i > $i > $o ) > $i ).

thf(decl_62,type,
    esk11_1: ( $i > $i > $o ) > $i ).

thf(decl_63,type,
    esk12_1: ( $i > $i > $o ) > $i ).

thf(decl_64,type,
    esk13_1: ( $i > $i > $o ) > $i ).

thf(decl_65,type,
    epred2_0: $i > $i > $o ).

thf(transitive_closure,axiom,
    ( tc
    = ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
        ! [X2: $i > $i > $o] :
          ( ( ( trans @ X2 )
            & ( subrel @ X1 @ X2 ) )
         => ( X2 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive_closure) ).

thf(subrel,axiom,
    ( subrel
    = ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( X1 @ X3 @ X4 )
         => ( X2 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',subrel) ).

thf(transitive,axiom,
    ( trans
    = ( ^ [X1: $i > $i > $o] :
        ! [X3: $i,X4: $i,X6: $i] :
          ( ( ( X1 @ X3 @ X4 )
            & ( X1 @ X4 @ X6 ) )
         => ( X1 @ X3 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).

thf(transitive_closure_is_transitive,conjecture,
    ! [X1: $i > $i > $o] : ( trans @ ( tc @ X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive) ).

thf(c_0_4,plain,
    ( tc
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
        ! [X2: $i > $i > $o] :
          ( ( ! [X16: $i,X17: $i,X18: $i] :
                ( ( ( X2 @ X16 @ X17 )
                  & ( X2 @ X17 @ X18 ) )
               => ( X2 @ X16 @ X18 ) )
            & ! [X19: $i,X20: $i] :
                ( ( Z0 @ X19 @ X20 )
               => ( X2 @ X19 @ X20 ) ) )
         => ( X2 @ Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive_closure]) ).

thf(c_0_5,plain,
    ( subrel
    = ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( Z0 @ X3 @ X4 )
         => ( Z1 @ X3 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[subrel]) ).

thf(c_0_6,plain,
    ( trans
    = ( ^ [Z0: $i > $i > $o] :
        ! [X3: $i,X4: $i,X6: $i] :
          ( ( ( Z0 @ X3 @ X4 )
            & ( Z0 @ X4 @ X6 ) )
         => ( Z0 @ X3 @ X6 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive]) ).

thf(c_0_7,plain,
    ( tc
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
        ! [X2: $i > $i > $o] :
          ( ( ! [X16: $i,X17: $i,X18: $i] :
                ( ( ( X2 @ X16 @ X17 )
                  & ( X2 @ X17 @ X18 ) )
               => ( X2 @ X16 @ X18 ) )
            & ! [X19: $i,X20: $i] :
                ( ( Z0 @ X19 @ X20 )
               => ( X2 @ X19 @ X20 ) ) )
         => ( X2 @ Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ~ ! [X1: $i > $i > $o,X164: $i,X165: $i,X166: $i] :
        ( ( ! [X158: $i > $i > $o] :
              ( ( ! [X159: $i,X160: $i,X161: $i] :
                    ( ( ( X158 @ X159 @ X160 )
                      & ( X158 @ X160 @ X161 ) )
                   => ( X158 @ X159 @ X161 ) )
                & ! [X162: $i,X163: $i] :
                    ( ( X1 @ X162 @ X163 )
                   => ( X158 @ X162 @ X163 ) ) )
             => ( X158 @ X164 @ X165 ) )
          & ! [X158: $i > $i > $o] :
              ( ( ! [X159: $i,X160: $i,X161: $i] :
                    ( ( ( X158 @ X159 @ X160 )
                      & ( X158 @ X160 @ X161 ) )
                   => ( X158 @ X159 @ X161 ) )
                & ! [X162: $i,X163: $i] :
                    ( ( X1 @ X162 @ X163 )
                   => ( X158 @ X162 @ X163 ) ) )
             => ( X158 @ X165 @ X166 ) ) )
       => ! [X158: $i > $i > $o] :
            ( ( ! [X159: $i,X160: $i,X161: $i] :
                  ( ( ( X158 @ X159 @ X160 )
                    & ( X158 @ X160 @ X161 ) )
                 => ( X158 @ X159 @ X161 ) )
              & ! [X162: $i,X163: $i] :
                  ( ( X1 @ X162 @ X163 )
                 => ( X158 @ X162 @ X163 ) ) )
           => ( X158 @ X164 @ X166 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[transitive_closure_is_transitive]),c_0_6]),c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ! [X171: $i > $i > $o,X177: $i > $i > $o,X184: $i,X185: $i,X186: $i,X187: $i,X188: $i] :
      ( ( ( epred1_0 @ ( esk7_1 @ X171 ) @ ( esk8_1 @ X171 ) )
        | ( X171 @ ( esk4_1 @ X171 ) @ ( esk5_1 @ X171 ) )
        | ( X171 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( X171 @ ( esk7_1 @ X171 ) @ ( esk8_1 @ X171 ) )
        | ( X171 @ ( esk4_1 @ X171 ) @ ( esk5_1 @ X171 ) )
        | ( X171 @ esk1_0 @ esk2_0 ) )
      & ( ( epred1_0 @ ( esk7_1 @ X171 ) @ ( esk8_1 @ X171 ) )
        | ( X171 @ ( esk5_1 @ X171 ) @ ( esk6_1 @ X171 ) )
        | ( X171 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( X171 @ ( esk7_1 @ X171 ) @ ( esk8_1 @ X171 ) )
        | ( X171 @ ( esk5_1 @ X171 ) @ ( esk6_1 @ X171 ) )
        | ( X171 @ esk1_0 @ esk2_0 ) )
      & ( ( epred1_0 @ ( esk7_1 @ X171 ) @ ( esk8_1 @ X171 ) )
        | ~ ( X171 @ ( esk4_1 @ X171 ) @ ( esk6_1 @ X171 ) )
        | ( X171 @ esk1_0 @ esk2_0 ) )
      & ( ~ ( X171 @ ( esk7_1 @ X171 ) @ ( esk8_1 @ X171 ) )
        | ~ ( X171 @ ( esk4_1 @ X171 ) @ ( esk6_1 @ X171 ) )
        | ( X171 @ esk1_0 @ esk2_0 ) )
      & ( ( epred1_0 @ ( esk12_1 @ X177 ) @ ( esk13_1 @ X177 ) )
        | ( X177 @ ( esk9_1 @ X177 ) @ ( esk10_1 @ X177 ) )
        | ( X177 @ esk2_0 @ esk3_0 ) )
      & ( ~ ( X177 @ ( esk12_1 @ X177 ) @ ( esk13_1 @ X177 ) )
        | ( X177 @ ( esk9_1 @ X177 ) @ ( esk10_1 @ X177 ) )
        | ( X177 @ esk2_0 @ esk3_0 ) )
      & ( ( epred1_0 @ ( esk12_1 @ X177 ) @ ( esk13_1 @ X177 ) )
        | ( X177 @ ( esk10_1 @ X177 ) @ ( esk11_1 @ X177 ) )
        | ( X177 @ esk2_0 @ esk3_0 ) )
      & ( ~ ( X177 @ ( esk12_1 @ X177 ) @ ( esk13_1 @ X177 ) )
        | ( X177 @ ( esk10_1 @ X177 ) @ ( esk11_1 @ X177 ) )
        | ( X177 @ esk2_0 @ esk3_0 ) )
      & ( ( epred1_0 @ ( esk12_1 @ X177 ) @ ( esk13_1 @ X177 ) )
        | ~ ( X177 @ ( esk9_1 @ X177 ) @ ( esk11_1 @ X177 ) )
        | ( X177 @ esk2_0 @ esk3_0 ) )
      & ( ~ ( X177 @ ( esk12_1 @ X177 ) @ ( esk13_1 @ X177 ) )
        | ~ ( X177 @ ( esk9_1 @ X177 ) @ ( esk11_1 @ X177 ) )
        | ( X177 @ esk2_0 @ esk3_0 ) )
      & ( ~ ( epred2_0 @ X184 @ X185 )
        | ~ ( epred2_0 @ X185 @ X186 )
        | ( epred2_0 @ X184 @ X186 ) )
      & ( ~ ( epred1_0 @ X187 @ X188 )
        | ( epred2_0 @ X187 @ X188 ) )
      & ~ ( epred2_0 @ esk1_0 @ esk3_0 ) ),
    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)],[c_0_8])])])])])]) ).

thf(c_0_10,negated_conjecture,
    ! [X3: $i,X4: $i,X6: $i] :
      ( ( epred2_0 @ X3 @ X6 )
      | ~ ( epred2_0 @ X3 @ X4 )
      | ~ ( epred2_0 @ X4 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
      | ( X1 @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
      | ( X1 @ esk2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_12,negated_conjecture,
    ! [X3: $i] :
      ( ( epred1_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) )
      | ( epred2_0 @ X3 @ ( esk11_1 @ epred2_0 ) )
      | ( epred2_0 @ esk2_0 @ esk3_0 )
      | ~ ( epred2_0 @ X3 @ ( esk10_1 @ epred2_0 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
      | ( X1 @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
      | ( X1 @ esk2_0 @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
      | ( X1 @ esk2_0 @ esk3_0 )
      | ~ ( X1 @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
      | ( X1 @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
      | ( X1 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_16,negated_conjecture,
    ! [X3: $i,X4: $i] :
      ( ( epred2_0 @ X3 @ X4 )
      | ~ ( epred1_0 @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_17,negated_conjecture,
    ( ( epred1_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) )
    | ( epred2_0 @ esk2_0 @ esk3_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

thf(c_0_18,negated_conjecture,
    ! [X3: $i] :
      ( ( epred1_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) )
      | ( epred2_0 @ X3 @ ( esk6_1 @ epred2_0 ) )
      | ( epred2_0 @ esk1_0 @ esk2_0 )
      | ~ ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_15]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
      | ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
      | ( X1 @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_20,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
      | ( X1 @ esk1_0 @ esk2_0 )
      | ~ ( X1 @ ( esk4_1 @ X1 ) @ ( esk6_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_21,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( X1 @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
      | ( X1 @ esk2_0 @ esk3_0 )
      | ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_22,negated_conjecture,
    ( ( epred2_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) )
    | ( epred2_0 @ esk2_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_23,negated_conjecture,
    ( ( epred1_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) )
    | ( epred2_0 @ esk1_0 @ esk2_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

thf(c_0_24,negated_conjecture,
    ( ( epred2_0 @ ( esk10_1 @ epred2_0 ) @ ( esk11_1 @ epred2_0 ) )
    | ( epred2_0 @ esk2_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_25,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( X1 @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
      | ( X1 @ esk2_0 @ esk3_0 )
      | ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_26,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( X1 @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
      | ( X1 @ esk1_0 @ esk2_0 )
      | ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_27,negated_conjecture,
    ( ( epred2_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) )
    | ( epred2_0 @ esk1_0 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_23]) ).

thf(c_0_28,negated_conjecture,
    ! [X3: $i] :
      ( ( epred2_0 @ X3 @ ( esk11_1 @ epred2_0 ) )
      | ( epred2_0 @ esk2_0 @ esk3_0 )
      | ~ ( epred2_0 @ X3 @ ( esk10_1 @ epred2_0 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_24]) ).

thf(c_0_29,negated_conjecture,
    ( ( epred2_0 @ ( esk9_1 @ epred2_0 ) @ ( esk10_1 @ epred2_0 ) )
    | ( epred2_0 @ esk2_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_22]) ).

thf(c_0_30,negated_conjecture,
    ( ( epred2_0 @ ( esk5_1 @ epred2_0 ) @ ( esk6_1 @ epred2_0 ) )
    | ( epred2_0 @ esk1_0 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

thf(c_0_31,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
      | ( X1 @ esk1_0 @ esk2_0 )
      | ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_32,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( X1 @ esk2_0 @ esk3_0 )
      | ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
      | ~ ( X1 @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_33,negated_conjecture,
    ( ( epred2_0 @ ( esk9_1 @ epred2_0 ) @ ( esk11_1 @ epred2_0 ) )
    | ( epred2_0 @ esk2_0 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_34,negated_conjecture,
    ! [X3: $i] :
      ( ( epred2_0 @ X3 @ ( esk6_1 @ epred2_0 ) )
      | ( epred2_0 @ esk1_0 @ esk2_0 )
      | ~ ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_30]) ).

thf(c_0_35,negated_conjecture,
    ( ( epred2_0 @ ( esk4_1 @ epred2_0 ) @ ( esk5_1 @ epred2_0 ) )
    | ( epred2_0 @ esk1_0 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_31,c_0_27]) ).

thf(c_0_36,negated_conjecture,
    epred2_0 @ esk2_0 @ esk3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_22]) ).

thf(c_0_37,negated_conjecture,
    ! [X1: $i > $i > $o] :
      ( ( X1 @ esk1_0 @ esk2_0 )
      | ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
      | ~ ( X1 @ ( esk4_1 @ X1 ) @ ( esk6_1 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_38,negated_conjecture,
    ( ( epred2_0 @ ( esk4_1 @ epred2_0 ) @ ( esk6_1 @ epred2_0 ) )
    | ( epred2_0 @ esk1_0 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

thf(c_0_39,negated_conjecture,
    ! [X3: $i] :
      ( ( epred2_0 @ X3 @ esk3_0 )
      | ~ ( epred2_0 @ X3 @ esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_36]) ).

thf(c_0_40,negated_conjecture,
    epred2_0 @ esk1_0 @ esk2_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_27]) ).

thf(c_0_41,negated_conjecture,
    ~ ( epred2_0 @ esk1_0 @ esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_42,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem    : SEU461^1 : TPTP v8.2.0. Released v3.6.0.
% 0.08/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n028.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Sun May 19 17:17:37 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.13/0.43  Running higher-order theorem proving
% 0.13/0.43  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/benchmark/theBenchmark.p
% 0.13/0.47  # Version: 3.1.0-ho
% 0.13/0.47  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.13/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47  # Starting new_ho_9 with 1500s (5) cores
% 0.13/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.13/0.47  # Starting sh1l with 300s (1) cores
% 0.13/0.47  # Starting post_as_ho10 with 300s (1) cores
% 0.13/0.47  # sh1l with pid 29741 completed with status 0
% 0.13/0.47  # Result found by sh1l
% 0.13/0.47  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.13/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47  # Starting new_ho_9 with 1500s (5) cores
% 0.13/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.13/0.47  # Starting sh1l with 300s (1) cores
% 0.13/0.47  # No SInE strategy applied
% 0.13/0.47  # Search class: HGUNF-FFSF11-SHSSMMBN
% 0.13/0.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.47  # Starting ehoh_best2_full_lfho with 181s (1) cores
% 0.13/0.47  # ehoh_best2_full_lfho with pid 29744 completed with status 0
% 0.13/0.47  # Result found by ehoh_best2_full_lfho
% 0.13/0.47  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.13/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47  # Starting new_ho_9 with 1500s (5) cores
% 0.13/0.47  # Starting post_as_ho1 with 300s (1) cores
% 0.13/0.47  # Starting sh1l with 300s (1) cores
% 0.13/0.47  # No SInE strategy applied
% 0.13/0.47  # Search class: HGUNF-FFSF11-SHSSMMBN
% 0.13/0.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.47  # Starting ehoh_best2_full_lfho with 181s (1) cores
% 0.13/0.47  # Preprocessing time       : 0.005 s
% 0.13/0.47  
% 0.13/0.47  # Proof found!
% 0.13/0.47  # SZS status Theorem
% 0.13/0.47  # SZS output start CNFRefutation
% See solution above
% 0.13/0.47  # Parsed axioms                        : 59
% 0.13/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.13/0.47  # Initial clauses                      : 44
% 0.13/0.47  # Removed in clause preprocessing      : 29
% 0.13/0.47  # Initial clauses in saturation        : 15
% 0.13/0.47  # Processed clauses                    : 69
% 0.13/0.47  # ...of these trivial                  : 3
% 0.13/0.47  # ...subsumed                          : 6
% 0.13/0.47  # ...remaining for further processing  : 60
% 0.13/0.47  # Other redundant clauses eliminated   : 2
% 0.13/0.47  # Clauses deleted for lack of memory   : 0
% 0.13/0.47  # Backward-subsumed                    : 4
% 0.13/0.47  # Backward-rewritten                   : 15
% 0.13/0.47  # Generated clauses                    : 200
% 0.13/0.47  # ...of the previous two non-redundant : 165
% 0.13/0.47  # ...aggressively subsumed             : 0
% 0.13/0.47  # Contextual simplify-reflections      : 5
% 0.13/0.47  # Paramodulations                      : 52
% 0.13/0.47  # Factorizations                       : 0
% 0.13/0.47  # NegExts                              : 3
% 0.13/0.47  # Equation resolutions                 : 2
% 0.13/0.47  # Disequality decompositions           : 0
% 0.13/0.47  # Total rewrite steps                  : 18
% 0.13/0.47  # ...of those cached                   : 13
% 0.13/0.47  # Propositional unsat checks           : 0
% 0.13/0.47  #    Propositional check models        : 0
% 0.13/0.47  #    Propositional check unsatisfiable : 0
% 0.13/0.47  #    Propositional clauses             : 0
% 0.13/0.47  #    Propositional clauses after purity: 0
% 0.13/0.47  #    Propositional unsat core size     : 0
% 0.13/0.47  #    Propositional preprocessing time  : 0.000
% 0.13/0.47  #    Propositional encoding time       : 0.000
% 0.13/0.47  #    Propositional solver time         : 0.000
% 0.13/0.47  #    Success case prop preproc time    : 0.000
% 0.13/0.47  #    Success case prop encoding time   : 0.000
% 0.13/0.47  #    Success case prop solver time     : 0.000
% 0.13/0.47  # Current number of processed clauses  : 36
% 0.13/0.47  #    Positive orientable unit clauses  : 7
% 0.13/0.47  #    Positive unorientable unit clauses: 0
% 0.13/0.47  #    Negative unit clauses             : 1
% 0.13/0.47  #    Non-unit-clauses                  : 28
% 0.13/0.47  # Current number of unprocessed clauses: 105
% 0.13/0.47  # ...number of literals in the above   : 361
% 0.13/0.47  # Current number of archived formulas  : 0
% 0.13/0.47  # Current number of archived clauses   : 24
% 0.13/0.47  # Clause-clause subsumption calls (NU) : 367
% 0.13/0.47  # Rec. Clause-clause subsumption calls : 260
% 0.13/0.47  # Non-unit clause-clause subsumptions  : 15
% 0.13/0.47  # Unit Clause-clause subsumption calls : 26
% 0.13/0.47  # Rewrite failures with RHS unbound    : 0
% 0.13/0.47  # BW rewrite match attempts            : 3
% 0.13/0.47  # BW rewrite match successes           : 3
% 0.13/0.47  # Condensation attempts                : 0
% 0.13/0.47  # Condensation successes               : 0
% 0.13/0.47  # Termbank termtop insertions          : 11088
% 0.13/0.47  # Search garbage collected termcells   : 989
% 0.13/0.47  
% 0.13/0.47  # -------------------------------------------------
% 0.13/0.47  # User time                : 0.015 s
% 0.13/0.47  # System time              : 0.009 s
% 0.13/0.47  # Total time               : 0.024 s
% 0.13/0.47  # Maximum resident set size: 2136 pages
% 0.13/0.47  
% 0.13/0.47  # -------------------------------------------------
% 0.13/0.47  # User time                : 0.016 s
% 0.13/0.47  # System time              : 0.012 s
% 0.13/0.47  # Total time               : 0.028 s
% 0.13/0.47  # Maximum resident set size: 1784 pages
% 0.13/0.47  % E---3.1 exiting
% 0.13/0.47  % E exiting
%------------------------------------------------------------------------------