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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWV451+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:55:33 PM UTC 2026

% Result   : Theorem 0.16s 5.97s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   46 (  21 unt;   0 def)
%            Number of atoms       :  327 ( 149 equ)
%            Maximal formula atoms :   51 (   7 avg)
%            Number of connectives :  437 ( 156   ~;  76   |; 131   &)
%                                         (   3 <=>;  71  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   26 (  26 usr;  16 con; 0-2 aty)
%            Number of variables   :  190 (  15 sgn 156   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj,conjecture,
    ! [X12,X13,X5,X6] :
      ( ( queue(host(X6)) = cons(m_NotNorm(X5),X12)
        & ! [X7,X16,X15,X14] :
            ( ( host(X14) = host(X15)
              & host(X16) = host(X7)
              & setIn(X15,alive)
              & setIn(X7,alive)
              & host(X15) != host(X7) )
           => ~ ( elem(m_Down(X16),queue(host(X15)))
                & elem(m_Down(X14),queue(host(X7))) ) )
        & ! [X7,X14] :
            ( ( host(X14) = host(X7)
              & X14 != X7 )
           => ( ~ setIn(X14,alive)
              | ~ setIn(X7,alive) ) )
        & ! [X7,X14] :
            ( ( host(X14) = host(X7)
              & leq(X14,X7)
              & ~ setIn(X7,alive) )
           => ~ setIn(X14,alive) )
        & ! [X7,X15,X14] :
            ( elem(m_Ack(X14,X7),queue(host(X15)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( elem(m_Halt(X14),queue(host(X7)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => host(X14) != host(X7) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( setIn(X14,alive)
           => ~ elem(m_Down(X14),queue(host(X7))) ) )
     => ( setIn(X6,alive)
       => ( ( index(elid,host(X6)) = X5
            & index(status,host(X6)) = norm
            & index(ldr,host(X6)) = host(X6) )
         => ( ( host(X6) = host(X13)
              & ~ setIn(X13,pids)
              & ! [X7] :
                  ( host(X6) = host(X7)
                 => leq(X7,X13) ) )
           => ( host(X13) = s(zero)
             => ( ~ leq(nbr_proc,host(X13))
               => ! [X7] :
                    ( s(host(X13)) = host(X7)
                   => ( host(X6) != host(X7)
                     => ! [X17,X18] :
                          ( s(host(X13)) != host(X18)
                         => ( host(X6) = host(X18)
                           => ! [X19] :
                                ( ( host(X19) = host(X18)
                                  & host(X17) = host(X7)
                                  & host(X18) != host(X7)
                                  & ( X18 = X13
                                    | ( setIn(X18,alive)
                                      & X18 != X6 ) )
                                  & ( X7 = X13
                                    | ( setIn(X7,alive)
                                      & X7 != X6 ) ) )
                               => ~ ( elem(m_Down(X19),snoc(queue(host(X7)),m_Halt(X13)))
                                    & elem(m_Down(X17),X12) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

fof(axiom_17,axiom,
    ! [X5,X6] : m_Down(X5) != m_Halt(X6),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_17) ).

fof(axiom_01,axiom,
    ! [X3,X4] :
      ( s(host(X3)) = host(X4)
     => host(X3) != host(X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_01) ).

fof(axiom_47,axiom,
    ! [X5,X6,X4] :
      ( elem(X5,snoc(X4,X6))
    <=> ( elem(X5,X4)
        | X5 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_47) ).

fof(axiom_46,axiom,
    ! [X5,X6,X4] :
      ( elem(X5,cons(X6,X4))
    <=> ( elem(X5,X4)
        | X5 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_46) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X12,X13,X5,X6] :
        ( ( queue(host(X6)) = cons(m_NotNorm(X5),X12)
          & ! [X7,X16,X15,X14] :
              ( ( host(X14) = host(X15)
                & host(X16) = host(X7)
                & setIn(X15,alive)
                & setIn(X7,alive)
                & host(X15) != host(X7) )
             => ~ ( elem(m_Down(X16),queue(host(X15)))
                  & elem(m_Down(X14),queue(host(X7))) ) )
          & ! [X7,X14] :
              ( ( host(X14) = host(X7)
                & X14 != X7 )
             => ( ~ setIn(X14,alive)
                | ~ setIn(X7,alive) ) )
          & ! [X7,X14] :
              ( ( host(X14) = host(X7)
                & leq(X14,X7)
                & ~ setIn(X7,alive) )
             => ~ setIn(X14,alive) )
          & ! [X7,X15,X14] :
              ( elem(m_Ack(X14,X7),queue(host(X15)))
             => ~ leq(host(X7),host(X14)) )
          & ! [X7,X14] :
              ( elem(m_Halt(X14),queue(host(X7)))
             => ~ leq(host(X7),host(X14)) )
          & ! [X7,X14] :
              ( elem(m_Down(X14),queue(host(X7)))
             => host(X14) != host(X7) )
          & ! [X7,X14] :
              ( elem(m_Down(X14),queue(host(X7)))
             => ~ setIn(X14,alive) )
          & ! [X7,X14] :
              ( setIn(X14,alive)
             => ~ elem(m_Down(X14),queue(host(X7))) ) )
       => ( setIn(X6,alive)
         => ( ( index(elid,host(X6)) = X5
              & index(status,host(X6)) = norm
              & index(ldr,host(X6)) = host(X6) )
           => ( ( host(X6) = host(X13)
                & ~ setIn(X13,pids)
                & ! [X7] :
                    ( host(X6) = host(X7)
                   => leq(X7,X13) ) )
             => ( host(X13) = s(zero)
               => ( ~ leq(nbr_proc,host(X13))
                 => ! [X7] :
                      ( s(host(X13)) = host(X7)
                     => ( host(X6) != host(X7)
                       => ! [X17,X18] :
                            ( s(host(X13)) != host(X18)
                           => ( host(X6) = host(X18)
                             => ! [X19] :
                                  ( ( host(X19) = host(X18)
                                    & host(X17) = host(X7)
                                    & host(X18) != host(X7)
                                    & ( X18 = X13
                                      | ( setIn(X18,alive)
                                        & X18 != X6 ) )
                                    & ( X7 = X13
                                      | ( setIn(X7,alive)
                                        & X7 != X6 ) ) )
                                 => ~ ( elem(m_Down(X19),snoc(queue(host(X7)),m_Halt(X13)))
                                      & elem(m_Down(X17),X12) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[conj]) ).

fof(c_0_6,plain,
    ! [X6,X5,X12] :
      ( epred1_3(X12,X5,X6)
    <=> ( queue(host(X6)) = cons(m_NotNorm(X5),X12)
        & ! [X7,X16,X15,X14] :
            ( ( host(X14) = host(X15)
              & host(X16) = host(X7)
              & setIn(X15,alive)
              & setIn(X7,alive)
              & host(X15) != host(X7) )
           => ~ ( elem(m_Down(X16),queue(host(X15)))
                & elem(m_Down(X14),queue(host(X7))) ) )
        & ! [X7,X14] :
            ( ( host(X14) = host(X7)
              & X14 != X7 )
           => ( ~ setIn(X14,alive)
              | ~ setIn(X7,alive) ) )
        & ! [X7,X14] :
            ( ( host(X14) = host(X7)
              & leq(X14,X7)
              & ~ setIn(X7,alive) )
           => ~ setIn(X14,alive) )
        & ! [X7,X15,X14] :
            ( elem(m_Ack(X14,X7),queue(host(X15)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( elem(m_Halt(X14),queue(host(X7)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => host(X14) != host(X7) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( setIn(X14,alive)
           => ~ elem(m_Down(X14),queue(host(X7))) ) ) ),
    introduced(definition) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X12,X13,X5,X6] :
        ( epred1_3(X12,X5,X6)
       => ( setIn(X6,alive)
         => ( ( index(elid,host(X6)) = X5
              & index(status,host(X6)) = norm
              & index(ldr,host(X6)) = host(X6) )
           => ( ( host(X6) = host(X13)
                & ~ setIn(X13,pids)
                & ! [X7] :
                    ( host(X6) = host(X7)
                   => leq(X7,X13) ) )
             => ( host(X13) = s(zero)
               => ( ~ leq(nbr_proc,host(X13))
                 => ! [X7] :
                      ( s(host(X13)) = host(X7)
                     => ( host(X6) != host(X7)
                       => ! [X17,X18] :
                            ( s(host(X13)) != host(X18)
                           => ( host(X6) = host(X18)
                             => ! [X19] :
                                  ( ( host(X19) = host(X18)
                                    & host(X17) = host(X7)
                                    & host(X18) != host(X7)
                                    & ( X18 = X13
                                      | ( setIn(X18,alive)
                                        & X18 != X6 ) )
                                    & ( X7 = X13
                                      | ( setIn(X7,alive)
                                        & X7 != X6 ) ) )
                                 => ~ ( elem(m_Down(X19),snoc(queue(host(X7)),m_Halt(X13)))
                                      & elem(m_Down(X17),X12) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5]),c_0_6]) ).

fof(c_0_8,plain,
    ! [X5,X6] : m_Down(X5) != m_Halt(X6),
    inference(fof_simplification,[status(thm)],[axiom_17]) ).

fof(c_0_9,plain,
    ! [X3,X4] :
      ( s(host(X3)) = host(X4)
     => host(X3) != host(X4) ),
    inference(fof_simplification,[status(thm)],[axiom_01]) ).

fof(c_0_10,negated_conjecture,
    ! [X153] :
      ( elem(m_Down(esk12_0),snoc(queue(host(esk9_0)),m_Halt(esk6_0)))
      & elem(m_Down(esk10_0),esk5_0)
      & host(esk12_0) = host(esk11_0)
      & host(esk10_0) = host(esk9_0)
      & host(esk11_0) != host(esk9_0)
      & ( esk11_0 = esk6_0
        | setIn(esk11_0,alive) )
      & ( esk11_0 = esk6_0
        | esk11_0 != esk8_0 )
      & ( esk9_0 = esk6_0
        | setIn(esk9_0,alive) )
      & ( esk9_0 = esk6_0
        | esk9_0 != esk8_0 )
      & host(esk8_0) = host(esk11_0)
      & s(host(esk6_0)) != host(esk11_0)
      & host(esk8_0) != host(esk9_0)
      & s(host(esk6_0)) = host(esk9_0)
      & ~ leq(nbr_proc,host(esk6_0))
      & host(esk6_0) = s(zero)
      & host(esk8_0) = host(esk6_0)
      & ~ setIn(esk6_0,pids)
      & ( leq(X153,esk6_0)
        | host(esk8_0) != host(X153) )
      & index(elid,host(esk8_0)) = esk7_0
      & index(status,host(esk8_0)) = norm
      & index(ldr,host(esk8_0)) = host(esk8_0)
      & setIn(esk8_0,alive)
      & epred1_3(esk5_0,esk7_0,esk8_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_7])])])])])]) ).

fof(c_0_11,plain,
    ! [X6,X5,X12] :
      ( epred1_3(X12,X5,X6)
     => ( queue(host(X6)) = cons(m_NotNorm(X5),X12)
        & ! [X7,X16,X15,X14] :
            ( ( host(X14) = host(X15)
              & host(X16) = host(X7)
              & setIn(X15,alive)
              & setIn(X7,alive)
              & host(X15) != host(X7) )
           => ~ ( elem(m_Down(X16),queue(host(X15)))
                & elem(m_Down(X14),queue(host(X7))) ) )
        & ! [X7,X14] :
            ( ( host(X14) = host(X7)
              & X14 != X7 )
           => ( ~ setIn(X14,alive)
              | ~ setIn(X7,alive) ) )
        & ! [X7,X14] :
            ( ( host(X14) = host(X7)
              & leq(X14,X7)
              & ~ setIn(X7,alive) )
           => ~ setIn(X14,alive) )
        & ! [X7,X15,X14] :
            ( elem(m_Ack(X14,X7),queue(host(X15)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( elem(m_Halt(X14),queue(host(X7)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => host(X14) != host(X7) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( setIn(X14,alive)
           => ~ elem(m_Down(X14),queue(host(X7))) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_6]) ).

fof(c_0_12,plain,
    ! [X103,X104,X105] :
      ( ( elem(X103,snoc(X105,X104))
        | ~ elem(X103,X105) )
      & ( elem(X103,snoc(X105,X104))
        | X103 != X104 )
      & ( elem(X103,X105)
        | X103 = X104
        | ~ elem(X103,snoc(X105,X104)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_47])])])]) ).

fof(c_0_13,plain,
    ! [X43,X44] : m_Down(X43) != m_Halt(X44),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).

fof(c_0_14,plain,
    ! [X22,X23] :
      ( host(X22) != host(X23)
      | s(host(X22)) != host(X23) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_15,negated_conjecture,
    host(esk12_0) = host(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    host(esk8_0) = host(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    s(host(esk6_0)) = host(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,negated_conjecture,
    host(esk8_0) = host(esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_19,plain,
    ! [X158,X159,X160,X161,X162,X163,X164,X165,X166,X167,X168,X169,X170,X171,X172,X173,X174,X175,X176,X177,X178,X179] :
      ( ( ~ epred1_3(X160,X159,X158)
        | queue(host(X158)) = cons(m_NotNorm(X159),X160) )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ elem(m_Down(X177),queue(host(X178)))
        | ~ elem(m_Down(X179),queue(host(X176)))
        | host(X179) != host(X178)
        | host(X177) != host(X176)
        | ~ setIn(X178,alive)
        | ~ setIn(X176,alive)
        | host(X178) = host(X176) )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ setIn(X175,alive)
        | ~ setIn(X174,alive)
        | host(X175) != host(X174)
        | X175 = X174 )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ setIn(X173,alive)
        | host(X173) != host(X172)
        | ~ leq(X173,X172)
        | setIn(X172,alive) )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ leq(host(X169),host(X171))
        | ~ elem(m_Ack(X171,X169),queue(host(X170))) )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ leq(host(X167),host(X168))
        | ~ elem(m_Halt(X168),queue(host(X167))) )
      & ( ~ epred1_3(X160,X159,X158)
        | host(X166) != host(X165)
        | ~ elem(m_Down(X166),queue(host(X165))) )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ setIn(X164,alive)
        | ~ elem(m_Down(X164),queue(host(X163))) )
      & ( ~ epred1_3(X160,X159,X158)
        | ~ elem(m_Down(X162),queue(host(X161)))
        | ~ setIn(X162,alive) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).

cnf(c_0_20,plain,
    ( ~ elem(X1,snoc(X2,X3))
    | elem(X1,X2)
    | X1 = X3 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_21,negated_conjecture,
    elem(m_Down(esk12_0),snoc(queue(host(esk9_0)),m_Halt(esk6_0))),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_22,plain,
    m_Down(X1) != m_Halt(X2),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,plain,
    ( host(X1) != host(X2)
    | s(host(X1)) != host(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_24,negated_conjecture,
    host(esk12_0) = host(esk8_0),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    s(host(esk8_0)) = host(esk9_0),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_26,plain,
    ! [X100,X101,X102] :
      ( ( elem(X100,cons(X101,X102))
        | ~ elem(X100,X102) )
      & ( elem(X100,cons(X101,X102))
        | X100 != X101 )
      & ( elem(X100,X102)
        | X100 = X101
        | ~ elem(X100,cons(X101,X102)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_46])])])]) ).

cnf(c_0_27,plain,
    ( ~ epred1_3(X3,X2,X1)
    | queue(host(X1)) = cons(m_NotNorm(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,negated_conjecture,
    epred1_3(esk5_0,esk7_0,esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_29,plain,
    ( ~ epred1_3(X5,X6,X7)
    | ~ elem(m_Down(X3),queue(host(X1)))
    | ~ elem(m_Down(X4),queue(host(X2)))
    | host(X4) != host(X1)
    | host(X3) != host(X2)
    | ~ setIn(X1,alive)
    | ~ setIn(X2,alive)
    | host(X1) = host(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_30,negated_conjecture,
    elem(m_Down(esk12_0),queue(host(esk9_0))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_31,negated_conjecture,
    ( host(esk8_0) != host(X1)
    | host(esk9_0) != host(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_32,plain,
    ( ~ elem(X1,X2)
    | elem(X1,cons(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    cons(m_NotNorm(esk7_0),esk5_0) = queue(host(esk8_0)),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ elem(m_Down(X1),queue(host(X2)))
    | ~ setIn(X2,alive)
    | ~ setIn(esk9_0,alive)
    | ~ epred1_3(X3,X4,X5)
    | host(X2) != host(esk8_0)
    | host(esk9_0) != host(X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]),c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ elem(X1,esk5_0)
    | elem(X1,queue(host(esk8_0))) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    setIn(esk8_0,alive),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ elem(m_Down(X1),esk5_0)
    | ~ setIn(esk9_0,alive)
    | ~ epred1_3(X2,X3,X4)
    | host(esk9_0) != host(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_38,negated_conjecture,
    elem(m_Down(esk10_0),esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_39,negated_conjecture,
    host(esk10_0) = host(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ setIn(esk9_0,alive)
    | ~ epred1_3(X1,X2,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).

cnf(c_0_41,negated_conjecture,
    ( esk9_0 = esk6_0
    | setIn(esk9_0,alive) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_42,negated_conjecture,
    ~ setIn(esk9_0,alive),
    inference(spm,[status(thm)],[c_0_40,c_0_28]) ).

cnf(c_0_43,negated_conjecture,
    host(esk8_0) != host(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_44,negated_conjecture,
    esk9_0 = esk6_0,
    inference(sr,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_18])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV451+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.39  % Computer : n015.cluster.edu
% 0.12/5.39  % Model    : x86_64 x86_64
% 0.12/5.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39  % Memory   : 8046.5625MB
% 0.12/5.39  % OS       : Linux 6.8.0-71-generic
% 0.12/5.39  % CPULimit : 300
% 0.12/5.39  % WCLimit  : 300
% 0.12/5.39  % DateTime : Mon Sep 21 08:55:26 UTC 2026
% 0.12/5.39  % CPUTime  : 
% 0.12/5.39  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.43  Running first-order theorem proving
% 0.16/5.43  Running: /export/starexec/sandbox2/solver/bin/eprover --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
% 0.16/5.97  % Version: 3.5.1
% 0.16/5.97  % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.97  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.97  % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.97  % Starting new_bool_3 with 300s (1) cores
% 0.16/5.97  % Starting new_bool_1 with 300s (1) cores
% 0.16/5.97  % Starting sh5l with 300s (1) cores
% 0.16/5.97  % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1091458 completed with status 0
% 0.16/5.97  % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.16/5.97  % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.97  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.97  % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.97  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.97  % No SInE strategy applied
% 0.16/5.97  % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.16/5.97  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.97  % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.97  % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.97  % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.16/5.97  % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.16/5.97  % Starting new_bool_3 with 136s (1) cores
% 0.16/5.97  % SAT001_MinMin_p005000_rr_RG with pid 1091466 completed with status 0
% 0.16/5.97  % Result found by SAT001_MinMin_p005000_rr_RG
% 0.16/5.97  % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/5.97  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.97  % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/5.97  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.97  % No SInE strategy applied
% 0.16/5.97  % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.16/5.97  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.97  % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.97  % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.16/5.97  % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.16/5.97  % Preprocessing time       : 0.003 s
% 0.16/5.97  % Presaturation interreduction done
% 0.16/5.97  
% 0.16/5.97  % Proof found!
% 0.16/5.97  % SZS status Theorem
% 0.16/5.97  % SZS output start CNFRefutation
% See solution above
% 0.16/5.97  % Parsed axioms                        : 67
% 0.16/5.97  % Removed by relevancy pruning/SinE    : 0
% 0.16/5.97  % Initial clauses                      : 128
% 0.16/5.97  % Removed in clause preprocessing      : 6
% 0.16/5.97  % Initial clauses in saturation        : 122
% 0.16/5.97  % Processed clauses                    : 4137
% 0.16/5.97  % ...of these trivial                  : 58
% 0.16/5.97  % ...subsumed                          : 2885
% 0.16/5.97  % ...remaining for further processing  : 1194
% 0.16/5.97  % Other redundant clauses eliminated   : 42
% 0.16/5.97  % Clauses deleted for lack of memory   : 0
% 0.16/5.97  % Backward-subsumed                    : 168
% 0.16/5.97  % Backward-rewritten                   : 27
% 0.16/5.97  % Generated clauses                    : 32212
% 0.16/5.97  % ...of the previous two non-redundant : 25002
% 0.16/5.97  % ...aggressively subsumed             : 0
% 0.16/5.97  % Contextual simplify-reflections      : 14
% 0.16/5.97  % Paramodulations                      : 32148
% 0.16/5.97  % Factorizations                       : 13
% 0.16/5.97  % NegExts                              : 0
% 0.16/5.97  % Equation resolutions                 : 50
% 0.16/5.97  % Disequality decompositions           : 0
% 0.16/5.97  % Total rewrite steps                  : 17756
% 0.16/5.97  % ...of those cached                   : 17563
% 0.16/5.97  % Propositional unsat checks           : 0
% 0.16/5.97  %    Propositional check models        : 0
% 0.16/5.97  %    Propositional check unsatisfiable : 0
% 0.16/5.97  %    Propositional clauses             : 0
% 0.16/5.97  %    Propositional clauses after purity: 0
% 0.16/5.97  %    Propositional unsat core size     : 0
% 0.16/5.97  %    Propositional preprocessing time  : 0.000
% 0.16/5.97  %    Propositional encoding time       : 0.000
% 0.16/5.97  %    Propositional solver time         : 0.000
% 0.16/5.97  %    Success case prop preproc time    : 0.000
% 0.16/5.97  %    Success case prop encoding time   : 0.000
% 0.16/5.97  %    Success case prop solver time     : 0.000
% 0.16/5.97  % Current number of processed clauses  : 877
% 0.16/5.97  %    Positive orientable unit clauses  : 78
% 0.16/5.97  %    Positive unorientable unit clauses: 0
% 0.16/5.97  %    Negative unit clauses             : 106
% 0.16/5.97  %    Non-unit-clauses                  : 693
% 0.16/5.97  % Current number of unprocessed clauses: 19315
% 0.16/5.97  % ...number of literals in the above   : 62692
% 0.16/5.97  % Current number of archived formulas  : 0
% 0.16/5.97  % Current number of archived clauses   : 310
% 0.16/5.97  % Clause-clause subsumption calls (NU) : 109237
% 0.16/5.97  % Rec. Clause-clause subsumption calls : 83948
% 0.16/5.97  % Non-unit clause-clause subsumptions  : 1575
% 0.16/5.97  % Unit Clause-clause subsumption calls : 6652
% 0.16/5.97  % Rewrite failures with RHS unbound    : 0
% 0.16/5.97  % BW rewrite match attempts            : 402
% 0.16/5.97  % BW rewrite match successes           : 15
% 0.16/5.97  % Condensation attempts                : 0
% 0.16/5.97  % Condensation successes               : 0
% 0.16/5.97  % Termbank termtop insertions          : 433780
% 0.16/5.97  % Search garbage collected termcells   : 1679
% 0.16/5.97  
% 0.16/5.97  % -------------------------------------------------
% 0.16/5.97  % User time                : 0.484 s
% 0.16/5.97  % System time              : 0.027 s
% 0.16/5.97  % Total time               : 0.511 s
% 0.16/5.97  % Maximum resident set size: 3976 pages
% 0.16/5.97  
% 0.16/5.97  % -------------------------------------------------
% 0.16/5.97  % User time                : 2.437 s
% 0.16/5.97  % System time              : 0.107 s
% 0.16/5.97  % Total time               : 2.543 s
% 0.16/5.97  % Maximum resident set size: 4608 pages
% 0.16/5.97  % E exiting
%------------------------------------------------------------------------------