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Prover9---2026-6A.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Prover9---2026-6A
% Problem  : LAT385+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n018.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 : Sun Sep 27 07:50:30 AM UTC 2026

% Result   : Theorem 0.09s 0.45s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   18 (   6 unt;   0 def)
%            Number of atoms       :  324 (   9 equ)
%            Maximal formula atoms :  159 (  18 avg)
%            Number of connectives :  430 ( 124   ~; 146   |; 140   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   53 (  10 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :  114 (   1 sgn 101   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__1123,axiom,
    ( isOn0(xf,xU)
    & szRzazndt0(xf) = xU
    & szDzozmdt0(xf) = szRzazndt0(xf)
    & isMonotone0(xf)
    & ! [W0,W1] :
        ( ( aElementOf0(W1,szDzozmdt0(xf))
          & aElementOf0(W0,szDzozmdt0(xf)) )
       => ( sdtlseqdt0(W0,W1)
         => sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ) )
    & aFunction0(xf)
    & aCompleteLattice0(xU)
    & ! [W0] :
        ( ( aSubsetOf0(W0,xU)
          | ( ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xU) )
            & aSet0(W0) ) )
       => ? [W1] :
            ( ? [W2] :
                ( aSupremumOfIn0(W2,W0,xU)
                & ! [W3] :
                    ( ( aUpperBoundOfIn0(W3,W0,xU)
                      | ( ! [W4] :
                            ( aElementOf0(W4,W0)
                           => sdtlseqdt0(W4,W3) )
                        & aElementOf0(W3,xU) ) )
                   => sdtlseqdt0(W2,W3) )
                & aUpperBoundOfIn0(W2,W0,xU)
                & ! [W3] :
                    ( aElementOf0(W3,W0)
                   => sdtlseqdt0(W3,W2) )
                & aElementOf0(W2,xU)
                & aElementOf0(W2,xU) )
            & aInfimumOfIn0(W1,W0,xU)
            & ! [W2] :
                ( ( aLowerBoundOfIn0(W2,W0,xU)
                  | ( ! [W3] :
                        ( aElementOf0(W3,W0)
                       => sdtlseqdt0(W2,W3) )
                    & aElementOf0(W2,xU) ) )
               => sdtlseqdt0(W2,W1) )
            & aLowerBoundOfIn0(W1,W0,xU)
            & ! [W2] :
                ( aElementOf0(W2,W0)
               => sdtlseqdt0(W1,W2) )
            & aElementOf0(W1,xU)
            & aElementOf0(W1,xU) ) )
    & aSet0(xU) ),
    file('theBenchmark.p',m__1123) ).

fof(m__1244,axiom,
    ( xP = cS1241(xU,xf,xT)
    & ! [W0] :
        ( ( ( ( aUpperBoundOfIn0(W0,xT,xU)
              | ! [W1] :
                  ( aElementOf0(W1,xT)
                 => sdtlseqdt0(W1,W0) ) )
            & sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
            & aElementOf0(W0,xU) )
         => aElementOf0(W0,xP) )
        & ( aElementOf0(W0,xP)
         => ( aUpperBoundOfIn0(W0,xT,xU)
            & ! [W1] :
                ( aElementOf0(W1,xT)
               => sdtlseqdt0(W1,W0) )
            & sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
            & aElementOf0(W0,xU) ) ) )
    & aSet0(xP) ),
    file('theBenchmark.p',m__1244) ).

fof(m__,conjecture,
    ? [W0] :
      ( aInfimumOfIn0(W0,xP,xU)
      | ( ! [W1] :
            ( ( aLowerBoundOfIn0(W1,xP,xU)
              & ! [W2] :
                  ( aElementOf0(W2,xP)
                 => sdtlseqdt0(W1,W2) )
              & aElementOf0(W1,xU) )
           => sdtlseqdt0(W1,W0) )
        & ( aLowerBoundOfIn0(W0,xP,xU)
          | ( ! [W1] :
                ( aElementOf0(W1,xP)
               => sdtlseqdt0(W0,W1) )
            & aElementOf0(W0,xU) ) )
        & aElementOf0(W0,xU) ) ),
    file('theBenchmark.p',m__) ).

fof(m___neg,negated_conjecture,
    ~ ? [W0] :
        ( aInfimumOfIn0(W0,xP,xU)
        | ( ! [W1] :
              ( ( aLowerBoundOfIn0(W1,xP,xU)
                & ! [W2] :
                    ( aElementOf0(W2,xP)
                   => sdtlseqdt0(W1,W2) )
                & aElementOf0(W1,xU) )
             => sdtlseqdt0(W1,W0) )
          & ( aLowerBoundOfIn0(W0,xP,xU)
            | ( ! [W1] :
                  ( aElementOf0(W1,xP)
                 => sdtlseqdt0(W0,W1) )
              & aElementOf0(W0,xU) ) )
          & aElementOf0(W0,xU) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(nnf_24,plain,
    ( isOn0(xf,xU)
    & szRzazndt0(xf) = xU
    & szRzazndt0(xf) = szDzozmdt0(xf)
    & isMonotone0(xf)
    & ! [W0,W1] :
        ( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
        | ~ sdtlseqdt0(W0,W1)
        | ~ aElementOf0(W1,szDzozmdt0(xf))
        | ~ aElementOf0(W0,szDzozmdt0(xf)) )
    & aFunction0(xf)
    & aCompleteLattice0(xU)
    & ! [X0] :
        ( ? [X2] :
            ( ? [W2] :
                ( aSupremumOfIn0(W2,X0,xU)
                & ! [W3] :
                    ( sdtlseqdt0(W2,W3)
                    | ( ~ aUpperBoundOfIn0(W3,X0,xU)
                      & ( ? [W4] :
                            ( ~ sdtlseqdt0(W4,W3)
                            & aElementOf0(W4,X0) )
                        | ~ aElementOf0(W3,xU) ) ) )
                & aUpperBoundOfIn0(W2,X0,xU)
                & ! [X6] :
                    ( sdtlseqdt0(X6,W2)
                    | ~ aElementOf0(X6,X0) )
                & aElementOf0(W2,xU)
                & aElementOf0(W2,xU) )
            & aInfimumOfIn0(X2,X0,xU)
            & ! [X4] :
                ( sdtlseqdt0(X4,X2)
                | ( ~ aLowerBoundOfIn0(X4,X0,xU)
                  & ( ? [X5] :
                        ( ~ sdtlseqdt0(X4,X5)
                        & aElementOf0(X5,X0) )
                    | ~ aElementOf0(X4,xU) ) ) )
            & aLowerBoundOfIn0(X2,X0,xU)
            & ! [X3] :
                ( sdtlseqdt0(X2,X3)
                | ~ aElementOf0(X3,X0) )
            & aElementOf0(X2,xU)
            & aElementOf0(X2,xU) )
        | ( ~ aSubsetOf0(X0,xU)
          & ( ? [X1] :
                ( ~ aElementOf0(X1,xU)
                & aElementOf0(X1,X0) )
            | ~ aSet0(X0) ) ) )
    & aSet0(xU) ),
    inference(fof_nnf,[status(thm)],[m__1123]) ).

fof(sk_m__1123_sk,plain,
    ( isOn0(xf,xU)
    & szRzazndt0(xf) = xU
    & szRzazndt0(xf) = szDzozmdt0(xf)
    & isMonotone0(xf)
    & ! [W0,W1] :
        ( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
        | ~ sdtlseqdt0(W0,W1)
        | ~ aElementOf0(W1,szDzozmdt0(xf))
        | ~ aElementOf0(W0,szDzozmdt0(xf)) )
    & aFunction0(xf)
    & aCompleteLattice0(xU)
    & ! [X0] :
        ( ( aSupremumOfIn0(sK3(X0),X0,xU)
          & ! [W3] :
              ( sdtlseqdt0(sK3(X0),W3)
              | ( ~ aUpperBoundOfIn0(W3,X0,xU)
                & ( ( ~ sdtlseqdt0(sK4(X0,W3),W3)
                    & aElementOf0(sK4(X0,W3),X0) )
                  | ~ aElementOf0(W3,xU) ) ) )
          & aUpperBoundOfIn0(sK3(X0),X0,xU)
          & ! [X6] :
              ( sdtlseqdt0(X6,sK3(X0))
              | ~ aElementOf0(X6,X0) )
          & aElementOf0(sK3(X0),xU)
          & aElementOf0(sK3(X0),xU)
          & aInfimumOfIn0(sK1(X0),X0,xU)
          & ! [X4] :
              ( sdtlseqdt0(X4,sK1(X0))
              | ( ~ aLowerBoundOfIn0(X4,X0,xU)
                & ( ( ~ sdtlseqdt0(X4,sK2(X0,X4))
                    & aElementOf0(sK2(X0,X4),X0) )
                  | ~ aElementOf0(X4,xU) ) ) )
          & aLowerBoundOfIn0(sK1(X0),X0,xU)
          & ! [X3] :
              ( sdtlseqdt0(sK1(X0),X3)
              | ~ aElementOf0(X3,X0) )
          & aElementOf0(sK1(X0),xU)
          & aElementOf0(sK1(X0),xU) )
        | ( ~ aSubsetOf0(X0,xU)
          & ( ( ~ aElementOf0(sK0(X0),xU)
              & aElementOf0(sK0(X0),X0) )
            | ~ aSet0(X0) ) ) )
    & aSet0(xU) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0)),skolemize(X5,sK2(X0,X4)),skolemize(W2,sK3(X0)),skolemize(W4,sK4(X0,W3))],[nnf_24]) ).

fof(sk_m__1123,plain,
    ( isOn0(xf,xU)
    & szRzazndt0(xf) = xU
    & szRzazndt0(xf) = szDzozmdt0(xf)
    & isMonotone0(xf)
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sdtlpdtrp0(xf,VAR_0),sdtlpdtrp0(xf,VAR_1))
        | ~ sdtlseqdt0(VAR_0,VAR_1)
        | ~ aElementOf0(VAR_1,szDzozmdt0(xf))
        | ~ aElementOf0(VAR_0,szDzozmdt0(xf)) )
    & aFunction0(xf)
    & aCompleteLattice0(xU)
    & ! [VAR_0] :
        ( aSupremumOfIn0(sK3(VAR_0),VAR_0,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | ~ aUpperBoundOfIn0(VAR_1,VAR_0,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | ~ sdtlseqdt0(sK4(VAR_0,VAR_1),VAR_1)
        | ~ aElementOf0(VAR_1,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | aElementOf0(sK4(VAR_0,VAR_1),VAR_0)
        | ~ aElementOf0(VAR_1,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0] :
        ( aUpperBoundOfIn0(sK3(VAR_0),VAR_0,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK3(VAR_0))
        | ~ aElementOf0(VAR_1,VAR_0)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0] :
        ( aElementOf0(sK3(VAR_0),xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0] :
        ( aInfimumOfIn0(sK1(VAR_0),VAR_0,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | ~ aLowerBoundOfIn0(VAR_1,VAR_0,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | ~ sdtlseqdt0(VAR_1,sK2(VAR_0,VAR_1))
        | ~ aElementOf0(VAR_1,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | aElementOf0(sK2(VAR_0,VAR_1),VAR_0)
        | ~ aElementOf0(VAR_1,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0] :
        ( aLowerBoundOfIn0(sK1(VAR_0),VAR_0,xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK1(VAR_0),VAR_1)
        | ~ aElementOf0(VAR_1,VAR_0)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0] :
        ( aElementOf0(sK1(VAR_0),xU)
        | ~ aSubsetOf0(VAR_0,xU) )
    & ! [VAR_0] :
        ( aSupremumOfIn0(sK3(VAR_0),VAR_0,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | ~ aUpperBoundOfIn0(VAR_1,VAR_0,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | ~ sdtlseqdt0(sK4(VAR_0,VAR_1),VAR_1)
        | ~ aElementOf0(VAR_1,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | aElementOf0(sK4(VAR_0,VAR_1),VAR_0)
        | ~ aElementOf0(VAR_1,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aUpperBoundOfIn0(sK3(VAR_0),VAR_0,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK3(VAR_0))
        | ~ aElementOf0(VAR_1,VAR_0)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aElementOf0(sK3(VAR_0),xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aInfimumOfIn0(sK1(VAR_0),VAR_0,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | ~ aLowerBoundOfIn0(VAR_1,VAR_0,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | ~ sdtlseqdt0(VAR_1,sK2(VAR_0,VAR_1))
        | ~ aElementOf0(VAR_1,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | aElementOf0(sK2(VAR_0,VAR_1),VAR_0)
        | ~ aElementOf0(VAR_1,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aLowerBoundOfIn0(sK1(VAR_0),VAR_0,xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK1(VAR_0),VAR_1)
        | ~ aElementOf0(VAR_1,VAR_0)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aElementOf0(sK1(VAR_0),xU)
        | ~ aElementOf0(sK0(VAR_0),xU)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aSupremumOfIn0(sK3(VAR_0),VAR_0,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | ~ aUpperBoundOfIn0(VAR_1,VAR_0,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | ~ sdtlseqdt0(sK4(VAR_0,VAR_1),VAR_1)
        | ~ aElementOf0(VAR_1,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK3(VAR_0),VAR_1)
        | aElementOf0(sK4(VAR_0,VAR_1),VAR_0)
        | ~ aElementOf0(VAR_1,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aUpperBoundOfIn0(sK3(VAR_0),VAR_0,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK3(VAR_0))
        | ~ aElementOf0(VAR_1,VAR_0)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aElementOf0(sK3(VAR_0),xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aInfimumOfIn0(sK1(VAR_0),VAR_0,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | ~ aLowerBoundOfIn0(VAR_1,VAR_0,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | ~ sdtlseqdt0(VAR_1,sK2(VAR_0,VAR_1))
        | ~ aElementOf0(VAR_1,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(VAR_1,sK1(VAR_0))
        | aElementOf0(sK2(VAR_0,VAR_1),VAR_0)
        | ~ aElementOf0(VAR_1,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aLowerBoundOfIn0(sK1(VAR_0),VAR_0,xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0,VAR_1] :
        ( sdtlseqdt0(sK1(VAR_0),VAR_1)
        | ~ aElementOf0(VAR_1,VAR_0)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & ! [VAR_0] :
        ( aElementOf0(sK1(VAR_0),xU)
        | aElementOf0(sK0(VAR_0),VAR_0)
        | ~ aSet0(VAR_0) )
    & aSet0(xU) ),
    inference(cnf_transformation,[status(thm)],[sk_m__1123_sk]) ).

cnf(c_93,plain,
    ( aInfimumOfIn0(sK1(A),A,xU)
    | aElementOf0(sK0(A),A)
    | ~ aSet0(A) ),
    inference(split_conjunct,[status(thm)],[sk_m__1123]) ).

cnf(c_107,plain,
    ( aInfimumOfIn0(sK1(A),A,xU)
    | ~ aElementOf0(sK0(A),xU)
    | ~ aSet0(A) ),
    inference(split_conjunct,[status(thm)],[sk_m__1123]) ).

cnf(c_144,plain,
    aSet0(xP),
    inference(clausify,[status(thm)],[m__1244]) ).

cnf(c_145,plain,
    ( aElementOf0(A,xU)
    | ~ aElementOf0(A,xP) ),
    inference(clausify,[status(thm)],[m__1244]) ).

cnf(c_166,negated_conjecture,
    ~ aInfimumOfIn0(A,xP,xU),
    inference(clausify,[status(thm)],[m___neg]) ).

cnf(c_422,plain,
    ( aInfimumOfIn0(sK1(xP),xP,xU)
    | aElementOf0(sK0(xP),xP) ),
    inference(resolve,[status(thm)],[c_144,c_93]) ).

cnf(c_222,negated_conjecture,
    aElementOf0(sK0(xP),xP),
    inference(resolve,[status(thm)],[c_166,c_422]) ).

cnf(c_311,plain,
    aElementOf0(sK0(xP),xU),
    inference(resolve,[status(thm)],[c_222,c_145]) ).

cnf(c_423,plain,
    ( aInfimumOfIn0(sK1(xP),xP,xU)
    | ~ aSet0(xP) ),
    inference(resolve,[status(thm)],[c_311,c_107]) ).

cnf(c_424,plain,
    aInfimumOfIn0(sK1(xP),xP,xU),
    inference(resolve,[status(thm)],[c_144,c_423]) ).

cnf(c_421,negated_conjecture,
    $false,
    inference(resolve,[status(thm)],[c_166,c_424]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LAT385+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37  % Computer : n018.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Fri Sep 25 21:41:05 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.38  % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38  % Process 2912336 was started by sandbox2 on n018,
% 0.09/0.38  % Fri Sep 25 21:41:05 2026
% 0.09/0.38  % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39  
% 0.09/0.39  % From the command line: assign(max_seconds, 300).
% 0.09/0.45  
% 0.09/0.45  % SZS status Theorem for theBenchmark
% 0.09/0.45  
% 0.09/0.45  % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.09/0.45  % Length of proof is 11.
% 0.09/0.45  % Level of proof is 4.
% 0.09/0.45  % Maximum clause weight is 21.000.
% 0.09/0.45  % Given clauses 156.
% 0.09/0.45  
% 0.09/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------