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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n008.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 : Fri Sep 25 02:20:30 PM UTC 2026

% Result   : Theorem 63.22s 8.56s
% Output   : Proof 63.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   98 (  58 unt;   3 def)
%            Number of atoms       :  255 ( 116 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :  287 ( 130   ~;  89   |;  54   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  11 con; 0-4 aty)
%            Number of variables   :   93 (   3 sgn  47   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f99,conjecture,
    xQ != slcrc0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f99_neg,negated_conjecture,
    ~ ( xQ != slcrc0 ),
    inference(negated_conjecture,[status(cth)],[f99]) ).

fof(f99_nnf,plain,
    xQ = slcrc0,
    inference(nnf_transformation,[status(thm)],[f99_neg]) ).

cnf(c222,plain,
    xQ = slcrc0,
    inference(cnf_transformation,[status(esa)],[f99_nnf]) ).

cnf(t0,plain,
    xQ = slcrc0,
    inference(equality_encoding,[status(esa)],[c222]) ).

cnf(t2864,plain,
    slcrc0 = xQ,
    inference(orient,[status(thm)],[t0]) ).

fof(f56,definition,
    ! [W0,W1] :
      ( ( aElementOf0(W1,szNzAzT0)
        & aSet0(W0) )
     => ! [W2] :
          ( W2 = slbdtsldtrb0(W0,W1)
        <=> ( ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( sbrdtbr0(W3) = W1
                  & aSubsetOf0(W3,W0) ) )
            & aSet0(W2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).

fof(f56_nnf,plain,
    ! [W0,W1] :
      ( ! [W2] :
          ( ( ? [W3] :
                ( ( sbrdtbr0(W3) = W1
                  & aSubsetOf0(W3,W0)
                  & ~ aElementOf0(W3,W2) )
                | ( ( sbrdtbr0(W3) != W1
                    | ~ aSubsetOf0(W3,W0) )
                  & aElementOf0(W3,W2) ) )
            | ~ aSet0(W2)
            | W2 = slbdtsldtrb0(W0,W1) )
          & ( ( ! [W3] :
                  ( ( sbrdtbr0(W3) != W1
                    | ~ aSubsetOf0(W3,W0)
                    | aElementOf0(W3,W2) )
                  & ( ( sbrdtbr0(W3) = W1
                      & aSubsetOf0(W3,W0) )
                    | ~ aElementOf0(W3,W2) ) )
              & aSet0(W2) )
            | W2 != slbdtsldtrb0(W0,W1) ) )
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aSet0(W0) ),
    inference(nnf_transformation,[status(thm)],[f56]) ).

fof(f56_sk,plain,
    ! [W0,W1,W2,W3] :
      ( ( ( ( sbrdtbr0(sk10(W0,W1,W2)) = W1
            & aSubsetOf0(sk10(W0,W1,W2),W0)
            & ~ aElementOf0(sk10(W0,W1,W2),W2) )
          | ( ( sbrdtbr0(sk10(W0,W1,W2)) != W1
              | ~ aSubsetOf0(sk10(W0,W1,W2),W0) )
            & aElementOf0(sk10(W0,W1,W2),W2) )
          | ~ aSet0(W2)
          | W2 = slbdtsldtrb0(W0,W1) )
        & ( ( ( sbrdtbr0(W3) != W1
              | ~ aSubsetOf0(W3,W0)
              | aElementOf0(W3,W2) )
            & ( ( sbrdtbr0(W3) = W1
                & aSubsetOf0(W3,W0) )
              | ~ aElementOf0(W3,W2) )
            & aSet0(W2) )
          | W2 != slbdtsldtrb0(W0,W1) ) )
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aSet0(W0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f56_nnf]) ).

cnf(c114,plain,
    ( sbrdtbr0(X3) = X1
    | ~ aElementOf0(X3,X2)
    | X2 != slbdtsldtrb0(X0,X1)
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f56_sk]) ).

cnf(t183,plain,
    ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,X2),ifeq(aElementOf0(X4,X3),true,sbrdtbr0(X4),X2),X2),X2),X2) = X2,
    inference(equality_encoding,[status(esa)],[c114]) ).

cnf(t264,plain,
    ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,X2),ifeq(aElementOf0(X4,X3),true,sbrdtbr0(X4),X2),X2),X2),X2) = X2,
    inference(orient,[status(thm)],[t183]) ).

cnf(t63,plain,
    ifeq(X1,X1,X2,X3) = X2,
    introduced(definition) ).

cnf(t256,plain,
    ifeq(X1,X1,X2,X3) = X2,
    inference(orient,[status(thm)],[t63]) ).

cnf(t265,plain,
    X1 = ifeq(aSet0(X2),true,ifeq(aElementOf0(X1,szNzAzT0),true,ifeq(aElementOf0(X3,slbdtsldtrb0(X2,X1)),true,sbrdtbr0(X3),X1),X1),X1),
    inference(cp,[status(thm)],[t264,t256]) ).

cnf(t5073,plain,
    ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(aElementOf0(X3,slbdtsldtrb0(X1,X2)),true,sbrdtbr0(X3),X2),X2),X2) = X2,
    inference(orient,[status(thm)],[t265]) ).

fof(f98,hypothesis,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).

fof(f98_nnf,plain,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
    inference(nnf_transformation,[status(thm)],[f98]) ).

cnf(c221,plain,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
    inference(cnf_transformation,[status(esa)],[f98_nnf]) ).

cnf(t61,plain,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)) = true,
    inference(equality_encoding,[status(esa)],[c221]) ).

cnf(t777,plain,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)) = true,
    inference(orient,[status(thm)],[t61]) ).

cnf(t5088,plain,
    xK = ifeq(aSet0(xO),true,ifeq(aElementOf0(xK,szNzAzT0),true,ifeq(true,true,sbrdtbr0(xQ),xK),xK),xK),
    inference(cp,[status(thm)],[t5073,t777]) ).

fof(f94,hypothesis,
    ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aSet0(xO) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).

fof(f94_nnf,plain,
    ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aSet0(xO) ),
    inference(nnf_transformation,[status(thm)],[f94]) ).

fof(f94_sk,plain,
    ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aSet0(xO) ),
    inference(skolemisation,[status(esa)],[f94_nnf]) ).

cnf(c213,plain,
    aSet0(xO),
    inference(cnf_transformation,[status(esa)],[f94_sk]) ).

cnf(t8,plain,
    aSet0(xO) = true,
    inference(equality_encoding,[status(esa)],[c213]) ).

cnf(t1243,plain,
    aSet0(xO) = true,
    inference(orient,[status(thm)],[t8]) ).

cnf(t5272,plain,
    xK = ifeq(true,true,ifeq(aElementOf0(xK,szNzAzT0),true,ifeq(true,true,sbrdtbr0(xQ),xK),xK),xK),
    inference(step,[status(thm)],[t5088,t1243]) ).

cnf(t5273,plain,
    xK = ifeq(aElementOf0(xK,szNzAzT0),true,ifeq(true,true,sbrdtbr0(xQ),xK),xK),
    inference(step,[status(thm)],[t5272,t256]) ).

fof(f73,hypothesis,
    aElementOf0(xK,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).

fof(f73_nnf,plain,
    aElementOf0(xK,szNzAzT0),
    inference(nnf_transformation,[status(thm)],[f73]) ).

cnf(c167,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnf_transformation,[status(esa)],[f73_nnf]) ).

cnf(t26,plain,
    aElementOf0(xK,szNzAzT0) = true,
    inference(equality_encoding,[status(esa)],[c167]) ).

cnf(t451,plain,
    aElementOf0(xK,szNzAzT0) = true,
    inference(orient,[status(thm)],[t26]) ).

cnf(t5274,plain,
    xK = ifeq(true,true,ifeq(true,true,sbrdtbr0(xQ),xK),xK),
    inference(step,[status(thm)],[t5273,t451]) ).

cnf(t5275,plain,
    xK = ifeq(true,true,sbrdtbr0(xQ),xK),
    inference(step,[status(thm)],[t5274,t256]) ).

cnf(t5276,plain,
    xK = sbrdtbr0(xQ),
    inference(step,[status(thm)],[t5275,t256]) ).

fof(f4,definition,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( ~ ? [W1] : aElementOf0(W1,W0)
        & aSet0(W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

fof(f4_nnf,plain,
    ! [W0] :
      ( ( ? [W1] : aElementOf0(W1,W0)
        | ~ aSet0(W0)
        | W0 = slcrc0 )
      & ( ( ! [W1] : ~ aElementOf0(W1,W0)
          & aSet0(W0) )
        | W0 != slcrc0 ) ),
    inference(nnf_transformation,[status(thm)],[f4]) ).

fof(f4_sk,plain,
    ! [W0,W1] :
      ( ( aElementOf0(sk0(W0),W0)
        | ~ aSet0(W0)
        | W0 = slcrc0 )
      & ( ( ~ aElementOf0(W1,W0)
          & aSet0(W0) )
        | W0 != slcrc0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).

cnf(c4,plain,
    ( aSet0(X0)
    | X0 != slcrc0 ),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

cnf(hi1,axiom,
    ifeq(X0,slcrc0,aSet0(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c4]) ).

cnf(hi209,axiom,
    or(X0,false) = X0,
    introduced(definition) ).

cnf(h567,plain,
    aSet0(or(slcrc0,false)) = true,
    inference(hyper_resolution,[status(thm)],[hi1,hi209]) ).

fof(f41,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( sbrdtbr0(W0) = sz00
      <=> W0 = slcrc0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).

fof(f41_nnf,plain,
    ! [W0] :
      ( ( ( W0 != slcrc0
          | sbrdtbr0(W0) = sz00 )
        & ( W0 = slcrc0
          | sbrdtbr0(W0) != sz00 ) )
      | ~ aSet0(W0) ),
    inference(nnf_transformation,[status(thm)],[f41]) ).

fof(f41_sk,plain,
    ! [W0] :
      ( ( ( W0 != slcrc0
          | sbrdtbr0(W0) = sz00 )
        & ( W0 = slcrc0
          | sbrdtbr0(W0) != sz00 ) )
      | ~ aSet0(W0) ),
    inference(skolemisation,[status(esa)],[f41_nnf]) ).

cnf(c77,plain,
    ( X0 != slcrc0
    | sbrdtbr0(X0) = sz00
    | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f41_sk]) ).

cnf(hi55,axiom,
    ifeq(aSet0(X0),true,ifeq(X0,slcrc0,sbrdtbr0(X0),sz00),sz00) = sz00,
    inference(equality_encoding,[status(esa)],[c77]) ).

cnf(t57,plain,
    sbrdtbr0(or(slcrc0,false)) = sz00,
    inference(hyper_resolution,[status(thm)],[hi55,h567,hi209]) ).

cnf(t40,plain,
    or(X1,false) = X1,
    introduced(definition) ).

cnf(t276,plain,
    or(X1,false) = X1,
    inference(orient,[status(thm)],[t40]) ).

cnf(t5158,plain,
    sbrdtbr0(slcrc0) = sz00,
    inference(step,[status(thm)],[t57,t276]) ).

cnf(t5159,plain,
    sbrdtbr0(xQ) = sz00,
    inference(step,[status(thm)],[t5158,t2864]) ).

cnf(t2974,plain,
    sbrdtbr0(xQ) = sz00,
    inference(orient,[status(thm)],[t5159]) ).

cnf(t5277,plain,
    xK = sz00,
    inference(step,[status(thm)],[t5276,t2974]) ).

cnf(t5095,plain,
    sz00 = xK,
    inference(orient,[status(thm)],[t5277]) ).

cnf(c5,plain,
    ( ~ aElementOf0(X1,X0)
    | X0 != slcrc0 ),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

fof(f7,axiom,
    ! [W0] :
      ( ( isCountable0(W0)
        & aSet0(W0) )
     => ~ isFinite0(W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).

fof(f7_nnf,plain,
    ! [W0] :
      ( ~ isFinite0(W0)
      | ~ isCountable0(W0)
      | ~ aSet0(W0) ),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [W0] :
      ( ~ isFinite0(W0)
      | ~ isCountable0(W0)
      | ~ aSet0(W0) ),
    inference(skolemisation,[status(esa)],[f7_nnf]) ).

cnf(c9,plain,
    ( ~ isFinite0(X0)
    | ~ isCountable0(X0)
    | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

fof(f8,axiom,
    ! [W0] :
      ( ( isCountable0(W0)
        & aSet0(W0) )
     => W0 != slcrc0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).

fof(f8_nnf,plain,
    ! [W0] :
      ( W0 != slcrc0
      | ~ isCountable0(W0)
      | ~ aSet0(W0) ),
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [W0] :
      ( W0 != slcrc0
      | ~ isCountable0(W0)
      | ~ aSet0(W0) ),
    inference(skolemisation,[status(esa)],[f8_nnf]) ).

cnf(c10,plain,
    ( X0 != slcrc0
    | ~ isCountable0(X0)
    | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

fof(f15,definition,
    ! [W0,W1] :
      ( ( aElement0(W1)
        & aSet0(W0) )
     => ! [W2] :
          ( W2 = sdtmndt0(W0,W1)
        <=> ( ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( W3 != W1
                  & aElementOf0(W3,W0)
                  & aElement0(W3) ) )
            & aSet0(W2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

fof(f15_nnf,plain,
    ! [W0,W1] :
      ( ! [W2] :
          ( ( ? [W3] :
                ( ( W3 != W1
                  & aElementOf0(W3,W0)
                  & aElement0(W3)
                  & ~ aElementOf0(W3,W2) )
                | ( ( W3 = W1
                    | ~ aElementOf0(W3,W0)
                    | ~ aElement0(W3) )
                  & aElementOf0(W3,W2) ) )
            | ~ aSet0(W2)
            | W2 = sdtmndt0(W0,W1) )
          & ( ( ! [W3] :
                  ( ( W3 = W1
                    | ~ aElementOf0(W3,W0)
                    | ~ aElement0(W3)
                    | aElementOf0(W3,W2) )
                  & ( ( W3 != W1
                      & aElementOf0(W3,W0)
                      & aElement0(W3) )
                    | ~ aElementOf0(W3,W2) ) )
              & aSet0(W2) )
            | W2 != sdtmndt0(W0,W1) ) )
      | ~ aElement0(W1)
      | ~ aSet0(W0) ),
    inference(nnf_transformation,[status(thm)],[f15]) ).

fof(f15_sk,plain,
    ! [W0,W1,W2,W3] :
      ( ( ( ( sk3(W0,W1,W2) != W1
            & aElementOf0(sk3(W0,W1,W2),W0)
            & aElement0(sk3(W0,W1,W2))
            & ~ aElementOf0(sk3(W0,W1,W2),W2) )
          | ( ( sk3(W0,W1,W2) = W1
              | ~ aElementOf0(sk3(W0,W1,W2),W0)
              | ~ aElement0(sk3(W0,W1,W2)) )
            & aElementOf0(sk3(W0,W1,W2),W2) )
          | ~ aSet0(W2)
          | W2 = sdtmndt0(W0,W1) )
        & ( ( ( W3 = W1
              | ~ aElementOf0(W3,W0)
              | ~ aElement0(W3)
              | aElementOf0(W3,W2) )
            & ( ( W3 != W1
                & aElementOf0(W3,W0)
                & aElement0(W3) )
              | ~ aElementOf0(W3,W2) )
            & aSet0(W2) )
          | W2 != sdtmndt0(W0,W1) ) )
      | ~ aElement0(W1)
      | ~ aSet0(W0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f15_nnf]) ).

cnf(c36,plain,
    ( X3 != X1
    | ~ aElementOf0(X3,X2)
    | X2 != sdtmndt0(X0,X1)
    | ~ aElement0(X1)
    | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f15_sk]) ).

fof(f24,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( szszuzczcdt0(W0) != sz00
        & aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).

fof(f24_nnf,plain,
    ! [W0] :
      ( ( szszuzczcdt0(W0) != sz00
        & aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(nnf_transformation,[status(thm)],[f24]) ).

fof(f24_sk,plain,
    ! [W0] :
      ( ( szszuzczcdt0(W0) != sz00
        & aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(skolemisation,[status(esa)],[f24_nnf]) ).

cnf(c56,plain,
    ( szszuzczcdt0(X0) != sz00
    | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[status(esa)],[f24_sk]) ).

fof(f27,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => W0 != szszuzczcdt0(W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).

fof(f27_nnf,plain,
    ! [W0] :
      ( W0 != szszuzczcdt0(W0)
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(nnf_transformation,[status(thm)],[f27]) ).

fof(f27_sk,plain,
    ! [W0] :
      ( W0 != szszuzczcdt0(W0)
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(skolemisation,[status(esa)],[f27_nnf]) ).

cnf(c60,plain,
    ( X0 != szszuzczcdt0(X0)
    | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[status(esa)],[f27_sk]) ).

fof(f30,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).

fof(f30_nnf,plain,
    ! [W0] :
      ( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(nnf_transformation,[status(thm)],[f30]) ).

fof(f30_sk,plain,
    ! [W0] :
      ( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(skolemisation,[status(esa)],[f30_nnf]) ).

cnf(c63,plain,
    ( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
    | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[status(esa)],[f30_sk]) ).

fof(f77,hypothesis,
    xK != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).

fof(f77_nnf,plain,
    xK != sz00,
    inference(nnf_transformation,[status(thm)],[f77]) ).

fof(f77_sk,plain,
    xK != sz00,
    inference(skolemisation,[status(esa)],[f77_nnf]) ).

cnf(c177,plain,
    xK != sz00,
    inference(cnf_transformation,[status(esa)],[f77_sk]) ).

fof(f78,hypothesis,
    xK != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).

fof(f78_nnf,plain,
    xK != sz00,
    inference(nnf_transformation,[status(thm)],[f78]) ).

fof(f78_sk,plain,
    xK != sz00,
    inference(skolemisation,[status(esa)],[f78_nnf]) ).

cnf(c178,plain,
    xK != sz00,
    inference(cnf_transformation,[status(esa)],[f78_sk]) ).

cnf(goal_0,negated_conjecture,
    true != false,
    inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c177,c178]) ).

cnf(g0_0,plain,
    true != ifeq(xK,sz00,false,true),
    inference(rw,[status(thm)],[goal_0]) ).

cnf(g0_1,plain,
    true != ifeq(xK,sz00,false,or(eq(xS,slcrc0),aElementOf0(szmzizndt0(xS),xS))),
    inference(rw,[status(thm)],[g0_0]) ).

cnf(g0_2,plain,
    true != ifeq(xK,sz00,false,or(eq(xS,xQ),aElementOf0(szmzizndt0(xS),xS))),
    inference(rw,[status(thm)],[g0_1,t2864]) ).

cnf(g0_3,plain,
    true != ifeq(xK,xK,false,or(eq(xS,xQ),aElementOf0(szmzizndt0(xS),xS))),
    inference(rw,[status(thm)],[g0_2,t5095]) ).

cnf(g0_4,plain,
    true != false,
    inference(rw,[status(thm)],[g0_3,t256]) ).

cnf(contradiction_0,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38  % Computer : n008.cluster.edu
% 0.12/0.38  % Model    : x86_64 x86_64
% 0.12/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38  % Memory   : 8046.5625MB
% 0.12/0.38  % OS       : Linux 6.8.0-71-generic
% 0.12/0.38  % CPULimit : 300
% 0.12/0.38  % WCLimit  : 300
% 0.12/0.38  % DateTime : Thu Sep 24 04:53:40 UTC 2026
% 0.12/0.39  % CPUTime  : 
% 0.12/0.39  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 63.22/8.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 63.22/8.56  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------