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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : NUM574+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n017.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 : Tue Sep 29 12:24:52 PM UTC 2026

% Result   : Theorem 0.15s 5.47s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  103 (  20 unt;   8 def)
%            Number of atoms       :  297 (  42 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  320 ( 126   ~; 136   |;  37   &)
%                                         (  10 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   16 (  14 usr;   9 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :   48 (   0 sgn  41   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

fof(f12,axiom,
    ! [X0] :
      ( aSet0(X0)
     => aSubsetOf0(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

fof(f23,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(f27,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ( X0 = sz00
        | ? [X1] :
            ( aElementOf0(X1,szNzAzT0)
            & X0 = szszuzczcdt0(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).

fof(f31,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).

fof(f75,axiom,
    ( aSubsetOf0(xS,szNzAzT0)
    & isCountable0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).

fof(f81,axiom,
    ( aFunction0(xN)
    & szDzozmdt0(xN) = szNzAzT0
    & sdtlpdtrp0(xN,sz00) = xS
    & ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
            & isCountable0(sdtlpdtrp0(xN,X0)) )
         => ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).

fof(f83,axiom,
    ( aElementOf0(xj,szNzAzT0)
    & aElementOf0(xi,szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).

fof(f85,axiom,
    ( ( sdtlseqdt0(xj,xi)
      & ? [X0] :
          ( aElementOf0(X0,szNzAzT0)
          & szszuzczcdt0(X0) = xi ) )
   => ( sdtlseqdt0(xj,xi)
     => aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786_02) ).

fof(f86,conjecture,
    ( sdtlseqdt0(xj,xi)
   => aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f87,negated_conjecture,
    ~ ( sdtlseqdt0(xj,xi)
     => aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
    inference(negated_conjecture,[status(cth)],[f86]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) ) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f104,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f127,plain,
    ! [X0] :
      ( X0 = sz00
      | ? [X1] :
          ( aElementOf0(X1,szNzAzT0)
          & X0 = szszuzczcdt0(X1) )
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f128,plain,
    ! [X0] :
      ( X0 = sz00
      | ? [X1] :
          ( aElementOf0(X1,szNzAzT0)
          & X0 = szszuzczcdt0(X1) )
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f127]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f196,plain,
    ( aFunction0(xN)
    & szDzozmdt0(xN) = szNzAzT0
    & sdtlpdtrp0(xN,sz00) = xS
    & ! [X0] :
        ( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ~ aElementOf0(X0,szNzAzT0) ) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f197,plain,
    ( aFunction0(xN)
    & szDzozmdt0(xN) = szNzAzT0
    & sdtlpdtrp0(xN,sz00) = xS
    & ! [X0] :
        ( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ~ aElementOf0(X0,szNzAzT0) ) ),
    inference(flattening,[],[f196]) ).

fof(f201,plain,
    ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    | ~ sdtlseqdt0(xj,xi)
    | ~ sdtlseqdt0(xj,xi)
    | ! [X0] :
        ( ~ aElementOf0(X0,szNzAzT0)
        | szszuzczcdt0(X0) != xi ) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f202,plain,
    ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    | ~ sdtlseqdt0(xj,xi)
    | ~ sdtlseqdt0(xj,xi)
    | ! [X0] :
        ( ~ aElementOf0(X0,szNzAzT0)
        | szszuzczcdt0(X0) != xi ) ),
    inference(flattening,[],[f201]) ).

fof(f203,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    & sdtlseqdt0(xj,xi) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f214,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ~ aSet0(X1)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) ) )
          & ( ( aSet0(X1)
              & ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) ) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f101]) ).

fof(f215,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ~ aSet0(X1)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) ) )
          & ( ( aSet0(X1)
              & ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) ) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(flattening,[],[f214]) ).

fof(f216,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ~ aSet0(X1)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) ) )
          & ( ( aSet0(X1)
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) ) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(rectify,[],[f215]) ).

fof(f217,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ~ aSet0(X1)
            | ( ~ aElementOf0(sK5(X0,X1),X0)
              & aElementOf0(sK5(X0,X1),X1) ) )
          & ( ( aSet0(X1)
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) ) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f216]) ).

fof(f230,plain,
    ! [X0] :
      ( X0 = sz00
      | ( aElementOf0(sK8(X0),szNzAzT0)
        & szszuzczcdt0(sK8(X0)) = X0 )
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f128]) ).

fof(f278,plain,
    ! [X0,X1] :
      ( ~ aSubsetOf0(X1,X0)
      | aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f217]) ).

fof(f282,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f316,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f321,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | szszuzczcdt0(sK8(X0)) = X0
      | sz00 = X0 ),
    inference(cnf_transformation,[],[f230]) ).

fof(f322,plain,
    ! [X0] :
      ( aElementOf0(sK8(X0),szNzAzT0)
      | sz00 = X0
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f325,plain,
    ! [X0] :
      ( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f417,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[],[f75]) ).

fof(f431,plain,
    xS = sdtlpdtrp0(xN,sz00),
    inference(cnf_transformation,[],[f197]) ).

fof(f436,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnf_transformation,[],[f83]) ).

fof(f437,plain,
    aElementOf0(xj,szNzAzT0),
    inference(cnf_transformation,[],[f83]) ).

fof(f439,plain,
    ! [X0] :
      ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      | ~ sdtlseqdt0(xj,xi)
      | ~ sdtlseqdt0(xj,xi)
      | ~ aElementOf0(X0,szNzAzT0)
      | szszuzczcdt0(X0) != xi ),
    inference(cnf_transformation,[],[f202]) ).

fof(f440,plain,
    sdtlseqdt0(xj,xi),
    inference(cnf_transformation,[],[f203]) ).

fof(f441,plain,
    ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
    inference(cnf_transformation,[],[f203]) ).

fof(f479,plain,
    ! [X0] :
      ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      | ~ sdtlseqdt0(xj,xi)
      | ~ aElementOf0(X0,szNzAzT0)
      | szszuzczcdt0(X0) != xi ),
    inference(duplicate_literal_removal,[],[f439]) ).

fof(f482,definition,
    ( spl25_1
  <=> ! [X0] :
        ( ~ aElementOf0(X0,szNzAzT0)
        | szszuzczcdt0(X0) != xi ) ),
    introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).

fof(f483,plain,
    ( ! [X0] :
        ( szszuzczcdt0(X0) != xi
        | ~ aElementOf0(X0,szNzAzT0) )
    | ~ spl25_1 ),
    inference(avatar_component_clause,[],[f482]) ).

fof(f485,definition,
    ( spl25_2
  <=> sdtlseqdt0(xj,xi) ),
    introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).

fof(f486,plain,
    ( sdtlseqdt0(xj,xi)
    | ~ spl25_2 ),
    inference(avatar_component_clause,[],[f485]) ).

fof(f489,definition,
    ( spl25_3
  <=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
    introduced(definition,[new_symbols(definition,[spl25_3])],[avatar_definition]) ).

fof(f490,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    | spl25_3 ),
    inference(avatar_component_clause,[],[f489]) ).

fof(f492,plain,
    ( spl25_1
    | ~ spl25_2
    | spl25_3 ),
    inference(avatar_split_clause,[],[f479,f489,f485,f482]) ).

fof(f508,plain,
    spl25_2,
    inference(avatar_split_clause,[],[f440,f485]) ).

fof(f509,plain,
    ~ spl25_3,
    inference(avatar_split_clause,[],[f441,f489]) ).

fof(f521,definition,
    ( spl25_8
  <=> aSet0(xS) ),
    introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).

fof(f522,plain,
    ( aSet0(xS)
    | ~ spl25_8 ),
    inference(avatar_component_clause,[],[f521]) ).

fof(f560,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[],[f278,f417]) ).

fof(f565,plain,
    aSet0(xS),
    inference(forward_subsumption_resolution,[],[f560,f316]) ).

fof(f566,plain,
    spl25_8,
    inference(avatar_split_clause,[],[f565,f521]) ).

fof(f747,definition,
    ( spl25_18
  <=> sz00 = xj ),
    introduced(definition,[new_symbols(definition,[spl25_18])],[avatar_definition]) ).

fof(f748,plain,
    ( sz00 = xj
    | ~ spl25_18 ),
    inference(avatar_component_clause,[],[f747]) ).

fof(f749,plain,
    ( sz00 != xj
    | spl25_18 ),
    inference(avatar_component_clause,[],[f747]) ).

fof(f770,definition,
    ( spl25_20
  <=> sz00 = xi ),
    introduced(definition,[new_symbols(definition,[spl25_20])],[avatar_definition]) ).

fof(f771,plain,
    ( sz00 = xi
    | ~ spl25_20 ),
    inference(avatar_component_clause,[],[f770]) ).

fof(f772,plain,
    ( sz00 != xi
    | spl25_20 ),
    inference(avatar_component_clause,[],[f770]) ).

fof(f856,plain,
    ( xj = szszuzczcdt0(sK8(xj))
    | sz00 = xj ),
    inference(resolution,[],[f321,f437]) ).

fof(f857,plain,
    ( xi = szszuzczcdt0(sK8(xi))
    | sz00 = xi ),
    inference(resolution,[],[f321,f436]) ).

fof(f864,plain,
    ( xi = szszuzczcdt0(sK8(xi))
    | spl25_20 ),
    inference(forward_subsumption_resolution,[],[f857,f772]) ).

fof(f865,plain,
    ( xj = szszuzczcdt0(sK8(xj))
    | spl25_18 ),
    inference(forward_subsumption_resolution,[],[f856,f749]) ).

fof(f941,plain,
    ( xi != xi
    | ~ aElementOf0(sK8(xi),szNzAzT0)
    | ~ spl25_1
    | spl25_20 ),
    inference(superposition,[],[f483,f864]) ).

fof(f942,plain,
    ( ~ aElementOf0(sK8(xi),szNzAzT0)
    | ~ spl25_1
    | spl25_20 ),
    inference(trivial_inequality_removal,[],[f941]) ).

fof(f944,definition,
    ( spl25_31
  <=> aElementOf0(sK8(xi),szNzAzT0) ),
    introduced(definition,[new_symbols(definition,[spl25_31])],[avatar_definition]) ).

fof(f946,plain,
    ( ~ aElementOf0(sK8(xi),szNzAzT0)
    | spl25_31 ),
    inference(avatar_component_clause,[],[f944]) ).

fof(f974,plain,
    ( ~ spl25_31
    | ~ spl25_1
    | spl25_20 ),
    inference(avatar_split_clause,[],[f942,f770,f482,f944]) ).

fof(f976,plain,
    ( sz00 = xi
    | ~ aElementOf0(xi,szNzAzT0)
    | spl25_31 ),
    inference(resolution,[],[f946,f322]) ).

fof(f985,plain,
    ( sz00 = xi
    | spl25_31 ),
    inference(forward_subsumption_resolution,[],[f976,f436]) ).

fof(f986,plain,
    ( spl25_20
    | spl25_31 ),
    inference(avatar_split_clause,[],[f985,f944,f770]) ).

fof(f990,plain,
    ( sdtlseqdt0(xj,sz00)
    | ~ spl25_2
    | ~ spl25_20 ),
    inference(superposition,[],[f486,f771]) ).

fof(f1086,plain,
    ( ~ sdtlseqdt0(xj,sz00)
    | ~ aElementOf0(sK8(xj),szNzAzT0)
    | spl25_18 ),
    inference(superposition,[],[f325,f865]) ).

fof(f1093,definition,
    ( spl25_38
  <=> aElementOf0(sK8(xj),szNzAzT0) ),
    introduced(definition,[new_symbols(definition,[spl25_38])],[avatar_definition]) ).

fof(f1095,plain,
    ( ~ aElementOf0(sK8(xj),szNzAzT0)
    | spl25_38 ),
    inference(avatar_component_clause,[],[f1093]) ).

fof(f1111,plain,
    ( ~ aElementOf0(sK8(xj),szNzAzT0)
    | ~ spl25_2
    | spl25_18
    | ~ spl25_20 ),
    inference(forward_subsumption_resolution,[],[f1086,f990]) ).

fof(f1117,plain,
    ( ~ spl25_38
    | ~ spl25_2
    | spl25_18
    | ~ spl25_20 ),
    inference(avatar_split_clause,[],[f1111,f770,f747,f485,f1093]) ).

fof(f1119,plain,
    ( sz00 = xj
    | ~ aElementOf0(xj,szNzAzT0)
    | spl25_38 ),
    inference(resolution,[],[f1095,f322]) ).

fof(f1128,plain,
    ( sz00 = xj
    | spl25_38 ),
    inference(forward_subsumption_resolution,[],[f1119,f437]) ).

fof(f1129,plain,
    ( spl25_18
    | spl25_38 ),
    inference(avatar_split_clause,[],[f1128,f1093,f747]) ).

fof(f1162,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
    | spl25_3
    | ~ spl25_18 ),
    inference(superposition,[],[f490,f748]) ).

fof(f1174,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
    | spl25_3
    | ~ spl25_18 ),
    inference(forward_demodulation,[],[f1162,f431]) ).

fof(f1175,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),xS)
    | spl25_3
    | ~ spl25_18
    | ~ spl25_20 ),
    inference(forward_demodulation,[],[f1174,f771]) ).

fof(f1176,plain,
    ( ~ aSubsetOf0(xS,xS)
    | spl25_3
    | ~ spl25_18
    | ~ spl25_20 ),
    inference(forward_demodulation,[],[f1175,f431]) ).

fof(f1181,plain,
    ( ~ aSet0(xS)
    | spl25_3
    | ~ spl25_18
    | ~ spl25_20 ),
    inference(resolution,[],[f1176,f282]) ).

fof(f1182,plain,
    ( $false
    | spl25_3
    | ~ spl25_8
    | ~ spl25_18
    | ~ spl25_20 ),
    inference(forward_subsumption_resolution,[],[f1181,f522]) ).

fof(f1183,plain,
    ( spl25_3
    | ~ spl25_8
    | ~ spl25_18
    | ~ spl25_20 ),
    inference(avatar_contradiction_clause,[],[f1182]) ).

cnf(s1,plain,
    ( spl25_1
    | ~ spl25_2
    | spl25_3 ),
    inference(sat_conversion,[],[f492]) ).

cnf(s5,plain,
    spl25_2,
    inference(sat_conversion,[],[f508]) ).

cnf(s6,plain,
    ~ spl25_3,
    inference(sat_conversion,[],[f509]) ).

cnf(s8,plain,
    spl25_8,
    inference(sat_conversion,[],[f566]) ).

cnf(s37,plain,
    ( ~ spl25_1
    | spl25_20
    | ~ spl25_31 ),
    inference(sat_conversion,[],[f974]) ).

cnf(s40,plain,
    ( spl25_20
    | spl25_31 ),
    inference(sat_conversion,[],[f986]) ).

cnf(s45,plain,
    ( ~ spl25_2
    | spl25_18
    | ~ spl25_20
    | ~ spl25_38 ),
    inference(sat_conversion,[],[f1117]) ).

cnf(s48,plain,
    ( spl25_18
    | spl25_38 ),
    inference(sat_conversion,[],[f1129]) ).

cnf(s51,plain,
    ( spl25_3
    | ~ spl25_8
    | ~ spl25_18
    | ~ spl25_20 ),
    inference(sat_conversion,[],[f1183]) ).

cnf(s70,plain,
    spl25_1,
    inference(rat,[],[s1,s6,s5]) ).

cnf(s71,plain,
    spl25_20,
    inference(rat,[],[s37,s40,s70]) ).

cnf(s73,plain,
    ~ spl25_18,
    inference(rat,[],[s51,s6,s8,s71]) ).

cnf(s74,plain,
    spl25_38,
    inference(rat,[],[s48,s73]) ).

cnf(s76,plain,
    $false,
    inference(rat,[],[s45,s71,s5,s74,s73]) ).

fof(f1184,plain,
    $false,
    inference(avatar_sat_refutation,[],[s76]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM574+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/5.39  % Computer : n017.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 : Sun Sep 27 20:29:11 UTC 2026
% 0.12/5.39  % CPUTime  : 
% 0.12/5.39  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/5.42  Running first-order model finding
% 0.15/5.42  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.47  % (2919472)Will run a generic schedule for satisfiability detection.
% 0.15/5.47  % (2919480)dis+10_1_sil=32000:sp=arity:random_seed=4138518380:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/5.47  % (2919478)% WARNING: option uhcvi not known.
% 0.15/5.47  % (2919477)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=24062121_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/5.47  % (2919478)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3700801229:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/5.47  % (2919479)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2626607150:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/5.47  % (2919481)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1289403480:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/5.47  % (2919482)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3521843498:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/5.47  % (2919483)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3345384879:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/5.47  % (2919480) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2919472-2919480"...
% 0.15/5.47  % (2919480)...printing done.
% 0.15/5.47  % (2919480)Refutation found. Thanks to Tanya!
% 0.15/5.47  % SZS status Theorem for theBenchmark
% 0.15/5.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/5.47  % (2919480)------------------------------
% 0.15/5.47  % (2919480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/5.47  % (2919480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/5.47  % (2919480)CaDiCaL version: 2.1.3
% 0.15/5.47  % (2919480)Termination reason: Refutation
% 0.15/5.47  % (2919480)Time elapsed: 0.011 s
% 0.15/5.47  % (2919480)Peak memory usage: 13 MB
% 0.15/5.47  % (2919480)Instructions burned: 26 (million)
% 0.15/5.47  % (2919472)Success in time 0.037 s
% 0.15/5.47  % Vampire exiting
%------------------------------------------------------------------------------