TSTP Solution File: SEU171+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n029.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 Apr 30 15:23:03 EDT 2024

% Result   : Theorem 5.41s 1.92s
% Output   : Refutation 5.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  102 (  31 unt;   0 def)
%            Number of atoms       :  293 (  85 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  318 ( 127   ~;  90   |;  64   &)
%                                         (  18 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  173 ( 152   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12652,plain,
    $false,
    inference(trivial_inequality_removal,[],[f12651]) ).

fof(f12651,plain,
    empty_set != empty_set,
    inference(superposition,[],[f297,f9014]) ).

fof(f9014,plain,
    empty_set = sK6,
    inference(forward_demodulation,[],[f7794,f7789]) ).

fof(f7789,plain,
    empty_set = sK8,
    inference(resolution,[],[f7784,f639]) ).

fof(f639,plain,
    ( ~ empty(sK6)
    | empty_set = sK8 ),
    inference(resolution,[],[f635,f386]) ).

fof(f386,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f164]) ).

fof(f164,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f101]) ).

fof(f101,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f635,plain,
    ( empty(sK8)
    | ~ empty(sK6) ),
    inference(resolution,[],[f407,f299]) ).

fof(f299,plain,
    element(sK8,sK6),
    inference(cnf_transformation,[],[f197]) ).

fof(f197,plain,
    ( ~ in(sK8,subset_complement(sK6,sK7))
    & ~ in(sK8,sK7)
    & element(sK8,sK6)
    & element(sK7,powerset(sK6))
    & empty_set != sK6 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f125,f196,f195,f194]) ).

fof(f194,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ in(X2,subset_complement(X0,X1))
                & ~ in(X2,X1)
                & element(X2,X0) )
            & element(X1,powerset(X0)) )
        & empty_set != X0 )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,subset_complement(sK6,X1))
              & ~ in(X2,X1)
              & element(X2,sK6) )
          & element(X1,powerset(sK6)) )
      & empty_set != sK6 ) ),
    introduced(choice_axiom,[]) ).

fof(f195,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ in(X2,subset_complement(sK6,X1))
            & ~ in(X2,X1)
            & element(X2,sK6) )
        & element(X1,powerset(sK6)) )
   => ( ? [X2] :
          ( ~ in(X2,subset_complement(sK6,sK7))
          & ~ in(X2,sK7)
          & element(X2,sK6) )
      & element(sK7,powerset(sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f196,plain,
    ( ? [X2] :
        ( ~ in(X2,subset_complement(sK6,sK7))
        & ~ in(X2,sK7)
        & element(X2,sK6) )
   => ( ~ in(sK8,subset_complement(sK6,sK7))
      & ~ in(sK8,sK7)
      & element(sK8,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,subset_complement(X0,X1))
              & ~ in(X2,X1)
              & element(X2,X0) )
          & element(X1,powerset(X0)) )
      & empty_set != X0 ),
    inference(flattening,[],[f124]) ).

fof(f124,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,subset_complement(X0,X1))
              & ~ in(X2,X1)
              & element(X2,X0) )
          & element(X1,powerset(X0)) )
      & empty_set != X0 ),
    inference(ennf_transformation,[],[f96]) ).

fof(f96,negated_conjecture,
    ~ ! [X0] :
        ( empty_set != X0
       => ! [X1] :
            ( element(X1,powerset(X0))
           => ! [X2] :
                ( element(X2,X0)
               => ( ~ in(X2,X1)
                 => in(X2,subset_complement(X0,X1)) ) ) ) ),
    inference(negated_conjecture,[],[f95]) ).

fof(f95,conjecture,
    ! [X0] :
      ( empty_set != X0
     => ! [X1] :
          ( element(X1,powerset(X0))
         => ! [X2] :
              ( element(X2,X0)
             => ( ~ in(X2,X1)
               => in(X2,subset_complement(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

fof(f407,plain,
    ! [X0,X1] :
      ( ~ element(X1,X0)
      | empty(X1)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f236]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( ( ( ( element(X1,X0)
            | ~ empty(X1) )
          & ( empty(X1)
            | ~ element(X1,X0) ) )
        | ~ empty(X0) )
      & ( ( ( element(X1,X0)
            | ~ in(X1,X0) )
          & ( in(X1,X0)
            | ~ element(X1,X0) ) )
        | empty(X0) ) ),
    inference(nnf_transformation,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( ( ( element(X1,X0)
        <=> empty(X1) )
        | ~ empty(X0) )
      & ( ( element(X1,X0)
        <=> in(X1,X0) )
        | empty(X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( empty(X0)
       => ( element(X1,X0)
        <=> empty(X1) ) )
      & ( ~ empty(X0)
       => ( element(X1,X0)
        <=> in(X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

fof(f7784,plain,
    empty(sK6),
    inference(resolution,[],[f7783,f299]) ).

fof(f7783,plain,
    ( ~ element(sK8,sK6)
    | empty(sK6) ),
    inference(resolution,[],[f7774,f405]) ).

fof(f405,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | ~ element(X1,X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f236]) ).

fof(f7774,plain,
    ~ in(sK8,sK6),
    inference(resolution,[],[f7772,f501]) ).

fof(f501,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f500]) ).

fof(f500,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f441]) ).

fof(f441,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f261]) ).

fof(f261,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK24(X0,X1) != X0
            | ~ in(sK24(X0,X1),X1) )
          & ( sK24(X0,X1) = X0
            | in(sK24(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f259,f260]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK24(X0,X1) != X0
          | ~ in(sK24(X0,X1),X1) )
        & ( sK24(X0,X1) = X0
          | in(sK24(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f258]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f7772,plain,
    ( ~ in(sK8,singleton(sK8))
    | ~ in(sK8,sK6) ),
    inference(superposition,[],[f6811,f3038]) ).

fof(f3038,plain,
    singleton(sK8) = set_difference(singleton(sK8),sK7),
    inference(resolution,[],[f3031,f334]) ).

fof(f334,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_difference(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f206]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | set_difference(X0,X1) != X0 )
      & ( set_difference(X0,X1) = X0
        | ~ disjoint(X0,X1) ) ),
    inference(nnf_transformation,[],[f105]) ).

fof(f105,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> set_difference(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).

fof(f3031,plain,
    disjoint(singleton(sK8),sK7),
    inference(trivial_inequality_removal,[],[f3011]) ).

fof(f3011,plain,
    ( empty_set != empty_set
    | disjoint(singleton(sK8),sK7) ),
    inference(superposition,[],[f424,f2999]) ).

fof(f2999,plain,
    empty_set = set_intersection2(singleton(sK8),sK7),
    inference(resolution,[],[f471,f2169]) ).

fof(f2169,plain,
    sP3(sK7,singleton(sK8),empty_set),
    inference(superposition,[],[f585,f2158]) ).

fof(f2158,plain,
    empty_set = set_intersection2(sK7,singleton(sK8)),
    inference(forward_demodulation,[],[f2142,f1144]) ).

fof(f1144,plain,
    ! [X0] : empty_set = set_difference(X0,X0),
    inference(resolution,[],[f347,f397]) ).

fof(f397,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f59]) ).

fof(f59,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f347,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | empty_set = set_difference(X0,X1) ),
    inference(cnf_transformation,[],[f213]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,axiom,
    ! [X0,X1] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).

fof(f2142,plain,
    set_intersection2(sK7,singleton(sK8)) = set_difference(sK7,sK7),
    inference(superposition,[],[f314,f2136]) ).

fof(f2136,plain,
    sK7 = set_difference(sK7,singleton(sK8)),
    inference(resolution,[],[f351,f300]) ).

fof(f300,plain,
    ~ in(sK8,sK7),
    inference(cnf_transformation,[],[f197]) ).

fof(f351,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | set_difference(X0,singleton(X1)) = X0 ),
    inference(cnf_transformation,[],[f215]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( ( set_difference(X0,singleton(X1)) = X0
        | in(X1,X0) )
      & ( ~ in(X1,X0)
        | set_difference(X0,singleton(X1)) != X0 ) ),
    inference(nnf_transformation,[],[f99]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( set_difference(X0,singleton(X1)) = X0
    <=> ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).

fof(f314,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).

fof(f585,plain,
    ! [X0,X1] : sP3(X1,X0,set_intersection2(X1,X0)),
    inference(superposition,[],[f508,f402]) ).

fof(f402,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f508,plain,
    ! [X0,X1] : sP3(X1,X0,set_intersection2(X0,X1)),
    inference(equality_resolution,[],[f470]) ).

fof(f470,plain,
    ! [X2,X0,X1] :
      ( sP3(X1,X0,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f280]) ).

fof(f280,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP3(X1,X0,X2) )
      & ( sP3(X1,X0,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f189]) ).

fof(f189,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP3(X1,X0,X2) ),
    inference(definition_folding,[],[f15,f188]) ).

fof(f188,plain,
    ! [X1,X0,X2] :
      ( sP3(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f15,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f471,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X1,X0,X2)
      | set_intersection2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f280]) ).

fof(f424,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) != empty_set
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f242]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | set_intersection2(X0,X1) != empty_set )
      & ( set_intersection2(X0,X1) = empty_set
        | ~ disjoint(X0,X1) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> set_intersection2(X0,X1) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(f6811,plain,
    ! [X0] :
      ( ~ in(sK8,set_difference(singleton(X0),sK7))
      | ~ in(X0,sK6) ),
    inference(resolution,[],[f6759,f343]) ).

fof(f343,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( ( subset(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ~ subset(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).

fof(f6759,plain,
    ! [X0] :
      ( ~ subset(X0,sK6)
      | ~ in(sK8,set_difference(X0,sK7)) ),
    inference(resolution,[],[f6614,f355]) ).

fof(f355,plain,
    ! [X2,X0,X1] :
      ( subset(set_difference(X0,X2),set_difference(X1,X2))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0,X1,X2] :
      ( subset(set_difference(X0,X2),set_difference(X1,X2))
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f77]) ).

fof(f77,axiom,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
     => subset(set_difference(X0,X2),set_difference(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).

fof(f6614,plain,
    ! [X0] :
      ( ~ subset(X0,set_difference(sK6,sK7))
      | ~ in(sK8,X0) ),
    inference(backward_demodulation,[],[f2645,f6589]) ).

fof(f6589,plain,
    subset_complement(sK6,sK7) = set_difference(sK6,sK7),
    inference(resolution,[],[f415,f298]) ).

fof(f298,plain,
    element(sK7,powerset(sK6)),
    inference(cnf_transformation,[],[f197]) ).

fof(f415,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | set_difference(X0,X1) = subset_complement(X0,X1) ),
    inference(cnf_transformation,[],[f174]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) = subset_complement(X0,X1)
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => set_difference(X0,X1) = subset_complement(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).

fof(f2645,plain,
    ! [X0] :
      ( ~ subset(X0,subset_complement(sK6,sK7))
      | ~ in(sK8,X0) ),
    inference(resolution,[],[f425,f301]) ).

fof(f301,plain,
    ~ in(sK8,subset_complement(sK6,sK7)),
    inference(cnf_transformation,[],[f197]) ).

fof(f425,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f246]) ).

fof(f246,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK19(X0,X1),X1)
          & in(sK19(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f244,f245]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK19(X0,X1),X1)
        & in(sK19(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f244,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f243]) ).

fof(f243,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f7794,plain,
    sK6 = sK8,
    inference(resolution,[],[f7784,f686]) ).

fof(f686,plain,
    ( ~ empty(sK6)
    | sK6 = sK8 ),
    inference(factoring,[],[f670]) ).

fof(f670,plain,
    ! [X0] :
      ( ~ empty(sK6)
      | ~ empty(X0)
      | sK8 = X0 ),
    inference(resolution,[],[f444,f635]) ).

fof(f444,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ empty(X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f106]) ).

fof(f106,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f297,plain,
    empty_set != sK6,
    inference(cnf_transformation,[],[f197]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Apr 29 20:40:19 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (21638)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (21642)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37  TRYING [1]
% 0.12/0.37  TRYING [2]
% 0.12/0.37  % (21643)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.38  TRYING [3]
% 0.12/0.39  % (21640)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.39  % (21645)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.40  % (21641)WARNING: value z3 for option sas not known
% 0.12/0.40  % (21644)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.19/0.41  % (21641)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.19/0.43  % (21639)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.43  TRYING [4]
% 0.19/0.50  TRYING [1]
% 0.19/0.50  TRYING [2]
% 0.19/0.52  TRYING [3]
% 0.19/0.57  TRYING [4]
% 0.93/0.65  TRYING [1]
% 1.05/0.68  TRYING [5]
% 1.05/0.69  TRYING [2]
% 1.53/0.84  TRYING [5]
% 2.17/1.14  TRYING [3]
% 3.95/1.53  TRYING [6]
% 4.94/1.80  TRYING [6]
% 5.41/1.91  % (21644)First to succeed.
% 5.41/1.92  % (21644)Refutation found. Thanks to Tanya!
% 5.41/1.92  % SZS status Theorem for theBenchmark
% 5.41/1.92  % SZS output start Proof for theBenchmark
% See solution above
% 5.41/1.92  % (21644)------------------------------
% 5.41/1.92  % (21644)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.41/1.92  % (21644)Termination reason: Refutation
% 5.41/1.92  
% 5.41/1.92  % (21644)Memory used [KB]: 4174
% 5.41/1.92  % (21644)Time elapsed: 1.526 s
% 5.41/1.92  % (21644)Instructions burned: 674 (million)
% 5.41/1.92  % (21644)------------------------------
% 5.41/1.92  % (21644)------------------------------
% 5.41/1.92  % (21638)Success in time 1.567 s
% 5.41/1.92  21639 Aborted by signal SIGHUP on /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.41/1.92  % (21639)------------------------------
% 5.41/1.92  % (21639)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.41/1.92  21645 Aborted by signal SIGHUP on /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.41/1.92  % (21645)------------------------------
% 5.41/1.92  % (21645)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.41/1.92  % (21645)Termination reason: Unknown
% 5.41/1.92  % (21645)Termination phase: Saturation
% 5.41/1.92  
% 5.41/1.92  % (21645)Memory used [KB]: 22951
% 5.41/1.92  % (21645)Time elapsed: 1.535 s
% 5.41/1.92  % (21645)Instructions burned: 1853 (million)
% 5.41/1.92  % (21639)Termination reason: Unknown
% 5.41/1.92  % (21639)Termination phase: Finite model building SAT solving
% 5.41/1.92  
% 5.41/1.92  % (21645)------------------------------
% 5.41/1.92  % (21645)------------------------------
% 5.41/1.92  Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.41/1.92  ???
% 5.41/1.92  % (21639)Memory used [KB]: 6146
% 5.41/1.92  % (21639)Time elapsed: 1.049 s
% 5.41/1.92  % (21639)Instructions burned: 920 (million)
% 5.41/1.92   ???
% 5.41/1.92    ???
% 5.41/1.92     ???
% 5.41/1.92  % (21639)------------------------------
% 5.41/1.92  % (21639)------------------------------
% 5.41/1.92  Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.41/1.92  ???
% 5.41/1.92   ???
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%------------------------------------------------------------------------------