TSTP Solution File: SET992+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET992+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n007.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 May 21 03:25:02 EDT 2024

% Result   : Theorem 9.97s 1.84s
% Output   : Refutation 9.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   97 (  38 unt;   0 def)
%            Number of atoms       :  282 (  78 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  289 ( 104   ~; 104   |;  55   &)
%                                         (  15 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   2 con; 0-2 aty)
%            Number of variables   :  145 ( 124   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f60356,plain,
    $false,
    inference(subsumption_resolution,[],[f60355,f60203]) ).

fof(f60203,plain,
    sK9(relation_rng(sK5)) != sK12(sK9(relation_rng(sK5)),relation_rng(sK5)),
    inference(superposition,[],[f3486,f60176]) ).

fof(f60176,plain,
    apply(sK5,sK4) = sK9(relation_rng(sK5)),
    inference(superposition,[],[f2280,f8410]) ).

fof(f8410,plain,
    sK4 = sK8(sK9(relation_rng(sK5)),sK5),
    inference(unit_resulting_resolution,[],[f172,f2383,f149]) ).

fof(f149,plain,
    ! [X3,X0,X1] :
      ( ~ sP3(X0,X1)
      | ~ in(X3,X1)
      | X0 = X3 ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( sP3(X0,X1)
        | ( ( sK12(X0,X1) != X0
            | ~ in(sK12(X0,X1),X1) )
          & ( sK12(X0,X1) = X0
            | in(sK12(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP3(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f92,f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK12(X0,X1) != X0
          | ~ in(sK12(X0,X1),X1) )
        & ( sK12(X0,X1) = X0
          | in(sK12(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( sP3(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP3(X0,X1) ) ),
    inference(rectify,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( sP3(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | ~ sP3(X0,X1) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f2383,plain,
    in(sK8(sK9(relation_rng(sK5)),sK5),singleton(sK4)),
    inference(forward_demodulation,[],[f2375,f110]) ).

fof(f110,plain,
    singleton(sK4) = relation_dom(sK5),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( relation_rng(sK5) != singleton(apply(sK5,sK4))
    & singleton(sK4) = relation_dom(sK5)
    & function(sK5)
    & relation(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f41,f71]) ).

fof(f71,plain,
    ( ? [X0,X1] :
        ( relation_rng(X1) != singleton(apply(X1,X0))
        & singleton(X0) = relation_dom(X1)
        & function(X1)
        & relation(X1) )
   => ( relation_rng(sK5) != singleton(apply(sK5,sK4))
      & singleton(sK4) = relation_dom(sK5)
      & function(sK5)
      & relation(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ? [X0,X1] :
      ( relation_rng(X1) != singleton(apply(X1,X0))
      & singleton(X0) = relation_dom(X1)
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ? [X0,X1] :
      ( relation_rng(X1) != singleton(apply(X1,X0))
      & singleton(X0) = relation_dom(X1)
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ( singleton(X0) = relation_dom(X1)
         => relation_rng(X1) = singleton(apply(X1,X0)) ) ),
    inference(negated_conjecture,[],[f25]) ).

fof(f25,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( singleton(X0) = relation_dom(X1)
       => relation_rng(X1) = singleton(apply(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).

fof(f2375,plain,
    in(sK8(sK9(relation_rng(sK5)),sK5),relation_dom(sK5)),
    inference(unit_resulting_resolution,[],[f2218,f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | in(sK8(X0,X1),relation_dom(X1)) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( apply(X1,X2) != X0
            | ~ in(X2,relation_dom(X1)) ) )
      & ( ( apply(X1,sK8(X0,X1)) = X0
          & in(sK8(X0,X1),relation_dom(X1)) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f81,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( apply(X1,X3) = X0
          & in(X3,relation_dom(X1)) )
     => ( apply(X1,sK8(X0,X1)) = X0
        & in(sK8(X0,X1),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( apply(X1,X2) != X0
            | ~ in(X2,relation_dom(X1)) ) )
      & ( ? [X3] :
            ( apply(X1,X3) = X0
            & in(X3,relation_dom(X1)) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f80]) ).

fof(f80,plain,
    ! [X2,X0] :
      ( ( sP0(X2,X0)
        | ! [X3] :
            ( apply(X0,X3) != X2
            | ~ in(X3,relation_dom(X0)) ) )
      & ( ? [X3] :
            ( apply(X0,X3) = X2
            & in(X3,relation_dom(X0)) )
        | ~ sP0(X2,X0) ) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X2,X0] :
      ( sP0(X2,X0)
    <=> ? [X3] :
          ( apply(X0,X3) = X2
          & in(X3,relation_dom(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f2218,plain,
    sP0(sK9(relation_rng(sK5)),sK5),
    inference(unit_resulting_resolution,[],[f2211,f1567]) ).

fof(f1567,plain,
    ( sP0(sK9(relation_rng(sK5)),sK5)
    | empty(relation_rng(sK5)) ),
    inference(resolution,[],[f1555,f634]) ).

fof(f634,plain,
    ! [X0] :
      ( in(sK9(X0),X0)
      | empty(X0) ),
    inference(resolution,[],[f146,f140]) ).

fof(f140,plain,
    ! [X0] : element(sK9(X0),X0),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0] : element(sK9(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f6,f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK9(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f6,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f1555,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(sK5))
      | sP0(X0,sK5) ),
    inference(resolution,[],[f132,f374]) ).

fof(f374,plain,
    sP1(sK5,relation_rng(sK5)),
    inference(unit_resulting_resolution,[],[f344,f169]) ).

fof(f169,plain,
    ! [X0] :
      ( ~ sP2(X0)
      | sP1(X0,relation_rng(X0)) ),
    inference(equality_resolution,[],[f130]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | relation_rng(X0) != X1
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ~ sP1(X0,X1) )
          & ( sP1(X0,X1)
            | relation_rng(X0) != X1 ) )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> sP1(X0,X1) )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f344,plain,
    sP2(sK5),
    inference(unit_resulting_resolution,[],[f109,f108,f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | sP2(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_folding,[],[f53,f67,f66,f65]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> sP0(X2,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

fof(f108,plain,
    relation(sK5),
    inference(cnf_transformation,[],[f72]) ).

fof(f109,plain,
    function(sK5),
    inference(cnf_transformation,[],[f72]) ).

fof(f132,plain,
    ! [X3,X0,X1] :
      ( ~ sP1(X0,X1)
      | ~ in(X3,X1)
      | sP0(X3,X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( ( ~ sP0(sK7(X0,X1),X0)
            | ~ in(sK7(X0,X1),X1) )
          & ( sP0(sK7(X0,X1),X0)
            | in(sK7(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ sP0(X3,X0) )
            & ( sP0(X3,X0)
              | ~ in(X3,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f77,f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ sP0(X2,X0)
            | ~ in(X2,X1) )
          & ( sP0(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ sP0(sK7(X0,X1),X0)
          | ~ in(sK7(X0,X1),X1) )
        & ( sP0(sK7(X0,X1),X0)
          | in(sK7(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] :
            ( ( ~ sP0(X2,X0)
              | ~ in(X2,X1) )
            & ( sP0(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ sP0(X3,X0) )
            & ( sP0(X3,X0)
              | ~ in(X3,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] :
            ( ( ~ sP0(X2,X0)
              | ~ in(X2,X1) )
            & ( sP0(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ sP0(X2,X0) )
            & ( sP0(X2,X0)
              | ~ in(X2,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f2211,plain,
    ~ empty(relation_rng(sK5)),
    inference(unit_resulting_resolution,[],[f2197,f157]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f2197,plain,
    in(apply(sK5,sK4),relation_rng(sK5)),
    inference(unit_resulting_resolution,[],[f374,f2191,f133]) ).

fof(f133,plain,
    ! [X3,X0,X1] :
      ( ~ sP1(X0,X1)
      | ~ sP0(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f2191,plain,
    sP0(apply(sK5,sK4),sK5),
    inference(forward_demodulation,[],[f2187,f2153]) ).

fof(f2153,plain,
    ! [X0] : sK9(singleton(X0)) = X0,
    inference(unit_resulting_resolution,[],[f588,f172,f149]) ).

fof(f588,plain,
    ! [X0] : in(sK9(singleton(X0)),singleton(X0)),
    inference(unit_resulting_resolution,[],[f117,f140,f146]) ).

fof(f117,plain,
    ! [X0] : ~ empty(singleton(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : ~ empty(singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

fof(f2187,plain,
    sP0(apply(sK5,sK9(singleton(sK4))),sK5),
    inference(unit_resulting_resolution,[],[f588,f2178]) ).

fof(f2178,plain,
    ! [X0] :
      ( ~ in(X0,singleton(sK4))
      | sP0(apply(sK5,X0),sK5) ),
    inference(superposition,[],[f170,f110]) ).

fof(f170,plain,
    ! [X2,X1] :
      ( ~ in(X2,relation_dom(X1))
      | sP0(apply(X1,X2),X1) ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1)
      | apply(X1,X2) != X0
      | ~ in(X2,relation_dom(X1)) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f172,plain,
    ! [X0] : sP3(X0,singleton(X0)),
    inference(equality_resolution,[],[f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ~ sP3(X0,X1) )
      & ( sP3(X0,X1)
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> sP3(X0,X1) ),
    inference(definition_folding,[],[f4,f69]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f2280,plain,
    sK9(relation_rng(sK5)) = apply(sK5,sK8(sK9(relation_rng(sK5)),sK5)),
    inference(subsumption_resolution,[],[f2276,f2211]) ).

fof(f2276,plain,
    ( sK9(relation_rng(sK5)) = apply(sK5,sK8(sK9(relation_rng(sK5)),sK5))
    | empty(relation_rng(sK5)) ),
    inference(resolution,[],[f137,f1567]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | apply(X1,sK8(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f83]) ).

fof(f3486,plain,
    apply(sK5,sK4) != sK12(apply(sK5,sK4),relation_rng(sK5)),
    inference(unit_resulting_resolution,[],[f461,f2197,f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | sK12(X0,X1) != X0
      | sP3(X0,X1) ),
    inference(inner_rewriting,[],[f152]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | sK12(X0,X1) != X0
      | ~ in(sK12(X0,X1),X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f461,plain,
    ~ sP3(apply(sK5,sK4),relation_rng(sK5)),
    inference(unit_resulting_resolution,[],[f111,f154]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ sP3(X0,X1)
      | singleton(X0) = X1 ),
    inference(cnf_transformation,[],[f95]) ).

fof(f111,plain,
    relation_rng(sK5) != singleton(apply(sK5,sK4)),
    inference(cnf_transformation,[],[f72]) ).

fof(f60355,plain,
    sK9(relation_rng(sK5)) = sK12(sK9(relation_rng(sK5)),relation_rng(sK5)),
    inference(forward_demodulation,[],[f60354,f60176]) ).

fof(f60354,plain,
    apply(sK5,sK4) = sK12(sK9(relation_rng(sK5)),relation_rng(sK5)),
    inference(forward_demodulation,[],[f60331,f60243]) ).

fof(f60243,plain,
    sK4 = sK8(sK12(sK9(relation_rng(sK5)),relation_rng(sK5)),sK5),
    inference(superposition,[],[f59450,f60176]) ).

fof(f59450,plain,
    sK4 = sK8(sK12(apply(sK5,sK4),relation_rng(sK5)),sK5),
    inference(unit_resulting_resolution,[],[f172,f15603,f149]) ).

fof(f15603,plain,
    in(sK8(sK12(apply(sK5,sK4),relation_rng(sK5)),sK5),singleton(sK4)),
    inference(forward_demodulation,[],[f15588,f110]) ).

fof(f15588,plain,
    in(sK8(sK12(apply(sK5,sK4),relation_rng(sK5)),sK5),relation_dom(sK5)),
    inference(unit_resulting_resolution,[],[f15564,f136]) ).

fof(f15564,plain,
    sP0(sK12(apply(sK5,sK4),relation_rng(sK5)),sK5),
    inference(unit_resulting_resolution,[],[f374,f5557,f132]) ).

fof(f5557,plain,
    in(sK12(apply(sK5,sK4),relation_rng(sK5)),relation_rng(sK5)),
    inference(subsumption_resolution,[],[f5439,f3486]) ).

fof(f5439,plain,
    ( apply(sK5,sK4) = sK12(apply(sK5,sK4),relation_rng(sK5))
    | in(sK12(apply(sK5,sK4),relation_rng(sK5)),relation_rng(sK5)) ),
    inference(resolution,[],[f151,f461]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | sK12(X0,X1) = X0
      | in(sK12(X0,X1),X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f60331,plain,
    sK12(sK9(relation_rng(sK5)),relation_rng(sK5)) = apply(sK5,sK8(sK12(sK9(relation_rng(sK5)),relation_rng(sK5)),sK5)),
    inference(unit_resulting_resolution,[],[f60213,f137]) ).

fof(f60213,plain,
    sP0(sK12(sK9(relation_rng(sK5)),relation_rng(sK5)),sK5),
    inference(superposition,[],[f15564,f60176]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET992+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 11:52:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (14806)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (14813)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)
% 0.14/0.38  % (14812)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)
% 0.14/0.38  % (14807)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (14808)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (14811)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)
% 0.14/0.39  % (14810)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  % (14809)WARNING: value z3 for option sas not known
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  % (14809)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)
% 0.14/0.39  TRYING [3]
% 0.20/0.40  TRYING [4]
% 0.20/0.41  TRYING [3]
% 0.20/0.41  TRYING [5]
% 0.20/0.43  TRYING [6]
% 0.20/0.45  TRYING [4]
% 0.20/0.47  TRYING [7]
% 0.20/0.51  TRYING [5]
% 1.20/0.53  TRYING [8]
% 1.89/0.64  TRYING [9]
% 2.38/0.72  TRYING [6]
% 3.55/0.87  TRYING [10]
% 7.51/1.47  TRYING [1]
% 7.51/1.47  TRYING [2]
% 7.51/1.47  TRYING [3]
% 7.51/1.47  TRYING [4]
% 7.51/1.48  TRYING [5]
% 7.90/1.49  TRYING [6]
% 7.90/1.52  TRYING [7]
% 8.37/1.56  TRYING [8]
% 8.97/1.69  TRYING [9]
% 9.97/1.83  % (14813)First to succeed.
% 9.97/1.83  % (14813)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14806"
% 9.97/1.84  % (14813)Refutation found. Thanks to Tanya!
% 9.97/1.84  % SZS status Theorem for theBenchmark
% 9.97/1.84  % SZS output start Proof for theBenchmark
% See solution above
% 9.97/1.84  % (14813)------------------------------
% 9.97/1.84  % (14813)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 9.97/1.84  % (14813)Termination reason: Refutation
% 9.97/1.84  
% 9.97/1.84  % (14813)Memory used [KB]: 22144
% 9.97/1.84  % (14813)Time elapsed: 1.457 s
% 9.97/1.84  % (14813)Instructions burned: 3479 (million)
% 9.97/1.84  % (14806)Success in time 1.461 s
%------------------------------------------------------------------------------