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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SEU284+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n026.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 12:52:43 PM UTC 2026

% Result   : Theorem 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  110 (   6 unt;   8 def)
%            Number of atoms       :  365 ( 102 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  423 ( 168   ~; 183   |;  57   &)
%                                         (   7 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   13 (  11 usr;   8 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :   88 (   0 sgn  62   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0] :
    ? [X1] :
      ( relation(X1)
      & function(X1)
      & relation_dom(X1) = X0
      & ! [X2] :
          ( in(X2,X0)
         => apply(X1,X2) = singleton(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
      ? [X1] :
        ( relation(X1)
        & function(X1)
        & relation_dom(X1) = X0
        & ! [X2] :
            ( in(X2,X0)
           => apply(X1,X2) = singleton(X2) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( ! [X1,X2,X3] :
            ( ( in(X1,X0)
              & X2 = singleton(X1)
              & X3 = singleton(X1) )
           => X2 = X3 )
        & ! [X1] :
            ~ ( in(X1,X0)
              & ! [X2] : X2 != singleton(X1) ) )
     => ? [X1] :
          ( relation(X1)
          & function(X1)
          & relation_dom(X1) = X0
          & ! [X2] :
              ( in(X2,X0)
             => apply(X1,X2) = singleton(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).

fof(f29,plain,
    ! [X0] :
      ( ( ! [X1,X2,X3] :
            ( ( in(X1,X0)
              & X2 = singleton(X1)
              & X3 = singleton(X1) )
           => X2 = X3 )
        & ! [X4] :
            ~ ( in(X4,X0)
              & ! [X5] : singleton(X4) != X5 ) )
     => ? [X6] :
          ( relation(X6)
          & function(X6)
          & relation_dom(X6) = X0
          & ! [X7] :
              ( in(X7,X0)
             => apply(X6,X7) = singleton(X7) ) ) ),
    inference(rectify,[],[f8]) ).

fof(f32,plain,
    ? [X0] :
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | relation_dom(X1) != X0
      | ? [X2] :
          ( apply(X1,X2) != singleton(X2)
          & in(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f34,plain,
    ! [X0] :
      ( ? [X6] :
          ( relation(X6)
          & function(X6)
          & relation_dom(X6) = X0
          & ! [X7] :
              ( apply(X6,X7) = singleton(X7)
              | ~ in(X7,X0) ) )
      | ? [X1,X2,X3] :
          ( X2 != X3
          & in(X1,X0)
          & X2 = singleton(X1)
          & X3 = singleton(X1) )
      | ? [X4] :
          ( in(X4,X0)
          & ! [X5] : singleton(X4) != X5 ) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f35,plain,
    ! [X0] :
      ( ? [X6] :
          ( relation(X6)
          & function(X6)
          & relation_dom(X6) = X0
          & ! [X7] :
              ( apply(X6,X7) = singleton(X7)
              | ~ in(X7,X0) ) )
      | ? [X1,X2,X3] :
          ( X2 != X3
          & in(X1,X0)
          & X2 = singleton(X1)
          & X3 = singleton(X1) )
      | ? [X4] :
          ( in(X4,X0)
          & ! [X5] : singleton(X4) != X5 ) ),
    inference(flattening,[],[f34]) ).

fof(f47,definition,
    ! [X0] :
      ( ? [X1,X2,X3] :
          ( X2 != X3
          & in(X1,X0)
          & X2 = singleton(X1)
          & X3 = singleton(X1) )
      | ~ sP0(X0) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X6] :
          ( relation(X6)
          & function(X6)
          & relation_dom(X6) = X0
          & ! [X7] :
              ( apply(X6,X7) = singleton(X7)
              | ~ in(X7,X0) ) )
      | sP0(X0)
      | ? [X4] :
          ( in(X4,X0)
          & ! [X5] : singleton(X4) != X5 ) ),
    inference(definition_folding,[],[f35,f47]) ).

fof(f49,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | relation_dom(X1) != sK1
      | ( apply(X1,sK2(X1)) != singleton(sK2(X1))
        & in(sK2(X1),sK1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X2,sK2(X1))],[f32]) ).

fof(f51,plain,
    ! [X0] :
      ( ? [X1,X2,X3] :
          ( X2 != X3
          & in(X1,X0)
          & X2 = singleton(X1)
          & X3 = singleton(X1) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f52,plain,
    ! [X0] :
      ( ( sK5(X0) != sK6(X0)
        & in(sK4(X0),X0)
        & sK5(X0) = singleton(sK4(X0))
        & sK6(X0) = singleton(sK4(X0)) )
      | ~ sP0(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X3,sK6(X0))],[f51]) ).

fof(f53,plain,
    ! [X0] :
      ( ? [X1] :
          ( relation(X1)
          & function(X1)
          & relation_dom(X1) = X0
          & ! [X2] :
              ( apply(X1,X2) = singleton(X2)
              | ~ in(X2,X0) ) )
      | sP0(X0)
      | ? [X3] :
          ( in(X3,X0)
          & ! [X4] : singleton(X3) != X4 ) ),
    inference(rectify,[],[f48]) ).

fof(f54,plain,
    ! [X0] :
      ( ( relation(sK7(X0))
        & function(sK7(X0))
        & relation_dom(sK7(X0)) = X0
        & ! [X2] :
            ( singleton(X2) = apply(sK7(X0),X2)
            | ~ in(X2,X0) ) )
      | sP0(X0)
      | ( in(sK8(X0),X0)
        & ! [X4] : singleton(sK8(X0)) != X4 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X3,sK8(X0))],[f53]) ).

fof(f61,plain,
    ! [X1] :
      ( relation_dom(X1) != sK1
      | ~ function(X1)
      | ~ relation(X1)
      | in(sK2(X1),sK1) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f62,plain,
    ! [X1] :
      ( apply(X1,sK2(X1)) != singleton(sK2(X1))
      | ~ function(X1)
      | relation_dom(X1) != sK1
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK6(X0) = singleton(sK4(X0)) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK5(X0) = singleton(sK4(X0)) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f69,plain,
    ! [X0] :
      ( sK5(X0) != sK6(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f70,plain,
    ! [X2,X0,X4] :
      ( singleton(X2) = apply(sK7(X0),X2)
      | ~ in(X2,X0)
      | sP0(X0)
      | singleton(sK8(X0)) != X4 ),
    inference(cnf_transformation,[],[f54]) ).

fof(f72,plain,
    ! [X0,X4] :
      ( relation_dom(sK7(X0)) = X0
      | sP0(X0)
      | singleton(sK8(X0)) != X4 ),
    inference(cnf_transformation,[],[f54]) ).

fof(f74,plain,
    ! [X0,X4] :
      ( function(sK7(X0))
      | sP0(X0)
      | singleton(sK8(X0)) != X4 ),
    inference(cnf_transformation,[],[f54]) ).

fof(f76,plain,
    ! [X0,X4] :
      ( relation(sK7(X0))
      | sP0(X0)
      | singleton(sK8(X0)) != X4 ),
    inference(cnf_transformation,[],[f54]) ).

fof(f101,plain,
    ! [X0] :
      ( relation(sK7(X0))
      | sP0(X0) ),
    inference(equality_resolution,[],[f76]) ).

fof(f102,plain,
    ! [X0] :
      ( function(sK7(X0))
      | sP0(X0) ),
    inference(equality_resolution,[],[f74]) ).

fof(f103,plain,
    ! [X0] :
      ( sP0(X0)
      | relation_dom(sK7(X0)) = X0 ),
    inference(equality_resolution,[],[f72]) ).

fof(f104,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | singleton(X2) = apply(sK7(X0),X2)
      | sP0(X0) ),
    inference(equality_resolution,[],[f70]) ).

fof(f156,plain,
    ! [X0] :
      ( sK6(X0) = singleton(sK4(X0))
      | relation_dom(sK7(X0)) = X0 ),
    inference(resolution,[],[f66,f103]) ).

fof(f157,plain,
    ! [X0] :
      ( sK5(X0) = singleton(sK4(X0))
      | relation_dom(sK7(X0)) = X0 ),
    inference(resolution,[],[f67,f103]) ).

fof(f211,plain,
    ! [X0] :
      ( sK5(X0) = sK6(X0)
      | relation_dom(sK7(X0)) = X0
      | relation_dom(sK7(X0)) = X0 ),
    inference(superposition,[],[f156,f157]) ).

fof(f212,plain,
    ! [X0] :
      ( relation_dom(sK7(X0)) = X0
      | sK5(X0) = sK6(X0) ),
    inference(duplicate_literal_removal,[],[f211]) ).

fof(f243,plain,
    ! [X0] :
      ( sK1 != X0
      | ~ function(sK7(X0))
      | ~ relation(sK7(X0))
      | in(sK2(sK7(X0)),sK1)
      | sK5(X0) = sK6(X0) ),
    inference(superposition,[],[f61,f212]) ).

fof(f244,plain,
    ( ~ function(sK7(sK1))
    | ~ relation(sK7(sK1))
    | in(sK2(sK7(sK1)),sK1)
    | sK5(sK1) = sK6(sK1) ),
    inference(equality_resolution,[],[f243]) ).

fof(f246,definition,
    ( spl15_5
  <=> sK5(sK1) = sK6(sK1) ),
    introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).

fof(f247,plain,
    ( sK5(sK1) != sK6(sK1)
    | spl15_5 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f248,plain,
    ( sK5(sK1) = sK6(sK1)
    | ~ spl15_5 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f250,definition,
    ( spl15_6
  <=> in(sK2(sK7(sK1)),sK1) ),
    introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).

fof(f252,plain,
    ( in(sK2(sK7(sK1)),sK1)
    | ~ spl15_6 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f254,definition,
    ( spl15_7
  <=> relation(sK7(sK1)) ),
    introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).

fof(f255,plain,
    ( relation(sK7(sK1))
    | ~ spl15_7 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f256,plain,
    ( ~ relation(sK7(sK1))
    | spl15_7 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f258,definition,
    ( spl15_8
  <=> function(sK7(sK1)) ),
    introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).

fof(f259,plain,
    ( function(sK7(sK1))
    | ~ spl15_8 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f260,plain,
    ( ~ function(sK7(sK1))
    | spl15_8 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f261,plain,
    ( spl15_5
    | spl15_6
    | ~ spl15_7
    | ~ spl15_8 ),
    inference(avatar_split_clause,[],[f244,f258,f254,f250,f246]) ).

fof(f262,plain,
    ( sP0(sK1)
    | spl15_7 ),
    inference(resolution,[],[f256,f101]) ).

fof(f266,plain,
    ( sK5(sK1) = singleton(sK4(sK1))
    | spl15_7 ),
    inference(resolution,[],[f262,f67]) ).

fof(f267,plain,
    ( sK6(sK1) = singleton(sK4(sK1))
    | spl15_7 ),
    inference(resolution,[],[f262,f66]) ).

fof(f286,plain,
    ( sK5(sK1) = sK6(sK1)
    | spl15_7 ),
    inference(forward_demodulation,[],[f267,f266]) ).

fof(f287,plain,
    ( spl15_5
    | spl15_7 ),
    inference(avatar_split_clause,[],[f286,f254,f246]) ).

fof(f299,plain,
    ( sK5(sK1) != sK5(sK1)
    | ~ sP0(sK1)
    | ~ spl15_5 ),
    inference(superposition,[],[f69,f248]) ).

fof(f300,plain,
    ( ~ sP0(sK1)
    | ~ spl15_5 ),
    inference(trivial_inequality_removal,[],[f299]) ).

fof(f301,plain,
    ( $false
    | ~ spl15_5
    | spl15_7 ),
    inference(forward_subsumption_resolution,[],[f300,f262]) ).

fof(f302,plain,
    ( ~ spl15_5
    | spl15_7 ),
    inference(avatar_contradiction_clause,[],[f301]) ).

fof(f311,plain,
    ( sK1 = relation_dom(sK7(sK1))
    | ~ spl15_5 ),
    inference(resolution,[],[f300,f103]) ).

fof(f346,plain,
    ( sK1 != sK1
    | ~ function(sK7(sK1))
    | ~ relation(sK7(sK1))
    | in(sK2(sK7(sK1)),sK1)
    | ~ spl15_5 ),
    inference(superposition,[],[f61,f311]) ).

fof(f347,plain,
    ( ~ function(sK7(sK1))
    | ~ relation(sK7(sK1))
    | in(sK2(sK7(sK1)),sK1)
    | ~ spl15_5 ),
    inference(trivial_inequality_removal,[],[f346]) ).

fof(f348,plain,
    ( ~ function(sK7(sK1))
    | in(sK2(sK7(sK1)),sK1)
    | ~ spl15_5
    | ~ spl15_7 ),
    inference(forward_subsumption_resolution,[],[f347,f255]) ).

fof(f364,plain,
    ( spl15_6
    | ~ spl15_8
    | ~ spl15_5
    | ~ spl15_7 ),
    inference(avatar_split_clause,[],[f348,f254,f246,f258,f250]) ).

fof(f404,definition,
    ( spl15_18
  <=> sK5(sK1) = singleton(sK4(sK1)) ),
    introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).

fof(f406,plain,
    ( sK5(sK1) = singleton(sK4(sK1))
    | ~ spl15_18 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f408,plain,
    ( sP0(sK1)
    | spl15_8 ),
    inference(resolution,[],[f260,f102]) ).

fof(f409,plain,
    ( $false
    | ~ spl15_5
    | spl15_8 ),
    inference(forward_subsumption_resolution,[],[f408,f300]) ).

fof(f410,plain,
    ( ~ spl15_5
    | spl15_8 ),
    inference(avatar_contradiction_clause,[],[f409]) ).

fof(f442,plain,
    ( singleton(sK2(sK7(sK1))) = apply(sK7(sK1),sK2(sK7(sK1)))
    | sP0(sK1)
    | ~ spl15_6 ),
    inference(resolution,[],[f252,f104]) ).

fof(f446,plain,
    ( singleton(sK2(sK7(sK1))) = apply(sK7(sK1),sK2(sK7(sK1)))
    | ~ spl15_5
    | ~ spl15_6 ),
    inference(forward_subsumption_resolution,[],[f442,f300]) ).

fof(f517,plain,
    ( singleton(sK2(sK7(sK1))) != singleton(sK2(sK7(sK1)))
    | ~ function(sK7(sK1))
    | sK1 != relation_dom(sK7(sK1))
    | ~ relation(sK7(sK1))
    | ~ spl15_5
    | ~ spl15_6 ),
    inference(superposition,[],[f62,f446]) ).

fof(f518,plain,
    ( ~ function(sK7(sK1))
    | sK1 != relation_dom(sK7(sK1))
    | ~ relation(sK7(sK1))
    | ~ spl15_5
    | ~ spl15_6 ),
    inference(trivial_inequality_removal,[],[f517]) ).

fof(f519,plain,
    ( sK1 != relation_dom(sK7(sK1))
    | ~ relation(sK7(sK1))
    | ~ spl15_5
    | ~ spl15_6
    | ~ spl15_8 ),
    inference(forward_subsumption_resolution,[],[f518,f259]) ).

fof(f520,plain,
    ( ~ relation(sK7(sK1))
    | ~ spl15_5
    | ~ spl15_6
    | ~ spl15_8 ),
    inference(forward_subsumption_resolution,[],[f519,f311]) ).

fof(f521,plain,
    ( $false
    | ~ spl15_5
    | ~ spl15_6
    | ~ spl15_7
    | ~ spl15_8 ),
    inference(forward_subsumption_resolution,[],[f520,f255]) ).

fof(f522,plain,
    ( ~ spl15_5
    | ~ spl15_6
    | ~ spl15_7
    | ~ spl15_8 ),
    inference(avatar_contradiction_clause,[],[f521]) ).

fof(f524,definition,
    ( spl15_25
  <=> sP0(sK1) ),
    introduced(definition,[new_symbols(definition,[spl15_25])],[avatar_definition]) ).

fof(f525,plain,
    ( ~ sP0(sK1)
    | spl15_25 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f526,plain,
    ( sP0(sK1)
    | ~ spl15_25 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f528,definition,
    ( spl15_26
  <=> singleton(sK2(sK7(sK1))) = apply(sK7(sK1),sK2(sK7(sK1))) ),
    introduced(definition,[new_symbols(definition,[spl15_26])],[avatar_definition]) ).

fof(f530,plain,
    ( singleton(sK2(sK7(sK1))) = apply(sK7(sK1),sK2(sK7(sK1)))
    | ~ spl15_26 ),
    inference(avatar_component_clause,[],[f528]) ).

fof(f531,plain,
    ( spl15_25
    | spl15_26
    | ~ spl15_6 ),
    inference(avatar_split_clause,[],[f442,f250,f528,f524]) ).

fof(f537,plain,
    ( sK5(sK1) = singleton(sK4(sK1))
    | ~ spl15_25 ),
    inference(resolution,[],[f526,f67]) ).

fof(f538,plain,
    ( sK6(sK1) = singleton(sK4(sK1))
    | ~ spl15_25 ),
    inference(resolution,[],[f526,f66]) ).

fof(f540,plain,
    ( spl15_18
    | ~ spl15_25 ),
    inference(avatar_split_clause,[],[f537,f524,f404]) ).

fof(f543,plain,
    ( sK5(sK1) = sK6(sK1)
    | ~ spl15_18
    | ~ spl15_25 ),
    inference(superposition,[],[f406,f538]) ).

fof(f549,plain,
    ( $false
    | spl15_5
    | ~ spl15_18
    | ~ spl15_25 ),
    inference(forward_subsumption_resolution,[],[f543,f247]) ).

fof(f550,plain,
    ( spl15_5
    | ~ spl15_18
    | ~ spl15_25 ),
    inference(avatar_contradiction_clause,[],[f549]) ).

fof(f552,plain,
    ( sK1 = relation_dom(sK7(sK1))
    | spl15_25 ),
    inference(resolution,[],[f525,f103]) ).

fof(f597,plain,
    ( singleton(sK2(sK7(sK1))) != singleton(sK2(sK7(sK1)))
    | ~ function(sK7(sK1))
    | sK1 != relation_dom(sK7(sK1))
    | ~ relation(sK7(sK1))
    | ~ spl15_26 ),
    inference(superposition,[],[f62,f530]) ).

fof(f598,plain,
    ( ~ function(sK7(sK1))
    | sK1 != relation_dom(sK7(sK1))
    | ~ relation(sK7(sK1))
    | ~ spl15_26 ),
    inference(trivial_inequality_removal,[],[f597]) ).

fof(f603,plain,
    ( $false
    | spl15_8
    | spl15_25 ),
    inference(forward_subsumption_resolution,[],[f408,f525]) ).

fof(f604,plain,
    ( spl15_8
    | spl15_25 ),
    inference(avatar_contradiction_clause,[],[f603]) ).

fof(f605,plain,
    ( ~ function(sK7(sK1))
    | ~ relation(sK7(sK1))
    | spl15_25
    | ~ spl15_26 ),
    inference(forward_subsumption_resolution,[],[f598,f552]) ).

fof(f606,plain,
    ( ~ function(sK7(sK1))
    | ~ spl15_7
    | spl15_25
    | ~ spl15_26 ),
    inference(forward_subsumption_resolution,[],[f605,f255]) ).

fof(f607,plain,
    ( ~ spl15_8
    | ~ spl15_7
    | spl15_25
    | ~ spl15_26 ),
    inference(avatar_split_clause,[],[f606,f528,f524,f254,f258]) ).

cnf(s4,plain,
    ( spl15_5
    | spl15_6
    | ~ spl15_7
    | ~ spl15_8 ),
    inference(sat_conversion,[],[f261]) ).

cnf(s5,plain,
    ( spl15_5
    | spl15_7 ),
    inference(sat_conversion,[],[f287]) ).

cnf(s6,plain,
    ( ~ spl15_5
    | spl15_7 ),
    inference(sat_conversion,[],[f302]) ).

cnf(s11,plain,
    ( ~ spl15_5
    | spl15_6
    | ~ spl15_7
    | ~ spl15_8 ),
    inference(sat_conversion,[],[f364]) ).

cnf(s16,plain,
    ( ~ spl15_5
    | spl15_8 ),
    inference(sat_conversion,[],[f410]) ).

cnf(s33,plain,
    ( ~ spl15_5
    | ~ spl15_6
    | ~ spl15_7
    | ~ spl15_8 ),
    inference(sat_conversion,[],[f522]) ).

cnf(s34,plain,
    ( ~ spl15_6
    | spl15_25
    | spl15_26 ),
    inference(sat_conversion,[],[f531]) ).

cnf(s36,plain,
    ( spl15_18
    | ~ spl15_25 ),
    inference(sat_conversion,[],[f540]) ).

cnf(s38,plain,
    ( spl15_5
    | ~ spl15_18
    | ~ spl15_25 ),
    inference(sat_conversion,[],[f550]) ).

cnf(s40,plain,
    ( spl15_8
    | spl15_25 ),
    inference(sat_conversion,[],[f604]) ).

cnf(s41,plain,
    ( ~ spl15_7
    | ~ spl15_8
    | spl15_25
    | ~ spl15_26 ),
    inference(sat_conversion,[],[f607]) ).

cnf(s43,plain,
    ( ~ spl15_25
    | spl15_5 ),
    inference(rat,[],[s38,s36]) ).

cnf(s44,plain,
    spl15_5,
    inference(rat,[],[s34,s4,s41,s40,s43,s5]) ).

cnf(s45,plain,
    spl15_8,
    inference(rat,[],[s16,s44]) ).

cnf(s46,plain,
    spl15_7,
    inference(rat,[],[s6,s44]) ).

cnf(s47,plain,
    ~ spl15_6,
    inference(rat,[],[s33,s45,s44,s46]) ).

cnf(s48,plain,
    $false,
    inference(rat,[],[s11,s45,s44,s47,s46]) ).

fof(f608,plain,
    $false,
    inference(avatar_sat_refutation,[],[s48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU284+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37  % Computer : n026.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Mon Sep 28 04:32:12 UTC 2026
% 0.14/0.38  % CPUTime  : 
% 0.14/0.38  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40  Running first-order model finding
% 0.14/0.40  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
% 0.21/0.46  % (3459970)Will run a generic schedule for satisfiability detection.
% 0.21/0.46  % (3459977)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=505994384:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.46  % (3459976)% WARNING: option uhcvi not known.
% 0.21/0.46  % (3459975)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=642723453_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.46  % (3459980)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3335281673:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.46  % (3459978)dis+10_1_sil=32000:sp=arity:random_seed=2588475403:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.46  % (3459981)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4226148226:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.46  % (3459979)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3062464298:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.46  % (3459976)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2390188950:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.46  % TRYING [1]
% 0.21/0.46  % TRYING [2]
% 0.21/0.46  % TRYING [3]
% 0.21/0.46  % TRYING [4]
% 0.21/0.46  % TRYING [5]
% 0.21/0.46  % (3459978) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3459970-3459978"...
% 0.21/0.46  % (3459976) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3459970-3459976"...
% 0.21/0.46  % (3459978)...printing done.
% 0.21/0.46  % (3459980) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3459970-3459980"...
% 0.21/0.46  % (3459978)Refutation found. Thanks to Tanya!
% 0.21/0.46  % SZS status Theorem for theBenchmark
% 0.21/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46  % (3459978)------------------------------
% 0.21/0.46  % (3459978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.46  % (3459978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.46  % (3459978)CaDiCaL version: 2.1.3
% 0.21/0.46  % (3459978)Termination reason: Refutation
% 0.21/0.46  % (3459978)Time elapsed: 0.014 s
% 0.21/0.46  % (3459978)Peak memory usage: 12 MB
% 0.21/0.46  % (3459978)Instructions burned: 19 (million)
% 0.21/0.46  % (3459970)Success in time 0.051 s
% 0.21/0.46  % Vampire exiting
%------------------------------------------------------------------------------