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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SEU271+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n013.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 12:52:40 PM UTC 2026

% Result   : Theorem 0.16s 0.51s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   66 (  15 unt;   0 def)
%            Number of atoms       :  306 (  53 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  392 ( 152   ~; 171   |;  52   &)
%                                         (  12 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :  151 ( 140   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X0,X1)
        & subset(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(f10,axiom,
    ! [X0] :
      ( relation(X0)
     => ( antisymmetric(X0)
      <=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => ( X1 = inclusion_relation(X0)
      <=> ( relation_field(X1) = X0
          & ! [X2,X3] :
              ( ( in(X2,X0)
                & in(X3,X0) )
             => ( in(ordered_pair(X2,X3),X1)
              <=> subset(X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).

fof(f12,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( is_antisymmetric_in(X0,X1)
        <=> ! [X2,X3] :
              ( ( in(X2,X1)
                & in(X3,X1)
                & in(ordered_pair(X2,X3),X0)
                & in(ordered_pair(X3,X2),X0) )
             => X2 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).

fof(f13,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f17,axiom,
    ! [X0] : relation(inclusion_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).

fof(f49,conjecture,
    ! [X0] : antisymmetric(inclusion_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).

fof(f50,negated_conjecture,
    ~ ! [X0] : antisymmetric(inclusion_relation(X0)),
    inference(negated_conjecture,[status(cth)],[f49]) ).

fof(f70,plain,
    ! [X0] :
      ( ( antisymmetric(X0)
      <=> is_antisymmetric_in(X0,relation_field(X0)) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( X1 = inclusion_relation(X0)
      <=> ( relation_field(X1) = X0
          & ! [X2,X3] :
              ( ( in(ordered_pair(X2,X3),X1)
              <=> subset(X2,X3) )
              | ~ in(X2,X0)
              | ~ in(X3,X0) ) ) )
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( X1 = inclusion_relation(X0)
      <=> ( relation_field(X1) = X0
          & ! [X2,X3] :
              ( ( in(ordered_pair(X2,X3),X1)
              <=> subset(X2,X3) )
              | ~ in(X2,X0)
              | ~ in(X3,X0) ) ) )
      | ~ relation(X1) ),
    inference(flattening,[],[f71]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( is_antisymmetric_in(X0,X1)
        <=> ! [X2,X3] :
              ( X2 = X3
              | ~ in(X2,X1)
              | ~ in(X3,X1)
              | ~ in(ordered_pair(X2,X3),X0)
              | ~ in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( is_antisymmetric_in(X0,X1)
        <=> ! [X2,X3] :
              ( X2 = X3
              | ~ in(X2,X1)
              | ~ in(X3,X1)
              | ~ in(ordered_pair(X2,X3),X0)
              | ~ in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f84,plain,
    ? [X0] : ~ antisymmetric(inclusion_relation(X0)),
    inference(ennf_transformation,[],[f50]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) )
      & ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) )
      & ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 ) ),
    inference(flattening,[],[f88]) ).

fof(f90,plain,
    ! [X0] :
      ( ( ( antisymmetric(X0)
          | ~ is_antisymmetric_in(X0,relation_field(X0)) )
        & ( is_antisymmetric_in(X0,relation_field(X0))
          | ~ antisymmetric(X0) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( ( X1 = inclusion_relation(X0)
          | relation_field(X1) != X0
          | ? [X2,X3] :
              ( ( ~ subset(X2,X3)
                | ~ in(ordered_pair(X2,X3),X1) )
              & ( subset(X2,X3)
                | in(ordered_pair(X2,X3),X1) )
              & in(X2,X0)
              & in(X3,X0) ) )
        & ( ( relation_field(X1) = X0
            & ! [X2,X3] :
                ( ( ( in(ordered_pair(X2,X3),X1)
                    | ~ subset(X2,X3) )
                  & ( subset(X2,X3)
                    | ~ in(ordered_pair(X2,X3),X1) ) )
                | ~ in(X2,X0)
                | ~ in(X3,X0) ) )
          | inclusion_relation(X0) != X1 ) )
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( ( X1 = inclusion_relation(X0)
          | relation_field(X1) != X0
          | ? [X2,X3] :
              ( ( ~ subset(X2,X3)
                | ~ in(ordered_pair(X2,X3),X1) )
              & ( subset(X2,X3)
                | in(ordered_pair(X2,X3),X1) )
              & in(X2,X0)
              & in(X3,X0) ) )
        & ( ( relation_field(X1) = X0
            & ! [X2,X3] :
                ( ( ( in(ordered_pair(X2,X3),X1)
                    | ~ subset(X2,X3) )
                  & ( subset(X2,X3)
                    | ~ in(ordered_pair(X2,X3),X1) ) )
                | ~ in(X2,X0)
                | ~ in(X3,X0) ) )
          | inclusion_relation(X0) != X1 ) )
      | ~ relation(X1) ),
    inference(flattening,[],[f91]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ( ( X1 = inclusion_relation(X0)
          | relation_field(X1) != X0
          | ? [X2,X3] :
              ( ( ~ subset(X2,X3)
                | ~ in(ordered_pair(X2,X3),X1) )
              & ( subset(X2,X3)
                | in(ordered_pair(X2,X3),X1) )
              & in(X2,X0)
              & in(X3,X0) ) )
        & ( ( relation_field(X1) = X0
            & ! [X4,X5] :
                ( ( ( in(ordered_pair(X4,X5),X1)
                    | ~ subset(X4,X5) )
                  & ( subset(X4,X5)
                    | ~ in(ordered_pair(X4,X5),X1) ) )
                | ~ in(X4,X0)
                | ~ in(X5,X0) ) )
          | inclusion_relation(X0) != X1 ) )
      | ~ relation(X1) ),
    inference(rectify,[],[f92]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( ( X1 = inclusion_relation(X0)
          | relation_field(X1) != X0
          | ( ( ~ subset(sK0(X0,X1),sK1(X0,X1))
              | ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
            & ( subset(sK0(X0,X1),sK1(X0,X1))
              | in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
            & in(sK0(X0,X1),X0)
            & in(sK1(X0,X1),X0) ) )
        & ( ( relation_field(X1) = X0
            & ! [X4,X5] :
                ( ( ( in(ordered_pair(X4,X5),X1)
                    | ~ subset(X4,X5) )
                  & ( subset(X4,X5)
                    | ~ in(ordered_pair(X4,X5),X1) ) )
                | ~ in(X4,X0)
                | ~ in(X5,X0) ) )
          | inclusion_relation(X0) != X1 ) )
      | ~ relation(X1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f93]) ).

fof(f95,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( is_antisymmetric_in(X0,X1)
            | ? [X2,X3] :
                ( X2 != X3
                & in(X2,X1)
                & in(X3,X1)
                & in(ordered_pair(X2,X3),X0)
                & in(ordered_pair(X3,X2),X0) ) )
          & ( ! [X2,X3] :
                ( X2 = X3
                | ~ in(X2,X1)
                | ~ in(X3,X1)
                | ~ in(ordered_pair(X2,X3),X0)
                | ~ in(ordered_pair(X3,X2),X0) )
            | ~ is_antisymmetric_in(X0,X1) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( is_antisymmetric_in(X0,X1)
            | ? [X2,X3] :
                ( X2 != X3
                & in(X2,X1)
                & in(X3,X1)
                & in(ordered_pair(X2,X3),X0)
                & in(ordered_pair(X3,X2),X0) ) )
          & ( ! [X4,X5] :
                ( X4 = X5
                | ~ in(X4,X1)
                | ~ in(X5,X1)
                | ~ in(ordered_pair(X4,X5),X0)
                | ~ in(ordered_pair(X5,X4),X0) )
            | ~ is_antisymmetric_in(X0,X1) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f95]) ).

fof(f97,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( is_antisymmetric_in(X0,X1)
            | ( sK2(X0,X1) != sK3(X0,X1)
              & in(sK2(X0,X1),X1)
              & in(sK3(X0,X1),X1)
              & in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
              & in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0) ) )
          & ( ! [X4,X5] :
                ( X4 = X5
                | ~ in(X4,X1)
                | ~ in(X5,X1)
                | ~ in(ordered_pair(X4,X5),X0)
                | ~ in(ordered_pair(X5,X4),X0) )
            | ~ is_antisymmetric_in(X0,X1) ) )
      | ~ relation(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f96]) ).

fof(f109,plain,
    ~ antisymmetric(inclusion_relation(sK14)),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f84]) ).

fof(f120,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f89]) ).

fof(f126,plain,
    ! [X0] :
      ( ~ is_antisymmetric_in(X0,relation_field(X0))
      | antisymmetric(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f127,plain,
    ! [X0,X1,X4,X5] :
      ( subset(X4,X5)
      | ~ in(ordered_pair(X4,X5),X1)
      | ~ in(X4,X0)
      | ~ in(X5,X0)
      | inclusion_relation(X0) != X1
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( relation_field(X1) = X0
      | inclusion_relation(X0) != X1
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( is_antisymmetric_in(X0,X1)
      | in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( is_antisymmetric_in(X0,X1)
      | in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( in(sK3(X0,X1),X1)
      | is_antisymmetric_in(X0,X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( in(sK2(X0,X1),X1)
      | is_antisymmetric_in(X0,X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( sK2(X0,X1) != sK3(X0,X1)
      | is_antisymmetric_in(X0,X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f140,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f142,plain,
    ! [X0] : relation(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f17]) ).

fof(f187,plain,
    ~ antisymmetric(inclusion_relation(sK14)),
    inference(cnf_transformation,[],[f109]) ).

fof(f194,plain,
    ! [X0,X1,X4,X5] :
      ( subset(X4,X5)
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
      | ~ in(X4,X0)
      | ~ in(X5,X0)
      | inclusion_relation(X0) != X1
      | ~ relation(X1) ),
    inference(definition_unfolding,[],[f127,f140]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( is_antisymmetric_in(X0,X1)
      | in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f136,f140]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( is_antisymmetric_in(X0,X1)
      | in(unordered_pair(unordered_pair(sK3(X0,X1),sK2(X0,X1)),singleton(sK3(X0,X1))),X0)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f135,f140]) ).

fof(f205,plain,
    ! [X0] :
      ( relation_field(inclusion_relation(X0)) = X0
      | ~ relation(inclusion_relation(X0)) ),
    inference(equality_resolution,[],[f129]) ).

fof(f207,plain,
    ! [X0,X4,X5] :
      ( subset(X4,X5)
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),inclusion_relation(X0))
      | ~ in(X4,X0)
      | ~ in(X5,X0)
      | ~ relation(inclusion_relation(X0)) ),
    inference(equality_resolution,[],[f194]) ).

fof(f299,plain,
    ! [X0] : relation_field(inclusion_relation(X0)) = X0,
    inference(forward_subsumption_resolution,[],[f205,f142]) ).

fof(f300,plain,
    ! [X0] :
      ( ~ is_antisymmetric_in(inclusion_relation(X0),X0)
      | antisymmetric(inclusion_relation(X0))
      | ~ relation(inclusion_relation(X0)) ),
    inference(superposition,[],[f126,f299]) ).

fof(f303,plain,
    ! [X0] :
      ( ~ is_antisymmetric_in(inclusion_relation(X0),X0)
      | antisymmetric(inclusion_relation(X0)) ),
    inference(forward_subsumption_resolution,[],[f300,f142]) ).

fof(f349,plain,
    ! [X0,X1] :
      ( in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0)
      | is_antisymmetric_in(X0,X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f195,f120]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),sK2(X0,X1))),X0)
      | is_antisymmetric_in(X0,X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f196,f120]) ).

fof(f351,plain,
    ! [X0,X1] :
      ( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0)
      | is_antisymmetric_in(X0,X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f350,f120]) ).

fof(f372,plain,
    ! [X0,X4,X5] :
      ( subset(X4,X5)
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),inclusion_relation(X0))
      | ~ in(X4,X0)
      | ~ in(X5,X0) ),
    inference(forward_subsumption_resolution,[],[f207,f142]) ).

fof(f373,plain,
    ! [X0,X4,X5] :
      ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),inclusion_relation(X0))
      | subset(X4,X5)
      | ~ in(X4,X0)
      | ~ in(X5,X0) ),
    inference(forward_demodulation,[],[f372,f120]) ).

fof(f379,plain,
    ! [X0,X1] :
      ( subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
      | ~ in(sK2(inclusion_relation(X0),X1),X0)
      | ~ in(sK3(inclusion_relation(X0),X1),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X1)
      | ~ relation(inclusion_relation(X0)) ),
    inference(resolution,[],[f373,f349]) ).

fof(f380,plain,
    ! [X2,X0,X1] :
      ( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),inclusion_relation(X2))
      | subset(X1,X0)
      | ~ in(X1,X2)
      | ~ in(X0,X2) ),
    inference(superposition,[],[f373,f120]) ).

fof(f383,plain,
    ! [X0,X1] :
      ( subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
      | ~ in(sK2(inclusion_relation(X0),X1),X0)
      | ~ in(sK3(inclusion_relation(X0),X1),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X1) ),
    inference(forward_subsumption_resolution,[],[f379,f142]) ).

fof(f656,plain,
    ! [X0,X1] :
      ( subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
      | ~ in(sK3(inclusion_relation(X0),X1),X0)
      | ~ in(sK2(inclusion_relation(X0),X1),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X1)
      | ~ relation(inclusion_relation(X0)) ),
    inference(resolution,[],[f380,f351]) ).

fof(f661,plain,
    ! [X0,X1] :
      ( subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
      | ~ in(sK3(inclusion_relation(X0),X1),X0)
      | ~ in(sK2(inclusion_relation(X0),X1),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X1) ),
    inference(forward_subsumption_resolution,[],[f656,f142]) ).

fof(f706,plain,
    ! [X0,X1] :
      ( ~ in(sK2(inclusion_relation(X0),X1),X0)
      | ~ in(sK3(inclusion_relation(X0),X1),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X1)
      | ~ subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
      | sK2(inclusion_relation(X0),X1) = sK3(inclusion_relation(X0),X1) ),
    inference(resolution,[],[f383,f124]) ).

fof(f1224,plain,
    ! [X0,X1] :
      ( ~ in(sK3(inclusion_relation(X0),X1),X0)
      | ~ in(sK2(inclusion_relation(X0),X1),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X1)
      | sK2(inclusion_relation(X0),X1) = sK3(inclusion_relation(X0),X1) ),
    inference(forward_subsumption_resolution,[],[f706,f661]) ).

fof(f1240,plain,
    ! [X0] :
      ( ~ in(sK2(inclusion_relation(X0),X0),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X0)
      | sK2(inclusion_relation(X0),X0) = sK3(inclusion_relation(X0),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X0)
      | ~ relation(inclusion_relation(X0)) ),
    inference(resolution,[],[f1224,f137]) ).

fof(f1242,plain,
    ! [X0] :
      ( ~ in(sK2(inclusion_relation(X0),X0),X0)
      | is_antisymmetric_in(inclusion_relation(X0),X0)
      | sK2(inclusion_relation(X0),X0) = sK3(inclusion_relation(X0),X0)
      | ~ relation(inclusion_relation(X0)) ),
    inference(duplicate_literal_removal,[],[f1240]) ).

fof(f1244,plain,
    ! [X0] :
      ( is_antisymmetric_in(inclusion_relation(X0),X0)
      | sK2(inclusion_relation(X0),X0) = sK3(inclusion_relation(X0),X0)
      | ~ relation(inclusion_relation(X0)) ),
    inference(forward_subsumption_resolution,[],[f1242,f138]) ).

fof(f1245,plain,
    ! [X0] :
      ( is_antisymmetric_in(inclusion_relation(X0),X0)
      | ~ relation(inclusion_relation(X0)) ),
    inference(forward_subsumption_resolution,[],[f1244,f139]) ).

fof(f1246,plain,
    ! [X0] : is_antisymmetric_in(inclusion_relation(X0),X0),
    inference(forward_subsumption_resolution,[],[f1245,f142]) ).

fof(f1247,plain,
    ! [X0] : antisymmetric(inclusion_relation(X0)),
    inference(resolution,[],[f1246,f303]) ).

fof(f1252,plain,
    $false,
    inference(resolution,[],[f1247,f187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU271+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40  % Computer : n013.cluster.edu
% 0.11/0.40  % Model    : x86_64 x86_64
% 0.11/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40  % Memory   : 8046.5625MB
% 0.11/0.40  % OS       : Linux 6.8.0-71-generic
% 0.11/0.40  % CPULimit : 300
% 0.11/0.40  % WCLimit  : 300
% 0.11/0.40  % DateTime : Mon Sep 28 04:25:07 UTC 2026
% 0.11/0.40  % CPUTime  : 
% 0.11/0.40  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43  Running first-order model finding
% 0.11/0.43  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.51  % (798922)Will run a generic schedule for satisfiability detection.
% 0.16/0.51  % (798927)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=497969035_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.51  % TRYING [1]
% 0.16/0.51  % (798928)% WARNING: option uhcvi not known.
% 0.16/0.51  % TRYING [2]
% 0.16/0.51  % TRYING [3]
% 0.16/0.51  % (798928)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1472052883:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.51  % (798929)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1898345265:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.51  % (798930)dis+10_1_sil=32000:sp=arity:random_seed=2761810063:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.51  % (798931)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1978528281:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.51  % (798932)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3718852420:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.51  % (798933)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4262389271:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.51  % TRYING [4]
% 0.16/0.51  % (798930) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-798922-798930"...
% 0.16/0.51  % (798930)...printing done.
% 0.16/0.51  % (798930)Refutation found. Thanks to Tanya!
% 0.16/0.51  % SZS status Theorem for theBenchmark
% 0.16/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51  % (798930)------------------------------
% 0.16/0.51  % (798930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.51  % (798930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.51  % (798930)CaDiCaL version: 2.1.3
% 0.16/0.51  % (798930)Termination reason: Refutation
% 0.16/0.51  % (798930)Time elapsed: 0.034 s
% 0.16/0.51  % (798930)Peak memory usage: 12 MB
% 0.16/0.51  % (798930)Instructions burned: 51 (million)
% 0.16/0.51  % (798922)Success in time 0.068 s
% 0.16/0.51  % Vampire exiting
%------------------------------------------------------------------------------