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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU203+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n008.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 : Fri Sep 25 02:55:53 PM UTC 2026

% Result   : Theorem 22.53s 13.84s
% Output   : CNFRefutation 22.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   66 (  10 unt;   0 def)
%            Number of atoms       :  269 (  18 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  339 ( 136   ~; 139   |;  49   &)
%                                         (   8 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   4 con; 0-3 aty)
%            Number of variables   :  162 (   0 sgn 134   !;  28   ?;  23   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( X2 = relation_image(X0,X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X4,X3),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f31,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(f124,conjecture,
    ! [X0,X1,X2] :
      ( relation(X2)
     => ( in(X0,relation_image(X2,X1))
      <=> ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).

fof(f125,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( relation(X2)
       => ( in(X0,relation_image(X2,X1))
        <=> ? [X3] :
              ( in(X3,X1)
              & in(ordered_pair(X3,X0),X2)
              & in(X3,relation_dom(X2)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f124]) ).

fof(f132,axiom,
    ! [X0,X1,X2] :
      ( relation(X2)
     => ( in(ordered_pair(X0,X1),X2)
       => ( in(X1,relation_rng(X2))
          & in(X0,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).

fof(f180,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f217,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( X2 = relation_image(X0,X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X4,X3),X0) ) ) ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f292,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & ( in(X0,relation_image(X2,X1))
      <~> ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) ) ) ),
    inference(ennf_transformation,[],[f125]) ).

fof(f298,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X2)
      | ~ in(ordered_pair(X0,X1),X2)
      | ( in(X1,relation_rng(X2))
        & in(X0,relation_dom(X2)) ) ),
    inference(ennf_transformation,[],[f132]) ).

fof(f299,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X2)
      | ~ in(ordered_pair(X0,X1),X2)
      | ( in(X1,relation_rng(X2))
        & in(X0,relation_dom(X2)) ) ),
    inference(flattening,[],[f298]) ).

fof(f377,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X1) != X2
            | ! [X3] :
                ( ( ~ in(X3,X2)
                  | ? [X4] :
                      ( in(X4,X1)
                      & in(ordered_pair(X4,X3),X0) ) )
                & ( ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X4,X3),X0) )
                  | in(X3,X2) ) ) )
          & ( ? [X3] :
                ( ( in(X3,X2)
                  | ? [X4] :
                      ( in(X4,X1)
                      & in(ordered_pair(X4,X3),X0) ) )
                & ( ~ in(X3,X2)
                  | ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X4,X3),X0) ) ) )
            | X2 = relation_image(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f217]) ).

fof(f378,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X1) != X2
            | ! [X6] :
                ( ( ~ in(X6,X2)
                  | ? [X8] :
                      ( in(X8,X1)
                      & in(ordered_pair(X8,X6),X0) ) )
                & ( ! [X7] :
                      ( ~ in(X7,X1)
                      | ~ in(ordered_pair(X7,X6),X0) )
                  | in(X6,X2) ) ) )
          & ( ? [X3] :
                ( ( in(X3,X2)
                  | ? [X5] :
                      ( in(X5,X1)
                      & in(ordered_pair(X5,X3),X0) ) )
                & ( ~ in(X3,X2)
                  | ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X4,X3),X0) ) ) )
            | X2 = relation_image(X0,X1) ) ) ),
    inference(rectify,[],[f377]) ).

fof(f379,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X1) != X2
            | ! [X6] :
                ( ( ~ in(X6,X2)
                  | ( in(sK8(X0,X1,X6),X1)
                    & in(ordered_pair(sK8(X0,X1,X6),X6),X0) ) )
                & ( ! [X7] :
                      ( ~ in(X7,X1)
                      | ~ in(ordered_pair(X7,X6),X0) )
                  | in(X6,X2) ) ) )
          & ( ( ( in(sK6(X0,X1,X2),X2)
                | ( in(sK7(X0,X1,X2),X1)
                  & in(ordered_pair(sK7(X0,X1,X2),sK6(X0,X1,X2)),X0) ) )
              & ( ~ in(sK6(X0,X1,X2),X2)
                | ! [X4] :
                    ( ~ in(X4,X1)
                    | ~ in(ordered_pair(X4,sK6(X0,X1,X2)),X0) ) ) )
            | X2 = relation_image(X0,X1) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X5,sK7(X0,X1,X2)),skolemize(X8,sK8(X0,X1,X6))],[f378]) ).

fof(f413,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) ) )
      & ( ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) )
        | subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f414,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) ) )
      & ( ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) )
        | subset(X0,X1) ) ),
    inference(rectify,[],[f413]) ).

fof(f415,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) ) )
      & ( ( in(sK29(X0,X1),X0)
          & ~ in(sK29(X0,X1),X1) )
        | subset(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X2,sK29(X0,X1))],[f414]) ).

fof(f463,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & ( in(X0,relation_image(X2,X1))
        | ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) ) )
      & ( ~ in(X0,relation_image(X2,X1))
        | ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(ordered_pair(X3,X0),X2)
            | ~ in(X3,relation_dom(X2)) ) ) ),
    inference(nnf_transformation,[],[f292]) ).

fof(f464,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & ( in(X0,relation_image(X2,X1))
        | ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) ) )
      & ( ~ in(X0,relation_image(X2,X1))
        | ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(ordered_pair(X3,X0),X2)
            | ~ in(X3,relation_dom(X2)) ) ) ),
    inference(flattening,[],[f463]) ).

fof(f465,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & ( in(X0,relation_image(X2,X1))
        | ? [X4] :
            ( in(X4,X1)
            & in(ordered_pair(X4,X0),X2)
            & in(X4,relation_dom(X2)) ) )
      & ( ~ in(X0,relation_image(X2,X1))
        | ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(ordered_pair(X3,X0),X2)
            | ~ in(X3,relation_dom(X2)) ) ) ),
    inference(rectify,[],[f464]) ).

fof(f466,plain,
    ( relation(sK59)
    & ( in(sK57,relation_image(sK59,sK58))
      | ( in(sK60,sK58)
        & in(ordered_pair(sK60,sK57),sK59)
        & in(sK60,relation_dom(sK59)) ) )
    & ( ~ in(sK57,relation_image(sK59,sK58))
      | ! [X3] :
          ( ~ in(X3,sK58)
          | ~ in(ordered_pair(X3,sK57),sK59)
          | ~ in(X3,relation_dom(sK59)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60]),skolemize(X0,sK57),skolemize(X1,sK58),skolemize(X2,sK59),skolemize(X4,sK60)],[f465]) ).

fof(f515,plain,
    ! [X2,X0,X1,X6] :
      ( ~ relation(X0)
      | relation_image(X0,X1) != X2
      | ~ in(X6,X2)
      | in(sK8(X0,X1,X6),X1) ),
    inference(cnf_transformation,[],[f379]) ).

fof(f516,plain,
    ! [X2,X0,X1,X6] :
      ( ~ relation(X0)
      | relation_image(X0,X1) != X2
      | ~ in(X6,X2)
      | in(ordered_pair(sK8(X0,X1,X6),X6),X0) ),
    inference(cnf_transformation,[],[f379]) ).

fof(f517,plain,
    ! [X2,X0,X1,X6,X7] :
      ( ~ relation(X0)
      | relation_image(X0,X1) != X2
      | ~ in(X7,X1)
      | ~ in(ordered_pair(X7,X6),X0)
      | in(X6,X2) ),
    inference(cnf_transformation,[],[f379]) ).

fof(f573,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f415]) ).

fof(f604,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f31]) ).

fof(f717,plain,
    relation(sK59),
    inference(cnf_transformation,[],[f466]) ).

fof(f718,plain,
    ( in(sK57,relation_image(sK59,sK58))
    | in(sK60,sK58) ),
    inference(cnf_transformation,[],[f466]) ).

fof(f719,plain,
    ( in(sK57,relation_image(sK59,sK58))
    | in(ordered_pair(sK60,sK57),sK59) ),
    inference(cnf_transformation,[],[f466]) ).

fof(f721,plain,
    ! [X3] :
      ( ~ in(sK57,relation_image(sK59,sK58))
      | ~ in(X3,sK58)
      | ~ in(ordered_pair(X3,sK57),sK59)
      | ~ in(X3,relation_dom(sK59)) ),
    inference(cnf_transformation,[],[f466]) ).

fof(f729,plain,
    ! [X2,X0,X1] :
      ( ~ relation(X2)
      | ~ in(ordered_pair(X0,X1),X2)
      | in(X0,relation_dom(X2)) ),
    inference(cnf_transformation,[],[f299]) ).

fof(f797,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f180]) ).

fof(f826,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
    inference(definition_unfolding,[],[f604,f797]) ).

fof(f848,plain,
    ! [X2,X0,X1,X6,X7] :
      ( ~ relation(X0)
      | relation_image(X0,X1) != X2
      | ~ in(X7,X1)
      | ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
      | in(X6,X2) ),
    inference(definition_unfolding,[],[f517,f826]) ).

fof(f849,plain,
    ! [X2,X0,X1,X6] :
      ( ~ relation(X0)
      | relation_image(X0,X1) != X2
      | ~ in(X6,X2)
      | in(unordered_pair(unordered_pair(sK8(X0,X1,X6),X6),unordered_pair(sK8(X0,X1,X6),sK8(X0,X1,X6))),X0) ),
    inference(definition_unfolding,[],[f516,f826]) ).

fof(f914,plain,
    ! [X3] :
      ( ~ in(sK57,relation_image(sK59,sK58))
      | ~ in(X3,sK58)
      | ~ in(unordered_pair(unordered_pair(X3,sK57),unordered_pair(X3,X3)),sK59)
      | ~ in(X3,relation_dom(sK59)) ),
    inference(definition_unfolding,[],[f721,f826]) ).

fof(f915,plain,
    ( in(sK57,relation_image(sK59,sK58))
    | in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),sK59) ),
    inference(definition_unfolding,[],[f719,f826]) ).

fof(f919,plain,
    ! [X2,X0,X1] :
      ( ~ relation(X2)
      | ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
      | in(X0,relation_dom(X2)) ),
    inference(definition_unfolding,[],[f729,f826]) ).

fof(f958,plain,
    ! [X0,X1,X6,X7] :
      ( ~ relation(X0)
      | ~ in(X7,X1)
      | ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
      | in(X6,relation_image(X0,X1)) ),
    inference(equality_resolution,[],[f848]) ).

fof(f959,plain,
    ! [X0,X1,X6] :
      ( ~ relation(X0)
      | ~ in(X6,relation_image(X0,X1))
      | in(unordered_pair(unordered_pair(sK8(X0,X1,X6),X6),unordered_pair(sK8(X0,X1,X6),sK8(X0,X1,X6))),X0) ),
    inference(equality_resolution,[],[f849]) ).

fof(f960,plain,
    ! [X0,X1,X6] :
      ( ~ relation(X0)
      | ~ in(X6,relation_image(X0,X1))
      | in(sK8(X0,X1,X6),X1) ),
    inference(equality_resolution,[],[f515]) ).

tcf(c_79,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( in(X1,relation_image(X2,X3))
      | ~ relation(X2)
      | ~ in(X0,X3)
      | ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
    inference(cnf_transformation,[],[f958]) ).

tcf(c_80,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(unordered_pair(unordered_pair(sK8(X1,X2,X0),X0),unordered_pair(sK8(X1,X2,X0),sK8(X1,X2,X0))),X1)
      | ~ relation(X1)
      | ~ in(X0,relation_image(X1,X2)) ),
    inference(cnf_transformation,[],[f959]) ).

tcf(c_81,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(sK8(X1,X2,X0),X2)
      | ~ relation(X1)
      | ~ in(X0,relation_image(X1,X2)) ),
    inference(cnf_transformation,[],[f960]) ).

tcf(c_136,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X2)
      | ~ subset(X1,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f573]) ).

tcf(c_277,negated_conjecture,
    ! [X0: $i] :
      ( ~ in(X0,sK58)
      | ~ in(X0,relation_dom(sK59))
      | ~ in(sK57,relation_image(sK59,sK58))
      | ~ in(unordered_pair(unordered_pair(X0,sK57),unordered_pair(X0,X0)),sK59) ),
    inference(cnf_transformation,[],[f914]) ).

tcf(c_279,negated_conjecture,
    ( in(sK57,relation_image(sK59,sK58))
    | in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),sK59) ),
    inference(cnf_transformation,[],[f915]) ).

tcf(c_280,negated_conjecture,
    ( in(sK60,sK58)
    | in(sK57,relation_image(sK59,sK58)) ),
    inference(cnf_transformation,[],[f718]) ).

tcf(c_281,negated_conjecture,
    relation(sK59),
    inference(cnf_transformation,[],[f717]) ).

tcf(c_288,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,relation_dom(X2))
      | ~ relation(X2)
      | ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
    inference(cnf_transformation,[],[f919]) ).

tcf(c_1852,plain,
    ( in(sK8(sK59,sK58,sK57),sK58)
    | ~ relation(sK59)
    | ~ in(sK57,relation_image(sK59,sK58)) ),
    inference(instantiation,[status(thm)],[c_81]) ).

tcf(c_2322,plain,
    ! [X0: $i] :
      ( in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),X0)
      | ~ subset(sK59,X0)
      | ~ in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),sK59) ),
    inference(instantiation,[status(thm)],[c_136]) ).

tcf(c_2461,plain,
    ! [X0: $i] :
      ( in(sK57,relation_image(sK59,X0))
      | ~ relation(sK59)
      | ~ in(sK60,X0)
      | ~ in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),sK59) ),
    inference(instantiation,[status(thm)],[c_79]) ).

tcf(c_3592,plain,
    ( in(unordered_pair(unordered_pair(sK8(sK59,sK58,sK57),sK57),unordered_pair(sK8(sK59,sK58,sK57),sK8(sK59,sK58,sK57))),sK59)
    | ~ relation(sK59)
    | ~ in(sK57,relation_image(sK59,sK58)) ),
    inference(instantiation,[status(thm)],[c_80]) ).

tcf(c_3777,plain,
    ( ~ in(sK57,relation_image(sK59,sK58))
    | ~ in(sK8(sK59,sK58,sK57),sK58)
    | ~ in(sK8(sK59,sK58,sK57),relation_dom(sK59))
    | ~ in(unordered_pair(unordered_pair(sK8(sK59,sK58,sK57),sK57),unordered_pair(sK8(sK59,sK58,sK57),sK8(sK59,sK58,sK57))),sK59) ),
    inference(instantiation,[status(thm)],[c_277]) ).

tcf(c_10587,plain,
    ( in(sK8(sK59,sK58,sK57),relation_dom(sK59))
    | ~ relation(sK59)
    | ~ in(unordered_pair(unordered_pair(sK8(sK59,sK58,sK57),sK57),unordered_pair(sK8(sK59,sK58,sK57),sK8(sK59,sK58,sK57))),sK59) ),
    inference(instantiation,[status(thm)],[c_288]) ).

tcf(c_10832,plain,
    ! [X0: $i] :
      ( in(sK60,sK58)
      | in(sK57,X0)
      | ~ subset(relation_image(sK59,sK58),X0) ),
    inference(superposition,[status(thm)],[c_280,c_136]) ).

tcf(c_10833,plain,
    ! [X0: $i] :
      ( in(sK57,relation_image(sK59,sK58))
      | in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),X0)
      | ~ subset(sK59,X0) ),
    inference(superposition,[status(thm)],[c_279,c_136]) ).

tcf(c_11405,plain,
    in(sK60,sK58),
    inference(global_subsumption_just,[status(thm)],[c_10832,c_281,c_280,c_1852,c_3592,c_3777,c_10587]) ).

tcf(c_11941,plain,
    ! [X0: $i] :
      ( ~ subset(sK59,X0)
      | in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_10833,c_281,c_279,c_1852,c_2322,c_3592,c_3777,c_10587]) ).

tcf(c_11942,plain,
    ! [X0: $i] :
      ( in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),X0)
      | ~ subset(sK59,X0) ),
    inference(renaming,[status(thm)],[c_11941]) ).

tcf(c_11964,plain,
    ( ~ subset(sK59,sK59)
    | ~ in(sK60,sK58)
    | ~ in(sK60,relation_dom(sK59))
    | ~ in(sK57,relation_image(sK59,sK58)) ),
    inference(superposition,[status(thm)],[c_11942,c_277]) ).

tcf(c_13182,plain,
    ~ in(sK57,relation_image(sK59,sK58)),
    inference(global_subsumption_just,[status(thm)],[c_11964,c_281,c_1852,c_3592,c_3777,c_10587]) ).

tcf(c_17836,plain,
    ( in(sK57,relation_image(sK59,sK58))
    | ~ relation(sK59)
    | ~ in(sK60,sK58)
    | ~ in(unordered_pair(unordered_pair(sK60,sK57),unordered_pair(sK60,sK60)),sK59) ),
    inference(instantiation,[status(thm)],[c_2461]) ).

tcf(c_17837,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_17836,c_13182,c_11405,c_279,c_281]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU203+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.39  % Computer : n008.cluster.edu
% 0.11/10.39  % Model    : x86_64 x86_64
% 0.11/10.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39  % Memory   : 8046.5625MB
% 0.11/10.39  % OS       : Linux 6.8.0-71-generic
% 0.11/10.39  % CPULimit : 300
% 0.11/10.39  % WCLimit  : 300
% 0.11/10.39  % DateTime : Thu Sep 24 13:10:56 UTC 2026
% 0.11/10.39  % CPUTime  : 
% 0.11/10.39  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/10.43  Running first-order theorem proving
% 0.16/10.43  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.44  
% 0.16/10.44  % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.44  
% 0.16/10.44  % Detected problem language: tptp
% 0.16/10.45  % Proving...
% 22.53/13.84  % SZS status Started for theBenchmark.p
% 22.53/13.84  % SZS status Theorem for theBenchmark.p
% 22.53/13.84  
% 22.53/13.84  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.53/13.84  
% 22.53/13.84  % ------  iProver source info
% 22.53/13.84  
% 22.53/13.84  % git: date: 2026-07-19 20:42:38 +0200
% 22.53/13.84  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.53/13.84  % git: non_committed_changes: false
% 22.53/13.84  
% 22.53/13.84  % ------ Parsing...
% 22.53/13.84  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 22.53/13.84  
% 22.53/13.84  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e % 
% 22.53/13.84  
% 22.53/13.84  % ------ Preprocessing...% 
% 22.53/13.84  
% 22.53/13.84  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 22.53/13.84  % ------ Proving...
% 22.53/13.84  % ------ Problem Properties 
% 22.53/13.84  
% 22.53/13.84  % 
% 22.53/13.84  % clauses                               313
% 22.53/13.84  % conjectures                           25
% 22.53/13.84  % EPR                                   32
% 22.53/13.84  % Horn                                  249
% 22.53/13.84  % unary                                 52
% 22.53/13.84  % binary                                105
% 22.53/13.84  % lits                                  829
% 22.53/13.84  % lits eq                               161
% 22.53/13.84  % fd_pure                               0
% 22.53/13.84  % fd_pseudo                             0
% 22.53/13.84  % fd_cond                               13
% 22.53/13.84  % fd_pseudo_cond                        65
% 22.53/13.84  % AC symbols                            0
% 22.53/13.84  
% 22.53/13.84  % ------ Input Options Time Limit: Unbounded
% 22.53/13.84  
% 22.53/13.84  
% 22.53/13.84  % ------ 
% 22.53/13.84  % Current options:
% 22.53/13.84  % ------ 
% 22.53/13.84  
% 22.53/13.84  
% 22.53/13.84  % 
% 22.53/13.84  
% 22.53/13.84  % ------ Proving...
% 22.53/13.84  % 
% 22.53/13.84  
% 22.53/13.84  % SZS status Theorem for theBenchmark.p
% 22.53/13.84  
% 22.53/13.84  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.53/13.84  
% 22.53/13.84  
%------------------------------------------------------------------------------