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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n017.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 02:55:46 PM UTC 2026

% Result   : Theorem 2.15s 1.18s
% Output   : CNFRefutation 2.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   73 (  22 unt;   4 def)
%            Number of atoms       :  290 (  46 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  324 ( 129   ~; 132   |;  46   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   3 con; 0-3 aty)
%            Number of variables   :  167 (   0 sgn 142   !;  25   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( X2 = set_union2(X0,X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( X1 = relation_dom(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( X1 = relation_rng(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f7,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(f8,axiom,
    ! [X0] :
      ( relation(X0)
     => relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).

fof(f33,conjecture,
    ! [X0,X1,X2] :
      ( relation(X2)
     => ( in(ordered_pair(X0,X1),X2)
       => ( in(X1,relation_field(X2))
          & in(X0,relation_field(X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).

fof(f34,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( relation(X2)
       => ( in(ordered_pair(X0,X1),X2)
         => ( in(X1,relation_field(X2))
            & in(X0,relation_field(X2)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f33]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( X1 = relation_dom(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f41,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( X1 = relation_rng(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f42,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f50,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & in(ordered_pair(X0,X1),X2)
      & ( ~ in(X1,relation_field(X2))
        | ~ in(X0,relation_field(X2)) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f51,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & in(ordered_pair(X0,X1),X2)
      & ( ~ in(X1,relation_field(X2))
        | ~ in(X0,relation_field(X2)) ) ),
    inference(flattening,[],[f50]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) != X2
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | in(X3,X1)
              | in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | in(X3,X0) )
            & ( ~ in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) ) )
        | X2 = set_union2(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) != X2
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | in(X3,X1)
              | in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | in(X3,X0) )
            & ( ~ in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) ) )
        | X2 = set_union2(X0,X1) ) ),
    inference(flattening,[],[f55]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) != X2
        | ! [X4] :
            ( ( ~ in(X4,X2)
              | in(X4,X1)
              | in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & ~ in(X4,X0) )
              | in(X4,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | in(X3,X0) )
            & ( ~ in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) ) )
        | X2 = set_union2(X0,X1) ) ),
    inference(rectify,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) != X2
        | ! [X4] :
            ( ( ~ in(X4,X2)
              | in(X4,X1)
              | in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & ~ in(X4,X0) )
              | in(X4,X2) ) ) )
      & ( ( ( in(sK0(X0,X1,X2),X2)
            | in(sK0(X0,X1,X2),X1)
            | in(sK0(X0,X1,X2),X0) )
          & ( ~ in(sK0(X0,X1,X2),X2)
            | ( ~ in(sK0(X0,X1,X2),X1)
              & ~ in(sK0(X0,X1,X2),X0) ) ) )
        | X2 = set_union2(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f57]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_dom(X0) != X1
            | ! [X2] :
                ( ( ~ in(X2,X1)
                  | ? [X3] : in(ordered_pair(X2,X3),X0) )
                & ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X3] : in(ordered_pair(X2,X3),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
            | X1 = relation_dom(X0) ) ) ),
    inference(nnf_transformation,[],[f40]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_dom(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | ? [X7] : in(ordered_pair(X5,X7),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
                  | in(X5,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X4] : in(ordered_pair(X2,X4),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
            | X1 = relation_dom(X0) ) ) ),
    inference(rectify,[],[f59]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_dom(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | in(ordered_pair(X5,sK3(X0,X5)),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
                  | in(X5,X1) ) ) )
          & ( ( ( in(sK1(X0,X1),X1)
                | in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) )
              & ( ~ in(sK1(X0,X1),X1)
                | ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0) ) )
            | X1 = relation_dom(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f60]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_rng(X0) != X1
            | ! [X2] :
                ( ( ~ in(X2,X1)
                  | ? [X3] : in(ordered_pair(X3,X2),X0) )
                & ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X3] : in(ordered_pair(X3,X2),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
            | X1 = relation_rng(X0) ) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f63,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_rng(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | ? [X7] : in(ordered_pair(X7,X5),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
                  | in(X5,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X4] : in(ordered_pair(X4,X2),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
            | X1 = relation_rng(X0) ) ) ),
    inference(rectify,[],[f62]) ).

fof(f64,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_rng(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | in(ordered_pair(sK6(X0,X5),X5),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
                  | in(X5,X1) ) ) )
          & ( ( ( in(sK4(X0,X1),X1)
                | in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0) )
              & ( ~ in(sK4(X0,X1),X1)
                | ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0) ) )
            | X1 = relation_rng(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f63]) ).

fof(f69,plain,
    ( relation(sK13)
    & in(ordered_pair(sK11,sK12),sK13)
    & ( ~ in(sK12,relation_field(sK13))
      | ~ in(sK11,relation_field(sK13)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f51]) ).

fof(f71,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f74,plain,
    ! [X2,X0,X1,X4] :
      ( set_union2(X0,X1) != X2
      | ~ in(X4,X1)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f75,plain,
    ! [X2,X0,X1,X4] :
      ( set_union2(X0,X1) != X2
      | ~ in(X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f80,plain,
    ! [X0,X1,X6,X5] :
      ( ~ relation(X0)
      | relation_dom(X0) != X1
      | ~ in(ordered_pair(X5,X6),X0)
      | in(X5,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f84,plain,
    ! [X0,X1,X6,X5] :
      ( ~ relation(X0)
      | relation_rng(X0) != X1
      | ~ in(ordered_pair(X6,X5),X0)
      | in(X5,X1) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f87,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f7]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f105,plain,
    relation(sK13),
    inference(cnf_transformation,[],[f69]) ).

fof(f106,plain,
    in(ordered_pair(sK11,sK12),sK13),
    inference(cnf_transformation,[],[f69]) ).

fof(f107,plain,
    ( ~ in(sK12,relation_field(sK13))
    | ~ in(sK11,relation_field(sK13)) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f113,plain,
    ! [X0,X1,X6,X5] :
      ( ~ relation(X0)
      | relation_dom(X0) != X1
      | ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
      | in(X5,X1) ),
    inference(definition_unfolding,[],[f80,f87]) ).

fof(f117,plain,
    ! [X0,X1,X6,X5] :
      ( ~ relation(X0)
      | relation_rng(X0) != X1
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | in(X5,X1) ),
    inference(definition_unfolding,[],[f84,f87]) ).

fof(f120,plain,
    in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK13),
    inference(definition_unfolding,[],[f106,f87]) ).

fof(f121,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X0)
      | in(X4,set_union2(X0,X1)) ),
    inference(equality_resolution,[],[f75]) ).

fof(f122,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X1)
      | in(X4,set_union2(X0,X1)) ),
    inference(equality_resolution,[],[f74]) ).

fof(f124,plain,
    ! [X0,X6,X5] :
      ( ~ relation(X0)
      | ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
      | in(X5,relation_dom(X0)) ),
    inference(equality_resolution,[],[f113]) ).

fof(f126,plain,
    ! [X0,X6,X5] :
      ( ~ relation(X0)
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | in(X5,relation_rng(X0)) ),
    inference(equality_resolution,[],[f117]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,set_union2(X1,X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f121]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,set_union2(X2,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

tcf(c_60,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,relation_dom(X2))
      | ~ relation(X2)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
    inference(cnf_transformation,[],[f124]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X1,relation_rng(X2))
      | ~ relation(X2)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
    inference(cnf_transformation,[],[f126]) ).

tcf(c_66,plain,
    ! [X0: $i] :
      ( ( set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) )
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

tcf(c_83,negated_conjecture,
    ( ~ in(sK12,relation_field(sK13))
    | ~ in(sK11,relation_field(sK13)) ),
    inference(cnf_transformation,[],[f107]) ).

tcf(c_84,negated_conjecture,
    in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK13),
    inference(cnf_transformation,[],[f120]) ).

tcf(c_85,negated_conjecture,
    relation(sK13),
    inference(cnf_transformation,[],[f105]) ).

tcf(c_301,plain,
    in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK13),
    inference(demodulation,[status(thm)],[c_84,c_50]) ).

tcf(c_346,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X1,relation_rng(X2))
      | ~ relation(X2)
      | ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
    inference(demodulation,[status(thm)],[c_64,c_50]) ).

tcf(c_356,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,relation_dom(X2))
      | ~ relation(X2)
      | ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
    inference(demodulation,[status(thm)],[c_60,c_50]) ).

tcf(c_792,definition,
    iPr_def_10 = singleton(sK11),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_793,definition,
    iPr_def_11 = unordered_pair(sK11,sK12),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_794,definition,
    iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
    introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).

tcf(c_795,definition,
    iPr_def_13 = relation_field(sK13),
    introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).

tcf(c_796,plain,
    in(iPr_def_12,sK13),
    inference(demodulation,[status(thm)],[c_301,c_793,c_792,c_794]) ).

tcf(c_797,negated_conjecture,
    relation(sK13),
    inference(demodulation,[status(thm)],[c_85]) ).

tcf(c_798,negated_conjecture,
    ( ~ in(sK12,iPr_def_13)
    | ~ in(sK11,iPr_def_13) ),
    inference(demodulation,[status(thm)],[c_83,c_795]) ).

tcf(c_1266,plain,
    ! [X0: $i] :
      ( in(sK12,relation_rng(X0))
      | ~ relation(X0)
      | ~ in(unordered_pair(singleton(sK11),iPr_def_11),X0) ),
    inference(superposition,[status(thm)],[c_793,c_346]) ).

tcf(c_1267,plain,
    ! [X0: $i] :
      ( in(sK12,relation_rng(X0))
      | ~ relation(X0)
      | ~ in(iPr_def_12,X0) ),
    inference(light_normalisation,[status(thm)],[c_1266,c_792,c_794]) ).

tcf(c_1307,plain,
    ! [X0: $i] :
      ( in(sK11,relation_dom(X0))
      | ~ relation(X0)
      | ~ in(unordered_pair(singleton(sK11),iPr_def_11),X0) ),
    inference(superposition,[status(thm)],[c_793,c_356]) ).

tcf(c_1312,plain,
    ! [X0: $i] :
      ( in(sK11,relation_dom(X0))
      | ~ relation(X0)
      | ~ in(iPr_def_12,X0) ),
    inference(light_normalisation,[status(thm)],[c_1307,c_792,c_794]) ).

tcf(c_1531,plain,
    set_union2(relation_dom(sK13),relation_rng(sK13)) = relation_field(sK13),
    inference(superposition,[status(thm)],[c_797,c_66]) ).

tcf(c_1533,plain,
    set_union2(relation_dom(sK13),relation_rng(sK13)) = iPr_def_13,
    inference(light_normalisation,[status(thm)],[c_1531,c_795]) ).

tcf(c_1566,plain,
    ! [X0: $i] :
      ( in(X0,iPr_def_13)
      | ~ in(X0,relation_dom(sK13)) ),
    inference(superposition,[status(thm)],[c_1533,c_55]) ).

tcf(c_1567,plain,
    ! [X0: $i] :
      ( in(X0,iPr_def_13)
      | ~ in(X0,relation_rng(sK13)) ),
    inference(superposition,[status(thm)],[c_1533,c_56]) ).

tcf(c_3122,plain,
    ( in(sK12,iPr_def_13)
    | ~ relation(sK13)
    | ~ in(iPr_def_12,sK13) ),
    inference(superposition,[status(thm)],[c_1267,c_1567]) ).

tcf(c_3127,plain,
    in(sK12,iPr_def_13),
    inference(forward_subsumption_resolution,[status(thm)],[c_3122,c_797,c_796]) ).

tcf(c_3137,plain,
    ~ in(sK11,iPr_def_13),
    inference(backward_subsumption_resolution,[status(thm)],[c_798,c_3127]) ).

tcf(c_3352,plain,
    ( in(sK11,iPr_def_13)
    | ~ relation(sK13)
    | ~ in(iPr_def_12,sK13) ),
    inference(superposition,[status(thm)],[c_1312,c_1566]) ).

tcf(c_3353,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3352,c_3137,c_797,c_796]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37  % Computer : n017.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
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Thu Sep 24 12:59:45 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41  Running first-order theorem proving
% 0.10/0.41  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42  
% 0.10/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42  
% 0.10/0.42  % Detected problem language: tptp
% 0.10/0.43  % Proving...
% 2.15/1.18  % SZS status Started for theBenchmark.p
% 2.15/1.18  % SZS status Theorem for theBenchmark.p
% 2.15/1.18  
% 2.15/1.18  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.15/1.18  
% 2.15/1.18  % ------  iProver source info
% 2.15/1.18  
% 2.15/1.18  % git: date: 2026-07-19 20:42:38 +0200
% 2.15/1.18  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.15/1.18  % git: non_committed_changes: false
% 2.15/1.18  
% 2.15/1.18  % ------ Parsing...
% 2.15/1.18  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 2.15/1.18  
% 2.15/1.18  % ------ Preprocessing... sup_sim: 9  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 2.15/1.18  
% 2.15/1.18  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 2.15/1.18  
% 2.15/1.18  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.15/1.18  % ------ Proving...
% 2.15/1.18  % ------ Problem Properties 
% 2.15/1.18  
% 2.15/1.18  % 
% 2.15/1.18  % clauses                               41
% 2.15/1.18  % conjectures                           2
% 2.15/1.18  % EPR                                   12
% 2.15/1.18  % Horn                                  36
% 2.15/1.18  % unary                                 17
% 2.15/1.18  % binary                                10
% 2.15/1.18  % lits                                  84
% 2.15/1.18  % lits eq                               18
% 2.15/1.18  % fd_pure                               0
% 2.15/1.18  % fd_pseudo                             0
% 2.15/1.18  % fd_cond                               1
% 2.15/1.18  % fd_pseudo_cond                        8
% 2.15/1.18  % AC symbols                            0
% 2.15/1.18  
% 2.15/1.18  % ------ Schedule dynamic 5 is on 
% 2.15/1.18  
% 2.15/1.18  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.15/1.18  
% 2.15/1.18  
% 2.15/1.18  % ------ 
% 2.15/1.18  % Current options:
% 2.15/1.18  % ------ 
% 2.15/1.18  
% 2.15/1.18  
% 2.15/1.18  % 
% 2.15/1.18  
% 2.15/1.18  % ------ Proving...
% 2.15/1.18  % 
% 2.15/1.18  
% 2.15/1.18  % SZS status Theorem for theBenchmark.p
% 2.15/1.18  
% 2.15/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.15/1.19  
%------------------------------------------------------------------------------