TSTP Solution File: SEU183+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU183+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 : Thu Aug 31 17:04:28 EDT 2023

% Result   : Theorem 56.63s 8.68s
% Output   : CNFRefutation 56.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   71 (  12 unt;   0 def)
%            Number of atoms       :  304 (  25 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  379 ( 146   ~; 144   |;  58   &)
%                                         (  10 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   2 con; 0-4 aty)
%            Number of variables   :  206 (   0 sgn; 150   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f22,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f24,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(f28,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation(X1)
         => ! [X2] :
              ( relation(X2)
             => ( relation_composition(X0,X1) = X2
              <=> ! [X3,X4] :
                    ( in(ordered_pair(X3,X4),X2)
                  <=> ? [X5] :
                        ( in(ordered_pair(X5,X4),X1)
                        & in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).

fof(f48,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(relation_composition(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(f104,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(f130,conjecture,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation(X1)
         => subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).

fof(f131,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => ! [X1] :
            ( relation(X1)
           => subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
    inference(negated_conjecture,[],[f130]) ).

fof(f147,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f176,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f178,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f182,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( relation_composition(X0,X1) = X2
              <=> ! [X3,X4] :
                    ( in(ordered_pair(X3,X4),X2)
                  <=> ? [X5] :
                        ( in(ordered_pair(X5,X4),X1)
                        & in(ordered_pair(X3,X5),X0) ) ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(flattening,[],[f188]) ).

fof(f230,plain,
    ! [X0,X1,X2] :
      ( ( in(X1,relation_rng(X2))
        & in(X0,relation_dom(X2)) )
      | ~ in(ordered_pair(X0,X1),X2)
      | ~ relation(X2) ),
    inference(ennf_transformation,[],[f104]) ).

fof(f231,plain,
    ! [X0,X1,X2] :
      ( ( in(X1,relation_rng(X2))
        & in(X0,relation_dom(X2)) )
      | ~ in(ordered_pair(X0,X1),X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f230]) ).

fof(f249,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
          & relation(X1) )
      & relation(X0) ),
    inference(ennf_transformation,[],[f131]) ).

fof(f322,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f323,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f322]) ).

fof(f324,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK16(X0,X1),X1)
        & in(sK16(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f325,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK16(X0,X1),X1)
          & in(sK16(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f323,f324]) ).

fof(f348,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f178]) ).

fof(f349,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f348]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
          | ~ in(sK25(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK25(X0,X1)),X0)
          | in(sK25(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK25(X0,X1)),X0)
     => in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f352,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK27(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
                | ~ in(sK25(X0,X1),X1) )
              & ( in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
                | in(sK25(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK27(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f349,f352,f351,f350]) ).

fof(f359,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( relation_composition(X0,X1) = X2
                  | ? [X3,X4] :
                      ( ( ! [X5] :
                            ( ~ in(ordered_pair(X5,X4),X1)
                            | ~ in(ordered_pair(X3,X5),X0) )
                        | ~ in(ordered_pair(X3,X4),X2) )
                      & ( ? [X5] :
                            ( in(ordered_pair(X5,X4),X1)
                            & in(ordered_pair(X3,X5),X0) )
                        | in(ordered_pair(X3,X4),X2) ) ) )
                & ( ! [X3,X4] :
                      ( ( in(ordered_pair(X3,X4),X2)
                        | ! [X5] :
                            ( ~ in(ordered_pair(X5,X4),X1)
                            | ~ in(ordered_pair(X3,X5),X0) ) )
                      & ( ? [X5] :
                            ( in(ordered_pair(X5,X4),X1)
                            & in(ordered_pair(X3,X5),X0) )
                        | ~ in(ordered_pair(X3,X4),X2) ) )
                  | relation_composition(X0,X1) != X2 ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f182]) ).

fof(f360,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( relation_composition(X0,X1) = X2
                  | ? [X3,X4] :
                      ( ( ! [X5] :
                            ( ~ in(ordered_pair(X5,X4),X1)
                            | ~ in(ordered_pair(X3,X5),X0) )
                        | ~ in(ordered_pair(X3,X4),X2) )
                      & ( ? [X6] :
                            ( in(ordered_pair(X6,X4),X1)
                            & in(ordered_pair(X3,X6),X0) )
                        | in(ordered_pair(X3,X4),X2) ) ) )
                & ( ! [X7,X8] :
                      ( ( in(ordered_pair(X7,X8),X2)
                        | ! [X9] :
                            ( ~ in(ordered_pair(X9,X8),X1)
                            | ~ in(ordered_pair(X7,X9),X0) ) )
                      & ( ? [X10] :
                            ( in(ordered_pair(X10,X8),X1)
                            & in(ordered_pair(X7,X10),X0) )
                        | ~ in(ordered_pair(X7,X8),X2) ) )
                  | relation_composition(X0,X1) != X2 ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(rectify,[],[f359]) ).

fof(f361,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( ( ! [X5] :
                ( ~ in(ordered_pair(X5,X4),X1)
                | ~ in(ordered_pair(X3,X5),X0) )
            | ~ in(ordered_pair(X3,X4),X2) )
          & ( ? [X6] :
                ( in(ordered_pair(X6,X4),X1)
                & in(ordered_pair(X3,X6),X0) )
            | in(ordered_pair(X3,X4),X2) ) )
     => ( ( ! [X5] :
              ( ~ in(ordered_pair(X5,sK31(X0,X1,X2)),X1)
              | ~ in(ordered_pair(sK30(X0,X1,X2),X5),X0) )
          | ~ in(ordered_pair(sK30(X0,X1,X2),sK31(X0,X1,X2)),X2) )
        & ( ? [X6] :
              ( in(ordered_pair(X6,sK31(X0,X1,X2)),X1)
              & in(ordered_pair(sK30(X0,X1,X2),X6),X0) )
          | in(ordered_pair(sK30(X0,X1,X2),sK31(X0,X1,X2)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f362,plain,
    ! [X0,X1,X2] :
      ( ? [X6] :
          ( in(ordered_pair(X6,sK31(X0,X1,X2)),X1)
          & in(ordered_pair(sK30(X0,X1,X2),X6),X0) )
     => ( in(ordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),X1)
        & in(ordered_pair(sK30(X0,X1,X2),sK32(X0,X1,X2)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f363,plain,
    ! [X0,X1,X7,X8] :
      ( ? [X10] :
          ( in(ordered_pair(X10,X8),X1)
          & in(ordered_pair(X7,X10),X0) )
     => ( in(ordered_pair(sK33(X0,X1,X7,X8),X8),X1)
        & in(ordered_pair(X7,sK33(X0,X1,X7,X8)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f364,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( relation_composition(X0,X1) = X2
                  | ( ( ! [X5] :
                          ( ~ in(ordered_pair(X5,sK31(X0,X1,X2)),X1)
                          | ~ in(ordered_pair(sK30(X0,X1,X2),X5),X0) )
                      | ~ in(ordered_pair(sK30(X0,X1,X2),sK31(X0,X1,X2)),X2) )
                    & ( ( in(ordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),X1)
                        & in(ordered_pair(sK30(X0,X1,X2),sK32(X0,X1,X2)),X0) )
                      | in(ordered_pair(sK30(X0,X1,X2),sK31(X0,X1,X2)),X2) ) ) )
                & ( ! [X7,X8] :
                      ( ( in(ordered_pair(X7,X8),X2)
                        | ! [X9] :
                            ( ~ in(ordered_pair(X9,X8),X1)
                            | ~ in(ordered_pair(X7,X9),X0) ) )
                      & ( ( in(ordered_pair(sK33(X0,X1,X7,X8),X8),X1)
                          & in(ordered_pair(X7,sK33(X0,X1,X7,X8)),X0) )
                        | ~ in(ordered_pair(X7,X8),X2) ) )
                  | relation_composition(X0,X1) != X2 ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33])],[f360,f363,f362,f361]) ).

fof(f408,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
            & relation(X1) )
        & relation(X0) )
   => ( ? [X1] :
          ( ~ subset(relation_rng(relation_composition(sK45,X1)),relation_rng(X1))
          & relation(X1) )
      & relation(sK45) ) ),
    introduced(choice_axiom,[]) ).

fof(f409,plain,
    ( ? [X1] :
        ( ~ subset(relation_rng(relation_composition(sK45,X1)),relation_rng(X1))
        & relation(X1) )
   => ( ~ subset(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))
      & relation(sK46) ) ),
    introduced(choice_axiom,[]) ).

fof(f410,plain,
    ( ~ subset(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))
    & relation(sK46)
    & relation(sK45) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46])],[f249,f409,f408]) ).

fof(f473,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK16(X0,X1),X0) ),
    inference(cnf_transformation,[],[f325]) ).

fof(f474,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK16(X0,X1),X1) ),
    inference(cnf_transformation,[],[f325]) ).

fof(f498,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK27(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f353]) ).

fof(f503,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f24]) ).

fof(f512,plain,
    ! [X2,X0,X1,X8,X7] :
      ( in(ordered_pair(sK33(X0,X1,X7,X8),X8),X1)
      | ~ in(ordered_pair(X7,X8),X2)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f364]) ).

fof(f526,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f597,plain,
    ! [X2,X0,X1] :
      ( in(X1,relation_rng(X2))
      | ~ in(ordered_pair(X0,X1),X2)
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f231]) ).

fof(f638,plain,
    relation(sK45),
    inference(cnf_transformation,[],[f410]) ).

fof(f639,plain,
    relation(sK46),
    inference(cnf_transformation,[],[f410]) ).

fof(f640,plain,
    ~ subset(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)),
    inference(cnf_transformation,[],[f410]) ).

fof(f658,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f147]) ).

fof(f675,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
    inference(definition_unfolding,[],[f503,f658]) ).

fof(f700,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f498,f675]) ).

fof(f711,plain,
    ! [X2,X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(sK33(X0,X1,X7,X8),X8),unordered_pair(sK33(X0,X1,X7,X8),sK33(X0,X1,X7,X8))),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f512,f675,f675]) ).

fof(f735,plain,
    ! [X2,X0,X1] :
      ( in(X1,relation_rng(X2))
      | ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
      | ~ relation(X2) ),
    inference(definition_unfolding,[],[f597,f675]) ).

fof(f797,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f700]) ).

fof(f801,plain,
    ! [X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(sK33(X0,X1,X7,X8),X8),unordered_pair(sK33(X0,X1,X7,X8),sK33(X0,X1,X7,X8))),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
      | ~ relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f711]) ).

cnf(c_102,plain,
    ( ~ in(sK16(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f474]) ).

cnf(c_103,plain,
    ( in(sK16(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_131,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(sK27(X1,X0),X0),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1) ),
    inference(cnf_transformation,[],[f797]) ).

cnf(c_144,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3))
    | ~ relation(relation_composition(X2,X3))
    | ~ relation(X2)
    | ~ relation(X3)
    | in(unordered_pair(unordered_pair(sK33(X2,X3,X0,X1),X1),unordered_pair(sK33(X2,X3,X0,X1),sK33(X2,X3,X0,X1))),X3) ),
    inference(cnf_transformation,[],[f801]) ).

cnf(c_155,plain,
    ( ~ relation(X0)
    | ~ relation(X1)
    | relation(relation_composition(X1,X0)) ),
    inference(cnf_transformation,[],[f526]) ).

cnf(c_225,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
    | ~ relation(X2)
    | in(X1,relation_rng(X2)) ),
    inference(cnf_transformation,[],[f735]) ).

cnf(c_267,negated_conjecture,
    ~ subset(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)),
    inference(cnf_transformation,[],[f640]) ).

cnf(c_268,negated_conjecture,
    relation(sK46),
    inference(cnf_transformation,[],[f639]) ).

cnf(c_269,negated_conjecture,
    relation(sK45),
    inference(cnf_transformation,[],[f638]) ).

cnf(c_556,plain,
    ( ~ relation(X0)
    | ~ relation(sK45)
    | relation(relation_composition(sK45,X0)) ),
    inference(instantiation,[status(thm)],[c_155]) ).

cnf(c_579,plain,
    ( ~ in(sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)),relation_rng(sK46))
    | subset(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)) ),
    inference(instantiation,[status(thm)],[c_102]) ).

cnf(c_580,plain,
    ( in(sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)),relation_rng(relation_composition(sK45,sK46)))
    | subset(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)) ),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_695,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK46)
    | ~ relation(sK46)
    | in(X1,relation_rng(sK46)) ),
    inference(instantiation,[status(thm)],[c_225]) ).

cnf(c_2200,plain,
    ( ~ in(sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)),relation_rng(relation_composition(sK45,sK46)))
    | ~ relation(relation_composition(sK45,sK46))
    | in(unordered_pair(unordered_pair(sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),unordered_pair(sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))))),relation_composition(sK45,sK46)) ),
    inference(instantiation,[status(thm)],[c_131]) ).

cnf(c_6092,plain,
    ( ~ relation(sK45)
    | ~ relation(sK46)
    | relation(relation_composition(sK45,sK46)) ),
    inference(instantiation,[status(thm)],[c_556]) ).

cnf(c_9255,plain,
    ( ~ in(unordered_pair(unordered_pair(sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),unordered_pair(sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))))),relation_composition(sK45,sK46))
    | ~ relation(relation_composition(sK45,sK46))
    | ~ relation(sK45)
    | ~ relation(sK46)
    | in(unordered_pair(unordered_pair(sK33(sK45,sK46,sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),unordered_pair(sK33(sK45,sK46,sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK33(sK45,sK46,sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))))),sK46) ),
    inference(instantiation,[status(thm)],[c_144]) ).

cnf(c_30459,plain,
    ( ~ in(unordered_pair(unordered_pair(sK33(sK45,sK46,sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),unordered_pair(sK33(sK45,sK46,sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK33(sK45,sK46,sK27(relation_composition(sK45,sK46),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))),sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46))))),sK46)
    | ~ relation(sK46)
    | in(sK16(relation_rng(relation_composition(sK45,sK46)),relation_rng(sK46)),relation_rng(sK46)) ),
    inference(instantiation,[status(thm)],[c_695]) ).

cnf(c_30460,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_30459,c_9255,c_6092,c_2200,c_580,c_579,c_267,c_268,c_269]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU183+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.15/0.34  % Computer : n026.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Wed Aug 23 14:17:01 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 56.63/8.68  % SZS status Started for theBenchmark.p
% 56.63/8.68  % SZS status Theorem for theBenchmark.p
% 56.63/8.68  
% 56.63/8.68  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 56.63/8.68  
% 56.63/8.68  ------  iProver source info
% 56.63/8.68  
% 56.63/8.68  git: date: 2023-05-31 18:12:56 +0000
% 56.63/8.68  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 56.63/8.68  git: non_committed_changes: false
% 56.63/8.68  git: last_make_outside_of_git: false
% 56.63/8.68  
% 56.63/8.68  ------ Parsing...
% 56.63/8.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 56.63/8.68  
% 56.63/8.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 1 0s  sf_e 
% 56.63/8.68  
% 56.63/8.68  ------ Preprocessing...
% 56.63/8.68  
% 56.63/8.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 56.63/8.68  ------ Proving...
% 56.63/8.68  ------ Problem Properties 
% 56.63/8.68  
% 56.63/8.68  
% 56.63/8.68  clauses                                 234
% 56.63/8.68  conjectures                             3
% 56.63/8.68  EPR                                     29
% 56.63/8.68  Horn                                    184
% 56.63/8.68  unary                                   46
% 56.63/8.68  binary                                  86
% 56.63/8.68  lits                                    578
% 56.63/8.68  lits eq                                 125
% 56.63/8.68  fd_pure                                 0
% 56.63/8.68  fd_pseudo                               0
% 56.63/8.68  fd_cond                                 10
% 56.63/8.68  fd_pseudo_cond                          50
% 56.63/8.68  AC symbols                              0
% 56.63/8.68  
% 56.63/8.68  ------ Input Options Time Limit: Unbounded
% 56.63/8.68  
% 56.63/8.68  
% 56.63/8.68  ------ 
% 56.63/8.68  Current options:
% 56.63/8.68  ------ 
% 56.63/8.68  
% 56.63/8.68  
% 56.63/8.68  
% 56.63/8.68  
% 56.63/8.68  ------ Proving...
% 56.63/8.68  
% 56.63/8.68  
% 56.63/8.68  % SZS status Theorem for theBenchmark.p
% 56.63/8.68  
% 56.63/8.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 56.63/8.68  
% 56.63/8.69  
%------------------------------------------------------------------------------