TSTP Solution File: SEU201+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU201+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 17:04:38 EDT 2023

% Result   : Theorem 12.22s 2.69s
% Output   : CNFRefutation 12.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   86 (   7 unt;   0 def)
%            Number of atoms       :  405 (  52 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  522 ( 203   ~; 217   |;  74   &)
%                                         (  12 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    7 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   2 con; 0-3 aty)
%            Number of variables   :  241 (   3 sgn; 173   !;  32   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ( relation_rng_restriction(X0,X1) = X2
          <=> ! [X3,X4] :
                ( in(ordered_pair(X3,X4),X2)
              <=> ( in(ordered_pair(X3,X4),X1)
                  & in(X4,X0) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f9,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(f10,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(f18,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => relation(relation_rng_restriction(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).

fof(f40,conjecture,
    ! [X0,X1] :
      ( relation(X1)
     => relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).

fof(f41,negated_conjecture,
    ~ ! [X0,X1] :
        ( relation(X1)
       => relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_rng_restriction(X0,X1) = X2
          <=> ! [X3,X4] :
                ( in(ordered_pair(X3,X4),X2)
              <=> ( in(ordered_pair(X3,X4),X1)
                  & in(X4,X0) ) ) )
          | ~ relation(X2) )
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( relation(relation_rng_restriction(X0,X1))
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f68,plain,
    ? [X0,X1] :
      ( relation_rng(relation_rng_restriction(X0,X1)) != set_intersection2(relation_rng(X1),X0)
      & relation(X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X1) = X2
              | ? [X3,X4] :
                  ( ( ~ in(ordered_pair(X3,X4),X1)
                    | ~ in(X4,X0)
                    | ~ in(ordered_pair(X3,X4),X2) )
                  & ( ( in(ordered_pair(X3,X4),X1)
                      & in(X4,X0) )
                    | in(ordered_pair(X3,X4),X2) ) ) )
            & ( ! [X3,X4] :
                  ( ( in(ordered_pair(X3,X4),X2)
                    | ~ in(ordered_pair(X3,X4),X1)
                    | ~ in(X4,X0) )
                  & ( ( in(ordered_pair(X3,X4),X1)
                      & in(X4,X0) )
                    | ~ in(ordered_pair(X3,X4),X2) ) )
              | relation_rng_restriction(X0,X1) != X2 ) )
          | ~ relation(X2) )
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X1) = X2
              | ? [X3,X4] :
                  ( ( ~ in(ordered_pair(X3,X4),X1)
                    | ~ in(X4,X0)
                    | ~ in(ordered_pair(X3,X4),X2) )
                  & ( ( in(ordered_pair(X3,X4),X1)
                      & in(X4,X0) )
                    | in(ordered_pair(X3,X4),X2) ) ) )
            & ( ! [X3,X4] :
                  ( ( in(ordered_pair(X3,X4),X2)
                    | ~ in(ordered_pair(X3,X4),X1)
                    | ~ in(X4,X0) )
                  & ( ( in(ordered_pair(X3,X4),X1)
                      & in(X4,X0) )
                    | ~ in(ordered_pair(X3,X4),X2) ) )
              | relation_rng_restriction(X0,X1) != X2 ) )
          | ~ relation(X2) )
      | ~ relation(X1) ),
    inference(flattening,[],[f82]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X1) = X2
              | ? [X3,X4] :
                  ( ( ~ in(ordered_pair(X3,X4),X1)
                    | ~ in(X4,X0)
                    | ~ in(ordered_pair(X3,X4),X2) )
                  & ( ( in(ordered_pair(X3,X4),X1)
                      & in(X4,X0) )
                    | in(ordered_pair(X3,X4),X2) ) ) )
            & ( ! [X5,X6] :
                  ( ( in(ordered_pair(X5,X6),X2)
                    | ~ in(ordered_pair(X5,X6),X1)
                    | ~ in(X6,X0) )
                  & ( ( in(ordered_pair(X5,X6),X1)
                      & in(X6,X0) )
                    | ~ in(ordered_pair(X5,X6),X2) ) )
              | relation_rng_restriction(X0,X1) != X2 ) )
          | ~ relation(X2) )
      | ~ relation(X1) ),
    inference(rectify,[],[f83]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( ( ~ in(ordered_pair(X3,X4),X1)
            | ~ in(X4,X0)
            | ~ in(ordered_pair(X3,X4),X2) )
          & ( ( in(ordered_pair(X3,X4),X1)
              & in(X4,X0) )
            | in(ordered_pair(X3,X4),X2) ) )
     => ( ( ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
          | ~ in(sK1(X0,X1,X2),X0)
          | ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) )
        & ( ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
            & in(sK1(X0,X1,X2),X0) )
          | in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X1) = X2
              | ( ( ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
                  | ~ in(sK1(X0,X1,X2),X0)
                  | ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) )
                & ( ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X1)
                    & in(sK1(X0,X1,X2),X0) )
                  | in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) ) ) )
            & ( ! [X5,X6] :
                  ( ( in(ordered_pair(X5,X6),X2)
                    | ~ in(ordered_pair(X5,X6),X1)
                    | ~ in(X6,X0) )
                  & ( ( in(ordered_pair(X5,X6),X1)
                      & in(X6,X0) )
                    | ~ in(ordered_pair(X5,X6),X2) ) )
              | relation_rng_restriction(X0,X1) != X2 ) )
          | ~ relation(X2) )
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f84,f85]) ).

fof(f87,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,[],[f57]) ).

fof(f88,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,[],[f87]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK2(X0,X1),X1)
        & in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK2(X0,X1),X1)
          & in(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f88,f89]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f91]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(rectify,[],[f92]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK3(X0,X1,X2),X1)
          | ~ in(sK3(X0,X1,X2),X0)
          | ~ in(sK3(X0,X1,X2),X2) )
        & ( ( in(sK3(X0,X1,X2),X1)
            & in(sK3(X0,X1,X2),X0) )
          | in(sK3(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK3(X0,X1,X2),X1)
            | ~ in(sK3(X0,X1,X2),X0)
            | ~ in(sK3(X0,X1,X2),X2) )
          & ( ( in(sK3(X0,X1,X2),X1)
              & in(sK3(X0,X1,X2),X0) )
            | in(sK3(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f93,f94]) ).

fof(f96,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,[],[f58]) ).

fof(f97,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,[],[f96]) ).

fof(f98,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,sK4(X0,X1)),X0)
          | ~ in(sK4(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
     => in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK6(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
                | ~ in(sK4(X0,X1),X1) )
              & ( in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0)
                | in(sK4(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK6(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f97,f100,f99,f98]) ).

fof(f116,plain,
    ( ? [X0,X1] :
        ( relation_rng(relation_rng_restriction(X0,X1)) != set_intersection2(relation_rng(X1),X0)
        & relation(X1) )
   => ( relation_rng(relation_rng_restriction(sK14,sK15)) != set_intersection2(relation_rng(sK15),sK14)
      & relation(sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ( relation_rng(relation_rng_restriction(sK14,sK15)) != set_intersection2(relation_rng(sK15),sK14)
    & relation(sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f68,f116]) ).

fof(f128,plain,
    ! [X2,X0,X1,X6,X5] :
      ( in(ordered_pair(X5,X6),X2)
      | ~ in(ordered_pair(X5,X6),X1)
      | ~ in(X6,X0)
      | relation_rng_restriction(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f132,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | in(sK3(X0,X1,X2),X0)
      | in(sK3(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | in(sK3(X0,X1,X2),X1)
      | in(sK3(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | ~ in(sK3(X0,X1,X2),X1)
      | ~ in(sK3(X0,X1,X2),X0)
      | ~ in(sK3(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f141,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK6(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f142,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X6,X5),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f145,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( relation(relation_rng_restriction(X0,X1))
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f173,plain,
    relation(sK15),
    inference(cnf_transformation,[],[f117]) ).

fof(f174,plain,
    relation_rng(relation_rng_restriction(sK14,sK15)) != set_intersection2(relation_rng(sK15),sK14),
    inference(cnf_transformation,[],[f117]) ).

fof(f189,plain,
    ! [X2,X0,X1,X6,X5] :
      ( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
      | ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
      | ~ in(X6,X0)
      | relation_rng_restriction(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1) ),
    inference(definition_unfolding,[],[f128,f145,f145]) ).

fof(f194,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f142,f145]) ).

fof(f195,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f141,f145]) ).

fof(f199,plain,
    ! [X0,X1,X6,X5] :
      ( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_rng_restriction(X0,X1))
      | ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X1)
      | ~ in(X6,X0)
      | ~ relation(relation_rng_restriction(X0,X1))
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f189]) ).

fof(f205,plain,
    ! [X0,X6,X5] :
      ( in(X5,relation_rng(X0))
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f194]) ).

fof(f206,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f195]) ).

cnf(c_59,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ relation(relation_rng_restriction(X3,X2))
    | ~ in(X1,X3)
    | ~ relation(X2)
    | in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X3,X2)) ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_64,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_65,plain,
    ( ~ in(sK3(X0,X1,X2),X0)
    | ~ in(sK3(X0,X1,X2),X1)
    | ~ in(sK3(X0,X1,X2),X2)
    | set_intersection2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_66,plain,
    ( set_intersection2(X0,X1) = X2
    | in(sK3(X0,X1,X2),X1)
    | in(sK3(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_67,plain,
    ( set_intersection2(X0,X1) = X2
    | in(sK3(X0,X1,X2),X0)
    | in(sK3(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_73,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ relation(X2)
    | in(X1,relation_rng(X2)) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_74,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(sK6(X1,X0),X0),singleton(sK6(X1,X0))),X1) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_75,plain,
    ( ~ relation(X0)
    | relation(relation_rng_restriction(X1,X0)) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_100,plain,
    ( ~ relation(X0)
    | subset(relation_rng(relation_rng_restriction(X1,X0)),X1) ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_101,plain,
    ( ~ relation(X0)
    | subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0)) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_102,negated_conjecture,
    set_intersection2(relation_rng(sK15),sK14) != relation_rng(relation_rng_restriction(sK14,sK15)),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_103,negated_conjecture,
    relation(sK15),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_177,plain,
    ( ~ relation(X0)
    | relation(relation_rng_restriction(X1,X0)) ),
    inference(prop_impl_just,[status(thm)],[c_75]) ).

cnf(c_396,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ in(X1,X3)
    | ~ relation(X2)
    | in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_rng_restriction(X3,X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_59,c_177]) ).

cnf(c_2375,plain,
    ( set_intersection2(relation_rng(sK15),sK14) = relation_rng(relation_rng_restriction(sK14,sK15))
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15)))
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(sK15)) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_2376,plain,
    ( set_intersection2(relation_rng(sK15),sK14) = relation_rng(relation_rng_restriction(sK14,sK15))
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15)))
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),sK14) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_2377,plain,
    ( ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15)))
    | ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(sK15))
    | ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),sK14)
    | set_intersection2(relation_rng(sK15),sK14) = relation_rng(relation_rng_restriction(sK14,sK15)) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_2434,plain,
    ( ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15)))
    | ~ subset(relation_rng(relation_rng_restriction(sK14,sK15)),X0)
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),X0) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_2742,plain,
    ( ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(sK15))
    | ~ relation(sK15)
    | in(unordered_pair(unordered_pair(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),singleton(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))))),sK15) ),
    inference(instantiation,[status(thm)],[c_74]) ).

cnf(c_2774,plain,
    ( ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15)))
    | ~ subset(relation_rng(relation_rng_restriction(sK14,sK15)),sK14)
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),sK14) ),
    inference(instantiation,[status(thm)],[c_2434]) ).

cnf(c_2775,plain,
    ( ~ relation(sK15)
    | subset(relation_rng(relation_rng_restriction(sK14,sK15)),sK14) ),
    inference(instantiation,[status(thm)],[c_100]) ).

cnf(c_2776,plain,
    ( ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15)))
    | ~ subset(relation_rng(relation_rng_restriction(sK14,sK15)),relation_rng(sK15))
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(sK15)) ),
    inference(instantiation,[status(thm)],[c_2434]) ).

cnf(c_2777,plain,
    ( ~ relation(sK15)
    | subset(relation_rng(relation_rng_restriction(sK14,sK15)),relation_rng(sK15)) ),
    inference(instantiation,[status(thm)],[c_101]) ).

cnf(c_2865,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),singleton(X0)),X1)
    | ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),sK14)
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(X0,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),singleton(X0)),relation_rng_restriction(sK14,X1)) ),
    inference(instantiation,[status(thm)],[c_396]) ).

cnf(c_3227,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),singleton(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))))),sK15)
    | ~ in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),sK14)
    | ~ relation(sK15)
    | in(unordered_pair(unordered_pair(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),singleton(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))))),relation_rng_restriction(sK14,sK15)) ),
    inference(instantiation,[status(thm)],[c_2865]) ).

cnf(c_3290,plain,
    ( ~ relation(sK15)
    | relation(relation_rng_restriction(sK14,sK15)) ),
    inference(instantiation,[status(thm)],[c_75]) ).

cnf(c_5133,plain,
    ( ~ in(unordered_pair(unordered_pair(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))),singleton(sK6(sK15,sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15)))))),relation_rng_restriction(sK14,sK15))
    | ~ relation(relation_rng_restriction(sK14,sK15))
    | in(sK3(relation_rng(sK15),sK14,relation_rng(relation_rng_restriction(sK14,sK15))),relation_rng(relation_rng_restriction(sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_5134,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5133,c_3290,c_3227,c_2777,c_2776,c_2775,c_2774,c_2742,c_2375,c_2376,c_2377,c_102,c_103]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU201+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.16/0.34  % Computer : n021.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Wed Aug 23 21:49:39 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.22/2.69  % SZS status Started for theBenchmark.p
% 12.22/2.69  % SZS status Theorem for theBenchmark.p
% 12.22/2.69  
% 12.22/2.69  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 12.22/2.69  
% 12.22/2.69  ------  iProver source info
% 12.22/2.69  
% 12.22/2.69  git: date: 2023-05-31 18:12:56 +0000
% 12.22/2.69  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 12.22/2.69  git: non_committed_changes: false
% 12.22/2.69  git: last_make_outside_of_git: false
% 12.22/2.69  
% 12.22/2.69  ------ Parsing...
% 12.22/2.69  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 12.22/2.69  
% 12.22/2.69  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 12.22/2.69  
% 12.22/2.69  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 12.22/2.69  
% 12.22/2.69  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 12.22/2.69  ------ Proving...
% 12.22/2.69  ------ Problem Properties 
% 12.22/2.69  
% 12.22/2.69  
% 12.22/2.69  clauses                                 62
% 12.22/2.69  conjectures                             2
% 12.22/2.69  EPR                                     21
% 12.22/2.69  Horn                                    54
% 12.22/2.69  unary                                   21
% 12.22/2.69  binary                                  18
% 12.22/2.69  lits                                    137
% 12.22/2.69  lits eq                                 16
% 12.22/2.69  fd_pure                                 0
% 12.22/2.69  fd_pseudo                               0
% 12.22/2.69  fd_cond                                 1
% 12.22/2.69  fd_pseudo_cond                          10
% 12.22/2.69  AC symbols                              0
% 12.22/2.69  
% 12.22/2.69  ------ Input Options Time Limit: Unbounded
% 12.22/2.69  
% 12.22/2.69  
% 12.22/2.69  ------ 
% 12.22/2.69  Current options:
% 12.22/2.69  ------ 
% 12.22/2.69  
% 12.22/2.69  
% 12.22/2.69  
% 12.22/2.69  
% 12.22/2.69  ------ Proving...
% 12.22/2.69  
% 12.22/2.69  
% 12.22/2.69  % SZS status Theorem for theBenchmark.p
% 12.22/2.69  
% 12.22/2.69  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.22/2.69  
% 12.22/2.70  
%------------------------------------------------------------------------------