TSTP Solution File: SEU012+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 : Fri May  3 03:04:21 EDT 2024

% Result   : Theorem 145.56s 20.19s
% Output   : CNFRefutation 145.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   70 (  17 unt;   0 def)
%            Number of atoms       :  354 ( 138 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  453 ( 169   ~; 166   |;  91   &)
%                                         (   9 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :  134 (   0 sgn  87   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(X1))
           => apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( in(X2,X0)
             => apply(X1,X2) = X2 )
          & relation_dom(X1) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(f34,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1] :
          ( ( function(X1)
            & relation(X1) )
         => ( ( relation_composition(X0,X1) = X0
              & relation_rng(X0) = relation_dom(X1) )
           => identity_relation(relation_dom(X1)) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).

fof(f35,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ! [X1] :
            ( ( function(X1)
              & relation(X1) )
           => ( ( relation_composition(X0,X1) = X0
                & relation_rng(X0) = relation_dom(X1) )
             => identity_relation(relation_dom(X1)) = X1 ) ) ),
    inference(negated_conjecture,[],[f34]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f48]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
          | ~ in(X0,relation_dom(X1))
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
          | ~ in(X0,relation_dom(X1))
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f66]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( apply(X1,X2) = X2
              | ~ in(X2,X0) )
          & relation_dom(X1) = X0 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( identity_relation(X0) = X1
      <=> ( ! [X2] :
              ( apply(X1,X2) = X2
              | ~ in(X2,X0) )
          & relation_dom(X1) = X0 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f70]) ).

fof(f73,plain,
    ? [X0] :
      ( ? [X1] :
          ( identity_relation(relation_dom(X1)) != X1
          & relation_composition(X0,X1) = X0
          & relation_rng(X0) = relation_dom(X1)
          & function(X1)
          & relation(X1) )
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f74,plain,
    ? [X0] :
      ( ? [X1] :
          ( identity_relation(relation_dom(X1)) != X1
          & relation_composition(X0,X1) = X0
          & relation_rng(X0) = relation_dom(X1)
          & function(X1)
          & relation(X1) )
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f81,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) ) )
                & ( ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f82,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( ? [X4] :
                      ( apply(X0,X4) = X2
                      & in(X4,relation_dom(X0)) )
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] :
                      ( apply(X0,X6) != X5
                      | ~ in(X6,relation_dom(X0)) ) )
                & ( ? [X7] :
                      ( apply(X0,X7) = X5
                      & in(X7,relation_dom(X0)) )
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f81]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( apply(X0,X3) != X2
                | ~ in(X3,relation_dom(X0)) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( apply(X0,X4) = X2
                & in(X4,relation_dom(X0)) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( apply(X0,X3) != sK0(X0,X1)
              | ~ in(X3,relation_dom(X0)) )
          | ~ in(sK0(X0,X1),X1) )
        & ( ? [X4] :
              ( apply(X0,X4) = sK0(X0,X1)
              & in(X4,relation_dom(X0)) )
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( apply(X0,X4) = sK0(X0,X1)
          & in(X4,relation_dom(X0)) )
     => ( sK0(X0,X1) = apply(X0,sK1(X0,X1))
        & in(sK1(X0,X1),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( apply(X0,X7) = X5
          & in(X7,relation_dom(X0)) )
     => ( apply(X0,sK2(X0,X5)) = X5
        & in(sK2(X0,X5),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] :
                    ( apply(X0,X3) != sK0(X0,X1)
                    | ~ in(X3,relation_dom(X0)) )
                | ~ in(sK0(X0,X1),X1) )
              & ( ( sK0(X0,X1) = apply(X0,sK1(X0,X1))
                  & in(sK1(X0,X1),relation_dom(X0)) )
                | in(sK0(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] :
                      ( apply(X0,X6) != X5
                      | ~ in(X6,relation_dom(X0)) ) )
                & ( ( apply(X0,sK2(X0,X5)) = X5
                    & in(sK2(X0,X5),relation_dom(X0)) )
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f82,f85,f84,f83]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X2] :
                ( apply(X1,X2) = X2
                | ~ in(X2,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X2] :
                ( apply(X1,X2) = X2
                | ~ in(X2,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f105]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ? [X2] :
              ( apply(X1,X2) != X2
              & in(X2,X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X3] :
                ( apply(X1,X3) = X3
                | ~ in(X3,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f106]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( apply(X1,X2) != X2
          & in(X2,X0) )
     => ( sK12(X0,X1) != apply(X1,sK12(X0,X1))
        & in(sK12(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ( sK12(X0,X1) != apply(X1,sK12(X0,X1))
            & in(sK12(X0,X1),X0) )
          | relation_dom(X1) != X0 )
        & ( ( ! [X3] :
                ( apply(X1,X3) = X3
                | ~ in(X3,X0) )
            & relation_dom(X1) = X0 )
          | identity_relation(X0) != X1 ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f107,f108]) ).

fof(f110,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( identity_relation(relation_dom(X1)) != X1
            & relation_composition(X0,X1) = X0
            & relation_rng(X0) = relation_dom(X1)
            & function(X1)
            & relation(X1) )
        & function(X0)
        & relation(X0) )
   => ( ? [X1] :
          ( identity_relation(relation_dom(X1)) != X1
          & sK13 = relation_composition(sK13,X1)
          & relation_dom(X1) = relation_rng(sK13)
          & function(X1)
          & relation(X1) )
      & function(sK13)
      & relation(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ( ? [X1] :
        ( identity_relation(relation_dom(X1)) != X1
        & sK13 = relation_composition(sK13,X1)
        & relation_dom(X1) = relation_rng(sK13)
        & function(X1)
        & relation(X1) )
   => ( sK14 != identity_relation(relation_dom(sK14))
      & sK13 = relation_composition(sK13,sK14)
      & relation_rng(sK13) = relation_dom(sK14)
      & function(sK14)
      & relation(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ( sK14 != identity_relation(relation_dom(sK14))
    & sK13 = relation_composition(sK13,sK14)
    & relation_rng(sK13) = relation_dom(sK14)
    & function(sK14)
    & relation(sK14)
    & function(sK13)
    & relation(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f74,f111,f110]) ).

fof(f116,plain,
    ! [X0,X1,X5] :
      ( in(sK2(X0,X5),relation_dom(X0))
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f117,plain,
    ! [X0,X1,X5] :
      ( apply(X0,sK2(X0,X5)) = X5
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f160,plain,
    ! [X2,X0,X1] :
      ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
      | ~ in(X0,relation_dom(X1))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( identity_relation(X0) = X1
      | in(sK12(X0,X1),X0)
      | relation_dom(X1) != X0
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( identity_relation(X0) = X1
      | sK12(X0,X1) != apply(X1,sK12(X0,X1))
      | relation_dom(X1) != X0
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f167,plain,
    relation(sK13),
    inference(cnf_transformation,[],[f112]) ).

fof(f168,plain,
    function(sK13),
    inference(cnf_transformation,[],[f112]) ).

fof(f169,plain,
    relation(sK14),
    inference(cnf_transformation,[],[f112]) ).

fof(f170,plain,
    function(sK14),
    inference(cnf_transformation,[],[f112]) ).

fof(f171,plain,
    relation_rng(sK13) = relation_dom(sK14),
    inference(cnf_transformation,[],[f112]) ).

fof(f172,plain,
    sK13 = relation_composition(sK13,sK14),
    inference(cnf_transformation,[],[f112]) ).

fof(f173,plain,
    sK14 != identity_relation(relation_dom(sK14)),
    inference(cnf_transformation,[],[f112]) ).

fof(f181,plain,
    ! [X0,X5] :
      ( apply(X0,sK2(X0,X5)) = X5
      | ~ in(X5,relation_rng(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f117]) ).

fof(f182,plain,
    ! [X0,X5] :
      ( in(sK2(X0,X5),relation_dom(X0))
      | ~ in(X5,relation_rng(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f116]) ).

fof(f183,plain,
    ! [X1] :
      ( identity_relation(relation_dom(X1)) = X1
      | sK12(relation_dom(X1),X1) != apply(X1,sK12(relation_dom(X1),X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f165]) ).

fof(f184,plain,
    ! [X1] :
      ( identity_relation(relation_dom(X1)) = X1
      | in(sK12(relation_dom(X1),X1),relation_dom(X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f164]) ).

cnf(c_56,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | apply(X1,sK2(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_57,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | in(sK2(X1,X0),relation_dom(X1)) ),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_96,plain,
    ( ~ in(X0,relation_dom(X1))
    | ~ function(X1)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ relation(X2)
    | apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_98,plain,
    ( apply(X0,sK12(relation_dom(X0),X0)) != sK12(relation_dom(X0),X0)
    | ~ function(X0)
    | ~ relation(X0)
    | identity_relation(relation_dom(X0)) = X0 ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_99,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | identity_relation(relation_dom(X0)) = X0
    | in(sK12(relation_dom(X0),X0),relation_dom(X0)) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_103,negated_conjecture,
    identity_relation(relation_dom(sK14)) != sK14,
    inference(cnf_transformation,[],[f173]) ).

cnf(c_104,negated_conjecture,
    relation_composition(sK13,sK14) = sK13,
    inference(cnf_transformation,[],[f172]) ).

cnf(c_105,negated_conjecture,
    relation_rng(sK13) = relation_dom(sK14),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_106,negated_conjecture,
    function(sK14),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_107,negated_conjecture,
    relation(sK14),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_108,negated_conjecture,
    function(sK13),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_109,negated_conjecture,
    relation(sK13),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_10515,plain,
    ( ~ in(X0,relation_dom(sK14))
    | ~ function(sK13)
    | ~ relation(sK13)
    | apply(sK13,sK2(sK13,X0)) = X0 ),
    inference(superposition,[status(thm)],[c_105,c_56]) ).

cnf(c_10516,plain,
    ( ~ in(X0,relation_dom(sK14))
    | apply(sK13,sK2(sK13,X0)) = X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10515,c_109,c_108]) ).

cnf(c_10526,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ relation(X2)
    | apply(relation_composition(X1,X2),sK2(X1,X0)) = apply(X2,apply(X1,sK2(X1,X0))) ),
    inference(superposition,[status(thm)],[c_57,c_96]) ).

cnf(c_10550,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | apply(sK13,sK2(sK13,sK12(relation_dom(sK14),sK14))) = sK12(relation_dom(sK14),sK14)
    | identity_relation(relation_dom(sK14)) = sK14 ),
    inference(superposition,[status(thm)],[c_99,c_10516]) ).

cnf(c_10553,plain,
    apply(sK13,sK2(sK13,sK12(relation_dom(sK14),sK14))) = sK12(relation_dom(sK14),sK14),
    inference(forward_subsumption_resolution,[status(thm)],[c_10550,c_103,c_107,c_106]) ).

cnf(c_12109,plain,
    ( ~ in(X0,relation_dom(sK14))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ function(sK13)
    | ~ relation(sK13)
    | apply(relation_composition(sK13,X1),sK2(sK13,X0)) = apply(X1,apply(sK13,sK2(sK13,X0))) ),
    inference(superposition,[status(thm)],[c_105,c_10526]) ).

cnf(c_12111,plain,
    ( ~ in(X0,relation_dom(sK14))
    | ~ function(X1)
    | ~ relation(X1)
    | apply(relation_composition(sK13,X1),sK2(sK13,X0)) = apply(X1,apply(sK13,sK2(sK13,X0))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12109,c_109,c_108]) ).

cnf(c_12116,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ function(sK14)
    | ~ relation(sK14)
    | apply(relation_composition(sK13,X0),sK2(sK13,sK12(relation_dom(sK14),sK14))) = apply(X0,apply(sK13,sK2(sK13,sK12(relation_dom(sK14),sK14))))
    | identity_relation(relation_dom(sK14)) = sK14 ),
    inference(superposition,[status(thm)],[c_99,c_12111]) ).

cnf(c_12139,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ function(sK14)
    | ~ relation(sK14)
    | apply(relation_composition(sK13,X0),sK2(sK13,sK12(relation_dom(sK14),sK14))) = apply(X0,sK12(relation_dom(sK14),sK14))
    | identity_relation(relation_dom(sK14)) = sK14 ),
    inference(demodulation,[status(thm)],[c_12116,c_10553]) ).

cnf(c_12140,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | apply(relation_composition(sK13,X0),sK2(sK13,sK12(relation_dom(sK14),sK14))) = apply(X0,sK12(relation_dom(sK14),sK14)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12139,c_103,c_107,c_106]) ).

cnf(c_12146,plain,
    ( ~ relation(sK14)
    | apply(relation_composition(sK13,sK14),sK2(sK13,sK12(relation_dom(sK14),sK14))) = apply(sK14,sK12(relation_dom(sK14),sK14)) ),
    inference(superposition,[status(thm)],[c_106,c_12140]) ).

cnf(c_12154,plain,
    ( ~ relation(sK14)
    | apply(sK14,sK12(relation_dom(sK14),sK14)) = sK12(relation_dom(sK14),sK14) ),
    inference(demodulation,[status(thm)],[c_12146,c_104,c_10553]) ).

cnf(c_12155,plain,
    apply(sK14,sK12(relation_dom(sK14),sK14)) = sK12(relation_dom(sK14),sK14),
    inference(forward_subsumption_resolution,[status(thm)],[c_12154,c_107]) ).

cnf(c_12195,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | identity_relation(relation_dom(sK14)) = sK14 ),
    inference(superposition,[status(thm)],[c_12155,c_98]) ).

cnf(c_12196,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_12195,c_103,c_107,c_106]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 18:11:35 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 145.56/20.19  % SZS status Started for theBenchmark.p
% 145.56/20.19  % SZS status Theorem for theBenchmark.p
% 145.56/20.19  
% 145.56/20.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 145.56/20.19  
% 145.56/20.19  ------  iProver source info
% 145.56/20.19  
% 145.56/20.19  git: date: 2024-05-02 19:28:25 +0000
% 145.56/20.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 145.56/20.19  git: non_committed_changes: false
% 145.56/20.19  
% 145.56/20.19  ------ Parsing...
% 145.56/20.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 145.56/20.19  
% 145.56/20.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 145.56/20.19  
% 145.56/20.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 145.56/20.19  
% 145.56/20.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 145.56/20.19  ------ Proving...
% 145.56/20.19  ------ Problem Properties 
% 145.56/20.19  
% 145.56/20.19  
% 145.56/20.19  clauses                                 60
% 145.56/20.19  conjectures                             7
% 145.56/20.19  EPR                                     23
% 145.56/20.19  Horn                                    55
% 145.56/20.19  unary                                   26
% 145.56/20.19  binary                                  13
% 145.56/20.19  lits                                    132
% 145.56/20.19  lits eq                                 17
% 145.56/20.19  fd_pure                                 0
% 145.56/20.19  fd_pseudo                               0
% 145.56/20.19  fd_cond                                 1
% 145.56/20.19  fd_pseudo_cond                          4
% 145.56/20.19  AC symbols                              0
% 145.56/20.19  
% 145.56/20.19  ------ Input Options Time Limit: Unbounded
% 145.56/20.19  
% 145.56/20.19  
% 145.56/20.19  ------ 
% 145.56/20.19  Current options:
% 145.56/20.19  ------ 
% 145.56/20.19  
% 145.56/20.19  
% 145.56/20.19  
% 145.56/20.19  
% 145.56/20.19  ------ Proving...
% 145.56/20.19  
% 145.56/20.19  
% 145.56/20.19  % SZS status Theorem for theBenchmark.p
% 145.56/20.19  
% 145.56/20.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 145.56/20.19  
% 145.56/20.19  
%------------------------------------------------------------------------------