TSTP Solution File: SEU221+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 17:04:52 EDT 2023

% Result   : Theorem 3.95s 1.13s
% Output   : CNFRefutation 3.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   82 (  17 unt;   0 def)
%            Number of atoms       :  439 ( 124 equ)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives :  600 ( 243   ~; 237   |;  95   &)
%                                         (   8 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :  116 (   0 sgn;  82   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( ( apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

fof(f9,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(function_inverse(X0))
        & relation(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(f34,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ! [X1] :
            ( ( function(X1)
              & relation(X1) )
           => ( function_inverse(X0) = X1
            <=> ( ! [X2,X3] :
                    ( ( ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) )
                     => ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) )
                    & ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                     => ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) ) ) )
                & relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( in(X0,relation_rng(X1))
          & one_to_one(X1) )
       => ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
          & apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).

fof(f36,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => one_to_one(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).

fof(f37,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( one_to_one(X0)
         => one_to_one(function_inverse(X0)) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f48,plain,
    ! [X0] :
      ( ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( X1 = X2
            | apply(X0,X1) != apply(X0,X2)
            | ~ in(X2,relation_dom(X0))
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

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

fof(f50,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f51,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f50]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & ( ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                    | apply(X1,X2) != X3
                    | ~ in(X2,relation_rng(X0)) ) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & ( ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                    | apply(X1,X2) != X3
                    | ~ in(X2,relation_rng(X0)) ) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f69]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f71]) ).

fof(f73,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f74,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f78,plain,
    ! [X2,X3,X0,X1] :
      ( sP0(X2,X3,X0,X1)
    <=> ( ( apply(X0,X3) = X2
          & in(X3,relation_dom(X0)) )
        | apply(X1,X2) != X3
        | ~ in(X2,relation_rng(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f79,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & sP0(X2,X3,X0,X1) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_folding,[],[f70,f78]) ).

fof(f80,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) ) )
        & ( ! [X1,X2] :
              ( X1 = X2
              | apply(X0,X1) != apply(X0,X2)
              | ~ in(X2,relation_dom(X0))
              | ~ in(X1,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f81,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X3) != apply(X0,X4)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f80]) ).

fof(f82,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & apply(X0,X1) = apply(X0,X2)
          & in(X2,relation_dom(X0))
          & in(X1,relation_dom(X0)) )
     => ( sK1(X0) != sK2(X0)
        & apply(X0,sK1(X0)) = apply(X0,sK2(X0))
        & in(sK2(X0),relation_dom(X0))
        & in(sK1(X0),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ( sK1(X0) != sK2(X0)
            & apply(X0,sK1(X0)) = apply(X0,sK2(X0))
            & in(sK2(X0),relation_dom(X0))
            & in(sK1(X0),relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X3) != apply(X0,X4)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f81,f82]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X2,X3] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                      | apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                    & sP0(X2,X3,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f79]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X2,X3] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                      | apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                    & sP0(X2,X3,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f105]) ).

fof(f107,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X4,X5] :
                    ( ( ( apply(X1,X4) = X5
                        & in(X4,relation_rng(X0)) )
                      | apply(X0,X5) != X4
                      | ~ in(X5,relation_dom(X0)) )
                    & sP0(X4,X5,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f106]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ( ( apply(X1,X2) != X3
              | ~ in(X2,relation_rng(X0)) )
            & apply(X0,X3) = X2
            & in(X3,relation_dom(X0)) )
          | ~ sP0(X2,X3,X0,X1) )
     => ( ( ( sK13(X0,X1) != apply(X1,sK12(X0,X1))
            | ~ in(sK12(X0,X1),relation_rng(X0)) )
          & sK12(X0,X1) = apply(X0,sK13(X0,X1))
          & in(sK13(X0,X1),relation_dom(X0)) )
        | ~ sP0(sK12(X0,X1),sK13(X0,X1),X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ( ( sK13(X0,X1) != apply(X1,sK12(X0,X1))
                  | ~ in(sK12(X0,X1),relation_rng(X0)) )
                & sK12(X0,X1) = apply(X0,sK13(X0,X1))
                & in(sK13(X0,X1),relation_dom(X0)) )
              | ~ sP0(sK12(X0,X1),sK13(X0,X1),X0,X1)
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X4,X5] :
                    ( ( ( apply(X1,X4) = X5
                        & in(X4,relation_rng(X0)) )
                      | apply(X0,X5) != X4
                      | ~ in(X5,relation_dom(X0)) )
                    & sP0(X4,X5,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f107,f108]) ).

fof(f110,plain,
    ( ? [X0] :
        ( ~ one_to_one(function_inverse(X0))
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( ~ one_to_one(function_inverse(sK14))
      & one_to_one(sK14)
      & function(sK14)
      & relation(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ( ~ one_to_one(function_inverse(sK14))
    & one_to_one(sK14)
    & function(sK14)
    & relation(sK14) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f74,f110]) ).

fof(f118,plain,
    ! [X3,X0,X4] :
      ( X3 = X4
      | apply(X0,X3) != apply(X0,X4)
      | ~ in(X4,relation_dom(X0))
      | ~ in(X3,relation_dom(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f119,plain,
    ! [X0] :
      ( one_to_one(X0)
      | in(sK1(X0),relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f120,plain,
    ! [X0] :
      ( one_to_one(X0)
      | in(sK2(X0),relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f121,plain,
    ! [X0] :
      ( one_to_one(X0)
      | apply(X0,sK1(X0)) = apply(X0,sK2(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f122,plain,
    ! [X0] :
      ( one_to_one(X0)
      | sK1(X0) != sK2(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f123,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f124,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( relation_rng(X0) = relation_dom(X1)
      | function_inverse(X0) != X1
      | ~ function(X1)
      | ~ relation(X1)
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( apply(X1,apply(function_inverse(X1),X0)) = X0
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f175,plain,
    relation(sK14),
    inference(cnf_transformation,[],[f111]) ).

fof(f176,plain,
    function(sK14),
    inference(cnf_transformation,[],[f111]) ).

fof(f177,plain,
    one_to_one(sK14),
    inference(cnf_transformation,[],[f111]) ).

fof(f178,plain,
    ~ one_to_one(function_inverse(sK14)),
    inference(cnf_transformation,[],[f111]) ).

fof(f190,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ function(function_inverse(X0))
      | ~ relation(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f166]) ).

cnf(c_53,plain,
    ( sK1(X0) != sK2(X0)
    | ~ function(X0)
    | ~ relation(X0)
    | one_to_one(X0) ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_54,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | apply(X0,sK1(X0)) = apply(X0,sK2(X0))
    | one_to_one(X0) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_55,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | in(sK2(X0),relation_dom(X0))
    | one_to_one(X0) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_56,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | in(sK1(X0),relation_dom(X0))
    | one_to_one(X0) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_57,plain,
    ( apply(X0,X1) != apply(X0,X2)
    | ~ in(X1,relation_dom(X0))
    | ~ in(X2,relation_dom(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_58,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | function(function_inverse(X0)) ),
    inference(cnf_transformation,[],[f124]) ).

cnf(c_59,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | relation(function_inverse(X0)) ),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_107,plain,
    ( ~ function(function_inverse(X0))
    | ~ relation(function_inverse(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | relation_dom(function_inverse(X0)) = relation_rng(X0) ),
    inference(cnf_transformation,[],[f190]) ).

cnf(c_109,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1)
    | apply(X1,apply(function_inverse(X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_110,negated_conjecture,
    ~ one_to_one(function_inverse(sK14)),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_111,negated_conjecture,
    one_to_one(sK14),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_112,negated_conjecture,
    function(sK14),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_113,negated_conjecture,
    relation(sK14),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_162,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | relation_dom(function_inverse(X0)) = relation_rng(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_107,c_59,c_58,c_107]) ).

cnf(c_2511,plain,
    ( function_inverse(sK14) != X0
    | ~ function(X0)
    | ~ relation(X0)
    | apply(X0,sK1(X0)) = apply(X0,sK2(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_110]) ).

cnf(c_2512,plain,
    ( ~ function(function_inverse(sK14))
    | ~ relation(function_inverse(sK14))
    | apply(function_inverse(sK14),sK1(function_inverse(sK14))) = apply(function_inverse(sK14),sK2(function_inverse(sK14))) ),
    inference(unflattening,[status(thm)],[c_2511]) ).

cnf(c_2522,plain,
    ( sK1(X0) != sK2(X0)
    | function_inverse(sK14) != X0
    | ~ function(X0)
    | ~ relation(X0) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_110]) ).

cnf(c_2523,plain,
    ( sK1(function_inverse(sK14)) != sK2(function_inverse(sK14))
    | ~ function(function_inverse(sK14))
    | ~ relation(function_inverse(sK14)) ),
    inference(unflattening,[status(thm)],[c_2522]) ).

cnf(c_7277,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | function(function_inverse(sK14)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_7389,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | relation_dom(function_inverse(sK14)) = relation_rng(sK14) ),
    inference(superposition,[status(thm)],[c_111,c_162]) ).

cnf(c_7397,plain,
    relation_dom(function_inverse(sK14)) = relation_rng(sK14),
    inference(forward_subsumption_resolution,[status(thm)],[c_7389,c_113,c_112]) ).

cnf(c_7478,plain,
    ( ~ function(function_inverse(sK14))
    | ~ relation(function_inverse(sK14))
    | in(sK1(function_inverse(sK14)),relation_rng(sK14))
    | one_to_one(function_inverse(sK14)) ),
    inference(superposition,[status(thm)],[c_7397,c_56]) ).

cnf(c_7479,plain,
    ( ~ function(function_inverse(sK14))
    | ~ relation(function_inverse(sK14))
    | in(sK2(function_inverse(sK14)),relation_rng(sK14))
    | one_to_one(function_inverse(sK14)) ),
    inference(superposition,[status(thm)],[c_7397,c_55]) ).

cnf(c_7496,plain,
    ( ~ function(function_inverse(sK14))
    | ~ relation(function_inverse(sK14))
    | in(sK2(function_inverse(sK14)),relation_rng(sK14)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7479,c_110]) ).

cnf(c_7500,plain,
    ( ~ function(function_inverse(sK14))
    | ~ relation(function_inverse(sK14))
    | in(sK1(function_inverse(sK14)),relation_rng(sK14)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7478,c_110]) ).

cnf(c_7623,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | relation(function_inverse(sK14)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_7624,plain,
    in(sK2(function_inverse(sK14)),relation_rng(sK14)),
    inference(global_subsumption_just,[status(thm)],[c_7496,c_113,c_112,c_7277,c_7496,c_7623]) ).

cnf(c_7653,plain,
    in(sK1(function_inverse(sK14)),relation_rng(sK14)),
    inference(global_subsumption_just,[status(thm)],[c_7500,c_113,c_112,c_7277,c_7500,c_7623]) ).

cnf(c_7706,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | ~ one_to_one(sK14)
    | apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14)))) = sK1(function_inverse(sK14)) ),
    inference(superposition,[status(thm)],[c_7653,c_109]) ).

cnf(c_7707,plain,
    ( ~ function(sK14)
    | ~ relation(sK14)
    | ~ one_to_one(sK14)
    | apply(sK14,apply(function_inverse(sK14),sK2(function_inverse(sK14)))) = sK2(function_inverse(sK14)) ),
    inference(superposition,[status(thm)],[c_7624,c_109]) ).

cnf(c_7713,plain,
    apply(sK14,apply(function_inverse(sK14),sK2(function_inverse(sK14)))) = sK2(function_inverse(sK14)),
    inference(forward_subsumption_resolution,[status(thm)],[c_7707,c_111,c_113,c_112]) ).

cnf(c_7714,plain,
    apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14)))) = sK1(function_inverse(sK14)),
    inference(forward_subsumption_resolution,[status(thm)],[c_7706,c_111,c_113,c_112]) ).

cnf(c_7884,plain,
    ( apply(sK14,X0) != sK2(function_inverse(sK14))
    | ~ in(apply(function_inverse(sK14),sK2(function_inverse(sK14))),relation_dom(sK14))
    | ~ in(X0,relation_dom(sK14))
    | ~ function(sK14)
    | ~ relation(sK14)
    | ~ one_to_one(sK14)
    | apply(function_inverse(sK14),sK2(function_inverse(sK14))) = X0 ),
    inference(superposition,[status(thm)],[c_7713,c_57]) ).

cnf(c_7900,plain,
    ( apply(sK14,X0) != sK2(function_inverse(sK14))
    | ~ in(apply(function_inverse(sK14),sK2(function_inverse(sK14))),relation_dom(sK14))
    | ~ in(X0,relation_dom(sK14))
    | apply(function_inverse(sK14),sK2(function_inverse(sK14))) = X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7884,c_111,c_113,c_112]) ).

cnf(c_7950,plain,
    ( sK1(function_inverse(sK14)) != sK2(function_inverse(sK14))
    | ~ in(apply(function_inverse(sK14),sK1(function_inverse(sK14))),relation_dom(sK14))
    | ~ in(apply(function_inverse(sK14),sK2(function_inverse(sK14))),relation_dom(sK14))
    | apply(function_inverse(sK14),sK1(function_inverse(sK14))) = apply(function_inverse(sK14),sK2(function_inverse(sK14))) ),
    inference(superposition,[status(thm)],[c_7714,c_7900]) ).

cnf(c_8242,plain,
    apply(function_inverse(sK14),sK1(function_inverse(sK14))) = apply(function_inverse(sK14),sK2(function_inverse(sK14))),
    inference(global_subsumption_just,[status(thm)],[c_7950,c_113,c_112,c_2512,c_7277,c_7623]) ).

cnf(c_8248,plain,
    apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14)))) = sK2(function_inverse(sK14)),
    inference(demodulation,[status(thm)],[c_7713,c_8242]) ).

cnf(c_8249,plain,
    sK1(function_inverse(sK14)) = sK2(function_inverse(sK14)),
    inference(light_normalisation,[status(thm)],[c_8248,c_7714]) ).

cnf(c_8270,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_8249,c_7623,c_7277,c_2523,c_112,c_113]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 18:20:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.95/1.13  % SZS status Started for theBenchmark.p
% 3.95/1.13  % SZS status Theorem for theBenchmark.p
% 3.95/1.13  
% 3.95/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.95/1.13  
% 3.95/1.13  ------  iProver source info
% 3.95/1.13  
% 3.95/1.13  git: date: 2023-05-31 18:12:56 +0000
% 3.95/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.95/1.13  git: non_committed_changes: false
% 3.95/1.13  git: last_make_outside_of_git: false
% 3.95/1.13  
% 3.95/1.13  ------ Parsing...
% 3.95/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.95/1.13  
% 3.95/1.13  ------ Preprocessing... sup_sim: 0  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 
% 3.95/1.13  
% 3.95/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.95/1.13  
% 3.95/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.95/1.13  ------ Proving...
% 3.95/1.13  ------ Problem Properties 
% 3.95/1.13  
% 3.95/1.13  
% 3.95/1.13  clauses                                 62
% 3.95/1.13  conjectures                             4
% 3.95/1.13  EPR                                     27
% 3.95/1.13  Horn                                    54
% 3.95/1.13  unary                                   21
% 3.95/1.13  binary                                  14
% 3.95/1.13  lits                                    169
% 3.95/1.13  lits eq                                 20
% 3.95/1.13  fd_pure                                 0
% 3.95/1.13  fd_pseudo                               0
% 3.95/1.13  fd_cond                                 1
% 3.95/1.13  fd_pseudo_cond                          6
% 3.95/1.13  AC symbols                              0
% 3.95/1.13  
% 3.95/1.13  ------ Schedule dynamic 5 is on 
% 3.95/1.13  
% 3.95/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.95/1.13  
% 3.95/1.13  
% 3.95/1.13  ------ 
% 3.95/1.13  Current options:
% 3.95/1.13  ------ 
% 3.95/1.13  
% 3.95/1.13  
% 3.95/1.13  
% 3.95/1.13  
% 3.95/1.13  ------ Proving...
% 3.95/1.13  
% 3.95/1.13  
% 3.95/1.13  % SZS status Theorem for theBenchmark.p
% 3.95/1.13  
% 3.95/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.95/1.14  
% 3.95/1.14  
%------------------------------------------------------------------------------