TSTP Solution File: SEU028+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n011.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 17:03:27 EDT 2023

% Result   : Theorem 3.63s 1.13s
% Output   : CNFRefutation 3.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  105 (  10 unt;   0 def)
%            Number of atoms       :  432 ( 137 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  573 ( 246   ~; 239   |;  66   &)
%                                         (   3 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-2 aty)
%            Number of variables   :  107 (   0 sgn;  76   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(function_inverse(X0))
        & relation(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(relation_composition(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1)
        & function(X0)
        & relation(X0) )
     => ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

fof(f34,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/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( in(X0,relation_dom(X1))
          & one_to_one(X1) )
       => ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
          & apply(function_inverse(X1),apply(X1,X0)) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).

fof(f38,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/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).

fof(f39,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
          & relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).

fof(f40,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
          & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).

fof(f42,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
          & relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).

fof(f43,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( one_to_one(X0)
         => ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
            & relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
    inference(negated_conjecture,[],[f42]) ).

fof(f56,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f57,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(flattening,[],[f58]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f62]) ).

fof(f76,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,[],[f34]) ).

fof(f77,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,[],[f76]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
        & apply(function_inverse(X1),apply(X1,X0)) = X0 )
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
        & apply(function_inverse(X1),apply(X1,X0)) = X0 )
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f81]) ).

fof(f83,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,[],[f38]) ).

fof(f84,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,[],[f83]) ).

fof(f85,plain,
    ! [X0] :
      ( ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
        & relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f86,plain,
    ! [X0] :
      ( ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
        & relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f85]) ).

fof(f87,plain,
    ! [X0] :
      ( ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
        & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f88,plain,
    ! [X0] :
      ( ( relation_rng(X0) = relation_rng(relation_composition(function_inverse(X0),X0))
        & relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f87]) ).

fof(f90,plain,
    ? [X0] :
      ( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
        | relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f91,plain,
    ? [X0] :
      ( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
        | relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f90]) ).

fof(f117,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,[],[f77]) ).

fof(f118,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,[],[f117]) ).

fof(f119,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,[],[f118]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( apply(X1,X2) != X2
          & in(X2,X0) )
     => ( sK11(X0,X1) != apply(X1,sK11(X0,X1))
        & in(sK11(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ( ( identity_relation(X0) = X1
          | ( sK11(X0,X1) != apply(X1,sK11(X0,X1))
            & in(sK11(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,[sK11])],[f119,f120]) ).

fof(f122,plain,
    ( ? [X0] :
        ( ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
          | relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) )
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
        | relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) )
      & one_to_one(sK12)
      & function(sK12)
      & relation(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ( ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
      | relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) )
    & one_to_one(sK12)
    & function(sK12)
    & relation(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f91,f122]) ).

fof(f130,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f131,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( function(relation_composition(X0,X1))
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( identity_relation(X0) = X1
      | in(sK11(X0,X1),X0)
      | relation_dom(X1) != X0
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( identity_relation(X0) = X1
      | sK11(X0,X1) != apply(X1,sK11(X0,X1))
      | relation_dom(X1) != X0
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
      | ~ in(X0,relation_dom(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f187,plain,
    ! [X0] :
      ( relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0)))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f189,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f192,plain,
    relation(sK12),
    inference(cnf_transformation,[],[f123]) ).

fof(f193,plain,
    function(sK12),
    inference(cnf_transformation,[],[f123]) ).

fof(f194,plain,
    one_to_one(sK12),
    inference(cnf_transformation,[],[f123]) ).

fof(f195,plain,
    ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
    | relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f199,plain,
    ! [X1] :
      ( identity_relation(relation_dom(X1)) = X1
      | sK11(relation_dom(X1),X1) != apply(X1,sK11(relation_dom(X1),X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f180]) ).

fof(f200,plain,
    ! [X1] :
      ( identity_relation(relation_dom(X1)) = X1
      | in(sK11(relation_dom(X1),X1),relation_dom(X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(equality_resolution,[],[f179]) ).

cnf(c_53,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | function(function_inverse(X0)) ),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_54,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | relation(function_inverse(X0)) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_55,plain,
    ( ~ relation(X0)
    | ~ relation(X1)
    | relation(relation_composition(X1,X0)) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_62,plain,
    ( ~ function(X0)
    | ~ function(X1)
    | ~ relation(X0)
    | ~ relation(X1)
    | function(relation_composition(X1,X0)) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_100,plain,
    ( apply(X0,sK11(relation_dom(X0),X0)) != sK11(relation_dom(X0),X0)
    | ~ function(X0)
    | ~ relation(X0)
    | identity_relation(relation_dom(X0)) = X0 ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_101,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | identity_relation(relation_dom(X0)) = X0
    | in(sK11(relation_dom(X0),X0),relation_dom(X0)) ),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_106,plain,
    ( ~ in(X0,relation_dom(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1)
    | apply(relation_composition(X1,function_inverse(X1)),X0) = X0 ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_108,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ one_to_one(X1)
    | apply(relation_composition(function_inverse(X1),X1),X0) = X0 ),
    inference(cnf_transformation,[],[f186]) ).

cnf(c_111,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ),
    inference(cnf_transformation,[],[f187]) ).

cnf(c_113,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | ~ one_to_one(X0)
    | relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_115,negated_conjecture,
    ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
    | relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) ),
    inference(cnf_transformation,[],[f195]) ).

cnf(c_116,negated_conjecture,
    one_to_one(sK12),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_117,negated_conjecture,
    function(sK12),
    inference(cnf_transformation,[],[f193]) ).

cnf(c_118,negated_conjecture,
    relation(sK12),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_143,plain,
    ( ~ function(sK12)
    | ~ relation(sK12)
    | relation(function_inverse(sK12)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_144,plain,
    ( ~ function(sK12)
    | ~ relation(sK12)
    | function(function_inverse(sK12)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_151,plain,
    ( ~ function(sK12)
    | ~ relation(sK12)
    | ~ one_to_one(sK12)
    | relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_153,plain,
    ( ~ function(sK12)
    | ~ relation(sK12)
    | ~ one_to_one(sK12)
    | relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12) ),
    inference(instantiation,[status(thm)],[c_111]) ).

cnf(c_907,plain,
    ( X0 != sK12
    | ~ in(X1,relation_rng(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | apply(relation_composition(function_inverse(X0),X0),X1) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_108,c_116]) ).

cnf(c_908,plain,
    ( ~ in(X0,relation_rng(sK12))
    | ~ function(sK12)
    | ~ relation(sK12)
    | apply(relation_composition(function_inverse(sK12),sK12),X0) = X0 ),
    inference(unflattening,[status(thm)],[c_907]) ).

cnf(c_910,plain,
    ( ~ in(X0,relation_rng(sK12))
    | apply(relation_composition(function_inverse(sK12),sK12),X0) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_908,c_118,c_117,c_908]) ).

cnf(c_931,plain,
    ( X0 != sK12
    | ~ in(X1,relation_dom(X0))
    | ~ function(X0)
    | ~ relation(X0)
    | apply(relation_composition(X0,function_inverse(X0)),X1) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_106,c_116]) ).

cnf(c_932,plain,
    ( ~ in(X0,relation_dom(sK12))
    | ~ function(sK12)
    | ~ relation(sK12)
    | apply(relation_composition(sK12,function_inverse(sK12)),X0) = X0 ),
    inference(unflattening,[status(thm)],[c_931]) ).

cnf(c_934,plain,
    ( ~ in(X0,relation_dom(sK12))
    | apply(relation_composition(sK12,function_inverse(sK12)),X0) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_932,c_118,c_117,c_932]) ).

cnf(c_971,plain,
    ( X0 != sK12
    | ~ function(X0)
    | ~ relation(X0)
    | relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ),
    inference(resolution_lifted,[status(thm)],[c_113,c_116]) ).

cnf(c_972,plain,
    ( ~ function(sK12)
    | ~ relation(sK12)
    | relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) ),
    inference(unflattening,[status(thm)],[c_971]) ).

cnf(c_973,plain,
    relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12),
    inference(global_subsumption_just,[status(thm)],[c_972,c_118,c_117,c_116,c_151]) ).

cnf(c_985,plain,
    ( X0 != sK12
    | ~ function(X0)
    | ~ relation(X0)
    | relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ),
    inference(resolution_lifted,[status(thm)],[c_111,c_116]) ).

cnf(c_986,plain,
    ( ~ function(sK12)
    | ~ relation(sK12)
    | relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12) ),
    inference(unflattening,[status(thm)],[c_985]) ).

cnf(c_987,plain,
    relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12),
    inference(global_subsumption_just,[status(thm)],[c_986,c_118,c_117,c_116,c_153]) ).

cnf(c_2802,plain,
    ( apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) != sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))
    | ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(relation_composition(function_inverse(sK12),sK12))
    | identity_relation(relation_dom(relation_composition(function_inverse(sK12),sK12))) = relation_composition(function_inverse(sK12),sK12) ),
    inference(superposition,[status(thm)],[c_973,c_100]) ).

cnf(c_2803,plain,
    ( apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) != sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
    | ~ function(relation_composition(sK12,function_inverse(sK12)))
    | ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | identity_relation(relation_dom(relation_composition(sK12,function_inverse(sK12)))) = relation_composition(sK12,function_inverse(sK12)) ),
    inference(superposition,[status(thm)],[c_987,c_100]) ).

cnf(c_2819,plain,
    ( apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) != sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
    | ~ function(relation_composition(sK12,function_inverse(sK12)))
    | ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(light_normalisation,[status(thm)],[c_2803,c_987]) ).

cnf(c_2824,plain,
    ( apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) != sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))
    | ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(relation_composition(function_inverse(sK12),sK12))
    | relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12)) ),
    inference(light_normalisation,[status(thm)],[c_2802,c_973]) ).

cnf(c_7946,plain,
    ( ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(relation_composition(function_inverse(sK12),sK12))
    | identity_relation(relation_dom(relation_composition(function_inverse(sK12),sK12))) = relation_composition(function_inverse(sK12),sK12)
    | in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12)) ),
    inference(superposition,[status(thm)],[c_973,c_101]) ).

cnf(c_7947,plain,
    ( ~ function(relation_composition(sK12,function_inverse(sK12)))
    | ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | identity_relation(relation_dom(relation_composition(sK12,function_inverse(sK12)))) = relation_composition(sK12,function_inverse(sK12))
    | in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12)) ),
    inference(superposition,[status(thm)],[c_987,c_101]) ).

cnf(c_7993,plain,
    ( ~ function(relation_composition(sK12,function_inverse(sK12)))
    | ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
    | in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12)) ),
    inference(light_normalisation,[status(thm)],[c_7947,c_987]) ).

cnf(c_7998,plain,
    ( ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(relation_composition(function_inverse(sK12),sK12))
    | relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12))
    | in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12)) ),
    inference(light_normalisation,[status(thm)],[c_7946,c_973]) ).

cnf(c_10977,plain,
    ( ~ function(relation_composition(sK12,function_inverse(sK12)))
    | ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) = sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(superposition,[status(thm)],[c_7993,c_934]) ).

cnf(c_11011,plain,
    ( ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(relation_composition(function_inverse(sK12),sK12))
    | apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) = sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))
    | relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12)) ),
    inference(superposition,[status(thm)],[c_7998,c_910]) ).

cnf(c_11057,plain,
    ( ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | ~ function(relation_composition(sK12,function_inverse(sK12)))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(global_subsumption_just,[status(thm)],[c_10977,c_2819,c_10977]) ).

cnf(c_11058,plain,
    ( ~ function(relation_composition(sK12,function_inverse(sK12)))
    | ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(renaming,[status(thm)],[c_11057]) ).

cnf(c_11066,plain,
    ( ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | ~ function(function_inverse(sK12))
    | ~ relation(function_inverse(sK12))
    | ~ function(sK12)
    | ~ relation(sK12)
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(superposition,[status(thm)],[c_62,c_11058]) ).

cnf(c_11068,plain,
    ( ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | ~ function(function_inverse(sK12))
    | ~ relation(function_inverse(sK12))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11066,c_118,c_117]) ).

cnf(c_11073,plain,
    ( ~ relation(relation_composition(sK12,function_inverse(sK12)))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(global_subsumption_just,[status(thm)],[c_11068,c_118,c_117,c_143,c_144,c_11068]) ).

cnf(c_11080,plain,
    ( ~ relation(function_inverse(sK12))
    | ~ relation(sK12)
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(superposition,[status(thm)],[c_55,c_11073]) ).

cnf(c_11082,plain,
    ( ~ relation(function_inverse(sK12))
    | relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11080,c_118]) ).

cnf(c_11251,plain,
    ( ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(relation_composition(function_inverse(sK12),sK12)) ),
    inference(global_subsumption_just,[status(thm)],[c_11011,c_118,c_117,c_143,c_115,c_2824,c_11011,c_11082]) ).

cnf(c_11258,plain,
    ( ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(function_inverse(sK12))
    | ~ relation(sK12) ),
    inference(superposition,[status(thm)],[c_55,c_11251]) ).

cnf(c_11260,plain,
    ( ~ function(relation_composition(function_inverse(sK12),sK12))
    | ~ relation(function_inverse(sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11258,c_118]) ).

cnf(c_11263,plain,
    ~ function(relation_composition(function_inverse(sK12),sK12)),
    inference(global_subsumption_just,[status(thm)],[c_11260,c_118,c_117,c_143,c_11260]) ).

cnf(c_11266,plain,
    ( ~ function(function_inverse(sK12))
    | ~ relation(function_inverse(sK12))
    | ~ function(sK12)
    | ~ relation(sK12) ),
    inference(superposition,[status(thm)],[c_62,c_11263]) ).

cnf(c_11268,plain,
    ( ~ function(function_inverse(sK12))
    | ~ relation(function_inverse(sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11266,c_118,c_117]) ).

cnf(c_11271,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_11268,c_144,c_143,c_117,c_118]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Aug 23 23:28:07 EDT 2023
% 0.12/0.34  % 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
% 3.63/1.13  % SZS status Started for theBenchmark.p
% 3.63/1.13  % SZS status Theorem for theBenchmark.p
% 3.63/1.13  
% 3.63/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.63/1.13  
% 3.63/1.13  ------  iProver source info
% 3.63/1.13  
% 3.63/1.13  git: date: 2023-05-31 18:12:56 +0000
% 3.63/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.63/1.13  git: non_committed_changes: false
% 3.63/1.13  git: last_make_outside_of_git: false
% 3.63/1.13  
% 3.63/1.13  ------ Parsing...
% 3.63/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.63/1.13  
% 3.63/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e 
% 3.63/1.13  
% 3.63/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.63/1.13  
% 3.63/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.63/1.13  ------ Proving...
% 3.63/1.13  ------ Problem Properties 
% 3.63/1.13  
% 3.63/1.13  
% 3.63/1.13  clauses                                 80
% 3.63/1.13  conjectures                             3
% 3.63/1.13  EPR                                     26
% 3.63/1.13  Horn                                    77
% 3.63/1.13  unary                                   34
% 3.63/1.13  binary                                  26
% 3.63/1.13  lits                                    150
% 3.63/1.13  lits eq                                 33
% 3.63/1.13  fd_pure                                 0
% 3.63/1.13  fd_pseudo                               0
% 3.63/1.13  fd_cond                                 1
% 3.63/1.13  fd_pseudo_cond                          1
% 3.63/1.13  AC symbols                              0
% 3.63/1.13  
% 3.63/1.13  ------ Schedule dynamic 5 is on 
% 3.63/1.13  
% 3.63/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.63/1.13  
% 3.63/1.13  
% 3.63/1.13  ------ 
% 3.63/1.13  Current options:
% 3.63/1.13  ------ 
% 3.63/1.13  
% 3.63/1.13  
% 3.63/1.13  
% 3.63/1.13  
% 3.63/1.13  ------ Proving...
% 3.63/1.13  
% 3.63/1.13  
% 3.63/1.13  % SZS status Theorem for theBenchmark.p
% 3.63/1.13  
% 3.63/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.63/1.13  
% 3.63/1.14  
%------------------------------------------------------------------------------