TSTP Solution File: SEU210+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 17:04:43 EDT 2023

% Result   : Theorem 0.47s 1.17s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  118 (  25 unt;   0 def)
%            Number of atoms       :  365 (  47 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  430 ( 183   ~; 161   |;  61   &)
%                                         (   8 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :  249 (  15 sgn; 144   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f5,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(f6,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(f15,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f21,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f23,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

fof(f26,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f31,axiom,
    ! [X0,X1,X2] :
      ( relation(X2)
     => ( in(X0,relation_inverse_image(X2,X1))
      <=> ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X0,X3),X2)
            & in(X3,relation_rng(X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).

fof(f32,conjecture,
    ! [X0,X1] :
      ( relation(X1)
     => ~ ( empty_set = relation_inverse_image(X1,X0)
          & subset(X0,relation_rng(X1))
          & empty_set != X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).

fof(f33,negated_conjecture,
    ~ ! [X0,X1] :
        ( relation(X1)
       => ~ ( empty_set = relation_inverse_image(X1,X0)
            & subset(X0,relation_rng(X1))
            & empty_set != X0 ) ),
    inference(negated_conjecture,[],[f32]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f39,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f40,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f41,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f44,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f46,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f49,plain,
    ! [X0] :
      ( ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( in(X0,relation_inverse_image(X2,X1))
      <=> ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X0,X3),X2)
            & in(X3,relation_rng(X2)) ) )
      | ~ relation(X2) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f52,plain,
    ? [X0,X1] :
      ( empty_set = relation_inverse_image(X1,X0)
      & subset(X0,relation_rng(X1))
      & empty_set != X0
      & relation(X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f53,plain,
    ? [X0,X1] :
      ( empty_set = relation_inverse_image(X1,X0)
      & subset(X0,relation_rng(X1))
      & empty_set != X0
      & relation(X1) ),
    inference(flattening,[],[f52]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f55]) ).

fof(f60,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f63,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,[],[f45]) ).

fof(f64,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,[],[f63]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK0(X0,X1),X1)
        & in(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK0(X0,X1),X1)
          & in(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f64,f65]) ).

fof(f67,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,[],[f46]) ).

fof(f68,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,[],[f67]) ).

fof(f69,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,sK1(X0,X1)),X0)
          | ~ in(sK1(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK1(X0,X1)),X0)
          | in(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK1(X0,X1)),X0)
     => in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK3(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK1(X0,X1)),X0)
                | ~ in(sK1(X0,X1),X1) )
              & ( in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0)
                | in(sK1(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK3(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f68,f71,f70,f69]) ).

fof(f73,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK4(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0] : element(sK4(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f73]) ).

fof(f79,plain,
    ( ? [X0] : empty(X0)
   => empty(sK7) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    empty(sK7),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f26,f79]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X0,relation_inverse_image(X2,X1))
          | ! [X3] :
              ( ~ in(X3,X1)
              | ~ in(ordered_pair(X0,X3),X2)
              | ~ in(X3,relation_rng(X2)) ) )
        & ( ? [X3] :
              ( in(X3,X1)
              & in(ordered_pair(X0,X3),X2)
              & in(X3,relation_rng(X2)) )
          | ~ in(X0,relation_inverse_image(X2,X1)) ) )
      | ~ relation(X2) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X0,relation_inverse_image(X2,X1))
          | ! [X3] :
              ( ~ in(X3,X1)
              | ~ in(ordered_pair(X0,X3),X2)
              | ~ in(X3,relation_rng(X2)) ) )
        & ( ? [X4] :
              ( in(X4,X1)
              & in(ordered_pair(X0,X4),X2)
              & in(X4,relation_rng(X2)) )
          | ~ in(X0,relation_inverse_image(X2,X1)) ) )
      | ~ relation(X2) ),
    inference(rectify,[],[f87]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( in(X4,X1)
          & in(ordered_pair(X0,X4),X2)
          & in(X4,relation_rng(X2)) )
     => ( in(sK11(X0,X1,X2),X1)
        & in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
        & in(sK11(X0,X1,X2),relation_rng(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X0,relation_inverse_image(X2,X1))
          | ! [X3] :
              ( ~ in(X3,X1)
              | ~ in(ordered_pair(X0,X3),X2)
              | ~ in(X3,relation_rng(X2)) ) )
        & ( ( in(sK11(X0,X1,X2),X1)
            & in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
            & in(sK11(X0,X1,X2),relation_rng(X2)) )
          | ~ in(X0,relation_inverse_image(X2,X1)) ) )
      | ~ relation(X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f88,f89]) ).

fof(f91,plain,
    ( ? [X0,X1] :
        ( empty_set = relation_inverse_image(X1,X0)
        & subset(X0,relation_rng(X1))
        & empty_set != X0
        & relation(X1) )
   => ( empty_set = relation_inverse_image(sK13,sK12)
      & subset(sK12,relation_rng(sK13))
      & empty_set != sK12
      & relation(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ( empty_set = relation_inverse_image(sK13,sK12)
    & subset(sK12,relation_rng(sK13))
    & empty_set != sK12
    & relation(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f53,f91]) ).

fof(f95,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f97,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f100,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK3(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f101,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X6,X5),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f104,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f105,plain,
    ! [X0] : element(sK4(X0),X0),
    inference(cnf_transformation,[],[f74]) ).

fof(f111,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f21]) ).

fof(f114,plain,
    ! [X0] :
      ( empty(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f120,plain,
    empty(sK7),
    inference(cnf_transformation,[],[f80]) ).

fof(f128,plain,
    ! [X2,X0,X1] :
      ( in(ordered_pair(X0,sK11(X0,X1,X2)),X2)
      | ~ in(X0,relation_inverse_image(X2,X1))
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f130,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,relation_inverse_image(X2,X1))
      | ~ in(X3,X1)
      | ~ in(ordered_pair(X0,X3),X2)
      | ~ in(X3,relation_rng(X2))
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f131,plain,
    relation(sK13),
    inference(cnf_transformation,[],[f92]) ).

fof(f132,plain,
    empty_set != sK12,
    inference(cnf_transformation,[],[f92]) ).

fof(f133,plain,
    subset(sK12,relation_rng(sK13)),
    inference(cnf_transformation,[],[f92]) ).

fof(f134,plain,
    empty_set = relation_inverse_image(sK13,sK12),
    inference(cnf_transformation,[],[f92]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f141,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f146,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,[],[f101,f104]) ).

fof(f147,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f100,f104]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,relation_inverse_image(X2,X1))
      | ~ in(X3,X1)
      | ~ in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),X2)
      | ~ in(X3,relation_rng(X2))
      | ~ relation(X2) ),
    inference(definition_unfolding,[],[f130,f104]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( in(unordered_pair(unordered_pair(X0,sK11(X0,X1,X2)),singleton(X0)),X2)
      | ~ in(X0,relation_inverse_image(X2,X1))
      | ~ relation(X2) ),
    inference(definition_unfolding,[],[f128,f104]) ).

fof(f151,plain,
    ! [X0,X6,X5] :
      ( in(X5,relation_rng(X0))
      | ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f146]) ).

fof(f152,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f147]) ).

cnf(c_50,plain,
    ( ~ empty(X0)
    | relation(X0) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_54,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_57,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ relation(X2)
    | in(X1,relation_rng(X2)) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_58,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(sK3(X1,X0),X0),singleton(sK3(X1,X0))),X1) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_59,plain,
    element(sK4(X0),X0),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_66,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_69,plain,
    ( ~ empty(X0)
    | empty(relation_rng(X0)) ),
    inference(cnf_transformation,[],[f114]) ).

cnf(c_74,plain,
    empty(sK7),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_81,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ in(X1,relation_rng(X2))
    | ~ in(X1,X3)
    | ~ relation(X2)
    | in(X0,relation_inverse_image(X2,X3)) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_83,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ relation(X1)
    | in(unordered_pair(unordered_pair(X0,sK11(X0,X2,X1)),singleton(X0)),X1) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_85,negated_conjecture,
    relation_inverse_image(sK13,sK12) = empty_set,
    inference(cnf_transformation,[],[f134]) ).

cnf(c_86,negated_conjecture,
    subset(sK12,relation_rng(sK13)),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_87,negated_conjecture,
    empty_set != sK12,
    inference(cnf_transformation,[],[f132]) ).

cnf(c_88,negated_conjecture,
    relation(sK13),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_90,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_95,plain,
    ( ~ empty(X0)
    | X0 = empty_set ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_96,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_97,plain,
    ( ~ empty(X0)
    | ~ empty(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_121,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
    | ~ in(X1,X3)
    | ~ relation(X2)
    | in(X0,relation_inverse_image(X2,X3)) ),
    inference(global_subsumption_just,[status(thm)],[c_81,c_57,c_81]) ).

cnf(c_129,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(prop_impl_just,[status(thm)],[c_96]) ).

cnf(c_137,plain,
    ( ~ empty(X0)
    | relation(X0) ),
    inference(prop_impl_just,[status(thm)],[c_50]) ).

cnf(c_702,plain,
    ( relation_rng(sK13) != X1
    | X0 != sK12
    | ~ in(X2,X0)
    | in(X2,X1) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_86]) ).

cnf(c_703,plain,
    ( ~ in(X0,sK12)
    | in(X0,relation_rng(sK13)) ),
    inference(unflattening,[status(thm)],[c_702]) ).

cnf(c_777,plain,
    ( X0 != X1
    | ~ in(X2,relation_inverse_image(X0,X3))
    | ~ empty(X1)
    | in(unordered_pair(unordered_pair(X2,sK11(X2,X3,X0)),singleton(X2)),X0) ),
    inference(resolution_lifted,[status(thm)],[c_83,c_137]) ).

cnf(c_778,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ empty(X1)
    | in(unordered_pair(unordered_pair(X0,sK11(X0,X2,X1)),singleton(X0)),X1) ),
    inference(unflattening,[status(thm)],[c_777]) ).

cnf(c_786,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ empty(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_778,c_129]) ).

cnf(c_792,plain,
    ( X0 != X1
    | ~ in(X2,relation_rng(X0))
    | ~ empty(X1)
    | in(unordered_pair(unordered_pair(sK3(X0,X2),X2),singleton(sK3(X0,X2))),X0) ),
    inference(resolution_lifted,[status(thm)],[c_58,c_137]) ).

cnf(c_793,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ empty(X1)
    | in(unordered_pair(unordered_pair(sK3(X1,X0),X0),singleton(sK3(X1,X0))),X1) ),
    inference(unflattening,[status(thm)],[c_792]) ).

cnf(c_801,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ empty(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_793,c_129]) ).

cnf(c_3270,plain,
    ( ~ empty(empty_set)
    | ~ empty(sK12)
    | empty_set = sK12 ),
    inference(instantiation,[status(thm)],[c_97]) ).

cnf(c_3367,plain,
    ( ~ empty(X0)
    | relation_rng(X0) = empty_set ),
    inference(superposition,[status(thm)],[c_69,c_95]) ).

cnf(c_5173,plain,
    ( in(sK4(X0),X0)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_59,c_90]) ).

cnf(c_5231,plain,
    relation_rng(sK7) = empty_set,
    inference(superposition,[status(thm)],[c_74,c_3367]) ).

cnf(c_5348,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ relation(X1)
    | ~ empty(X1) ),
    inference(superposition,[status(thm)],[c_58,c_96]) ).

cnf(c_5355,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ relation(X1)
    | ~ empty(X1) ),
    inference(superposition,[status(thm)],[c_83,c_96]) ).

cnf(c_5358,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ in(X0,X2)
    | ~ relation(X1)
    | in(sK3(X1,X0),relation_inverse_image(X1,X2)) ),
    inference(superposition,[status(thm)],[c_58,c_121]) ).

cnf(c_5371,plain,
    ( ~ in(X0,relation_rng(X1))
    | ~ empty(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_5348,c_801]) ).

cnf(c_5382,plain,
    ( ~ in(X0,empty_set)
    | ~ empty(sK7) ),
    inference(superposition,[status(thm)],[c_5231,c_5371]) ).

cnf(c_5391,plain,
    ( ~ in(X0,relation_inverse_image(X1,X2))
    | ~ empty(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_5355,c_786]) ).

cnf(c_5398,plain,
    ( ~ in(X0,empty_set)
    | ~ empty(sK13) ),
    inference(superposition,[status(thm)],[c_85,c_5391]) ).

cnf(c_5417,plain,
    ~ in(X0,empty_set),
    inference(global_subsumption_just,[status(thm)],[c_5398,c_74,c_5382]) ).

cnf(c_5996,plain,
    ( ~ in(X0,relation_rng(sK13))
    | ~ in(X0,sK12)
    | ~ relation(sK13)
    | in(sK3(sK13,X0),empty_set) ),
    inference(superposition,[status(thm)],[c_85,c_5358]) ).

cnf(c_6107,plain,
    ( ~ in(X0,sK12)
    | in(sK3(sK13,X0),empty_set) ),
    inference(global_subsumption_just,[status(thm)],[c_5996,c_88,c_703,c_5996]) ).

cnf(c_6114,plain,
    ~ in(X0,sK12),
    inference(superposition,[status(thm)],[c_6107,c_5417]) ).

cnf(c_6130,plain,
    empty(sK12),
    inference(superposition,[status(thm)],[c_5173,c_6114]) ).

cnf(c_6131,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_6130,c_3270,c_87,c_66]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n031.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 15:45:20 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.47/1.17  % SZS status Started for theBenchmark.p
% 0.47/1.17  % SZS status Theorem for theBenchmark.p
% 0.47/1.17  
% 0.47/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.47/1.17  
% 0.47/1.17  ------  iProver source info
% 0.47/1.17  
% 0.47/1.17  git: date: 2023-05-31 18:12:56 +0000
% 0.47/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.47/1.17  git: non_committed_changes: false
% 0.47/1.17  git: last_make_outside_of_git: false
% 0.47/1.17  
% 0.47/1.17  ------ Parsing...
% 0.47/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.47/1.17  
% 0.47/1.17  ------ 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 
% 0.47/1.17  
% 0.47/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.47/1.17  
% 0.47/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.47/1.17  ------ Proving...
% 0.47/1.17  ------ Problem Properties 
% 0.47/1.17  
% 0.47/1.17  
% 0.47/1.17  clauses                                 47
% 0.47/1.17  conjectures                             4
% 0.47/1.17  EPR                                     21
% 0.47/1.17  Horn                                    43
% 0.47/1.17  unary                                   20
% 0.47/1.17  binary                                  13
% 0.47/1.17  lits                                    91
% 0.47/1.17  lits eq                                 7
% 0.47/1.17  fd_pure                                 0
% 0.47/1.17  fd_pseudo                               0
% 0.47/1.17  fd_cond                                 1
% 0.47/1.17  fd_pseudo_cond                          3
% 0.47/1.17  AC symbols                              0
% 0.47/1.17  
% 0.47/1.17  ------ Input Options Time Limit: Unbounded
% 0.47/1.17  
% 0.47/1.17  
% 0.47/1.17  ------ 
% 0.47/1.17  Current options:
% 0.47/1.17  ------ 
% 0.47/1.17  
% 0.47/1.17  
% 0.47/1.17  
% 0.47/1.17  
% 0.47/1.17  ------ Proving...
% 0.47/1.17  
% 0.47/1.17  
% 0.47/1.17  % SZS status Theorem for theBenchmark.p
% 0.47/1.17  
% 0.47/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.47/1.17  
% 0.90/1.18  
%------------------------------------------------------------------------------