TSTP Solution File: SET721+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET721+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n032.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 03:01:21 EDT 2024

% Result   : Theorem 72.13s 10.71s
% Output   : CNFRefutation 72.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   80 (   7 unt;   0 def)
%            Number of atoms       :  412 (  26 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  526 ( 194   ~; 198   |; 101   &)
%                                         (  10 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-5 aty)
%            Number of variables   :  310 (   0 sgn 202   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [X5,X0,X1] :
      ( maps(X5,X0,X1)
    <=> ( ! [X2,X6,X7] :
            ( ( member(X7,X1)
              & member(X6,X1)
              & member(X2,X0) )
           => ( ( apply(X5,X2,X7)
                & apply(X5,X2,X6) )
             => X6 = X7 ) )
        & ! [X2] :
            ( member(X2,X0)
           => ? [X4] :
                ( apply(X5,X2,X4)
                & member(X4,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).

fof(f14,axiom,
    ! [X9,X5,X0,X1,X10,X2,X11] :
      ( ( member(X11,X10)
        & member(X2,X0) )
     => ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
      <=> ? [X4] :
            ( apply(X9,X4,X11)
            & apply(X5,X2,X4)
            & member(X4,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).

fof(f17,axiom,
    ! [X5,X0,X1] :
      ( injective(X5,X0,X1)
    <=> ! [X12,X13,X4] :
          ( ( member(X4,X1)
            & member(X13,X0)
            & member(X12,X0) )
         => ( ( apply(X5,X13,X4)
              & apply(X5,X12,X4) )
           => X12 = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).

fof(f29,conjecture,
    ! [X5,X9,X0,X1,X10] :
      ( ( injective(compose_function(X9,X5,X0,X1,X10),X0,X10)
        & maps(X9,X1,X10)
        & maps(X5,X0,X1) )
     => injective(X5,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII12) ).

fof(f30,negated_conjecture,
    ~ ! [X5,X9,X0,X1,X10] :
        ( ( injective(compose_function(X9,X5,X0,X1,X10),X0,X10)
          & maps(X9,X1,X10)
          & maps(X5,X0,X1) )
       => injective(X5,X0,X1) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( ! [X3,X4,X5] :
            ( ( member(X5,X2)
              & member(X4,X2)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X5)
                & apply(X0,X3,X4) )
             => X4 = X5 ) )
        & ! [X6] :
            ( member(X6,X1)
           => ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) ) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( member(X6,X4)
        & member(X5,X2) )
     => ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( injective(X0,X1,X2)
    <=> ! [X3,X4,X5] :
          ( ( member(X5,X2)
            & member(X4,X1)
            & member(X3,X1) )
         => ( ( apply(X0,X4,X5)
              & apply(X0,X3,X5) )
           => X3 = X4 ) ) ),
    inference(rectify,[],[f17]) ).

fof(f57,plain,
    ~ ! [X0,X1,X2,X3,X4] :
        ( ( injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
          & maps(X1,X3,X4)
          & maps(X0,X2,X3) )
       => injective(X0,X2,X3) ),
    inference(rectify,[],[f30]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
     => ( ! [X3,X4,X5] :
            ( ( member(X5,X2)
              & member(X4,X2)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X5)
                & apply(X0,X3,X4) )
             => X4 = X5 ) )
        & ! [X6] :
            ( member(X6,X1)
           => ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f40]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4,X5] :
            ( X4 = X5
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X3,X4)
            | ~ member(X5,X2)
            | ~ member(X4,X2)
            | ~ member(X3,X1) )
        & ! [X6] :
            ( ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) )
            | ~ member(X6,X1) ) )
      | ~ maps(X0,X1,X2) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4,X5] :
            ( X4 = X5
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X3,X4)
            | ~ member(X5,X2)
            | ~ member(X4,X2)
            | ~ member(X3,X1) )
        & ! [X6] :
            ( ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) )
            | ~ member(X6,X1) ) )
      | ~ maps(X0,X1,X2) ),
    inference(flattening,[],[f61]) ).

fof(f63,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f64,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(flattening,[],[f63]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( injective(X0,X1,X2)
    <=> ! [X3,X4,X5] :
          ( X3 = X4
          | ~ apply(X0,X4,X5)
          | ~ apply(X0,X3,X5)
          | ~ member(X5,X2)
          | ~ member(X4,X1)
          | ~ member(X3,X1) ) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( injective(X0,X1,X2)
    <=> ! [X3,X4,X5] :
          ( X3 = X4
          | ~ apply(X0,X4,X5)
          | ~ apply(X0,X3,X5)
          | ~ member(X5,X2)
          | ~ member(X4,X1)
          | ~ member(X3,X1) ) ),
    inference(flattening,[],[f65]) ).

fof(f69,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ~ injective(X0,X2,X3)
      & injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
      & maps(X1,X3,X4)
      & maps(X0,X2,X3) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f70,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ~ injective(X0,X2,X3)
      & injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
      & maps(X1,X3,X4)
      & maps(X0,X2,X3) ),
    inference(flattening,[],[f69]) ).

fof(f93,plain,
    ! [X0,X2,X6] :
      ( ? [X7] :
          ( apply(X0,X6,X7)
          & member(X7,X2) )
     => ( apply(X0,X6,sK3(X0,X2,X6))
        & member(sK3(X0,X2,X6),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4,X5] :
            ( X4 = X5
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X3,X4)
            | ~ member(X5,X2)
            | ~ member(X4,X2)
            | ~ member(X3,X1) )
        & ! [X6] :
            ( ( apply(X0,X6,sK3(X0,X2,X6))
              & member(sK3(X0,X2,X6),X2) )
            | ~ member(X6,X1) ) )
      | ~ maps(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f62,f93]) ).

fof(f95,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) ) )
        & ( ? [X7] :
              ( apply(X0,X7,X6)
              & apply(X1,X5,X7)
              & member(X7,X3) )
          | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f96,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) ) )
        & ( ? [X8] :
              ( apply(X0,X8,X6)
              & apply(X1,X5,X8)
              & member(X8,X3) )
          | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(rectify,[],[f95]) ).

fof(f97,plain,
    ! [X0,X1,X3,X5,X6] :
      ( ? [X8] :
          ( apply(X0,X8,X6)
          & apply(X1,X5,X8)
          & member(X8,X3) )
     => ( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
        & apply(X1,X5,sK4(X0,X1,X3,X5,X6))
        & member(sK4(X0,X1,X3,X5,X6),X3) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) ) )
        & ( ( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
            & apply(X1,X5,sK4(X0,X1,X3,X5,X6))
            & member(sK4(X0,X1,X3,X5,X6),X3) )
          | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f96,f97]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( ( injective(X0,X1,X2)
        | ? [X3,X4,X5] :
            ( X3 != X4
            & apply(X0,X4,X5)
            & apply(X0,X3,X5)
            & member(X5,X2)
            & member(X4,X1)
            & member(X3,X1) ) )
      & ( ! [X3,X4,X5] :
            ( X3 = X4
            | ~ apply(X0,X4,X5)
            | ~ apply(X0,X3,X5)
            | ~ member(X5,X2)
            | ~ member(X4,X1)
            | ~ member(X3,X1) )
        | ~ injective(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ( injective(X0,X1,X2)
        | ? [X3,X4,X5] :
            ( X3 != X4
            & apply(X0,X4,X5)
            & apply(X0,X3,X5)
            & member(X5,X2)
            & member(X4,X1)
            & member(X3,X1) ) )
      & ( ! [X6,X7,X8] :
            ( X6 = X7
            | ~ apply(X0,X7,X8)
            | ~ apply(X0,X6,X8)
            | ~ member(X8,X2)
            | ~ member(X7,X1)
            | ~ member(X6,X1) )
        | ~ injective(X0,X1,X2) ) ),
    inference(rectify,[],[f99]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( X3 != X4
          & apply(X0,X4,X5)
          & apply(X0,X3,X5)
          & member(X5,X2)
          & member(X4,X1)
          & member(X3,X1) )
     => ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
        & apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
        & apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
        & member(sK7(X0,X1,X2),X2)
        & member(sK6(X0,X1,X2),X1)
        & member(sK5(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ( injective(X0,X1,X2)
        | ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
          & apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
          & apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
          & member(sK7(X0,X1,X2),X2)
          & member(sK6(X0,X1,X2),X1)
          & member(sK5(X0,X1,X2),X1) ) )
      & ( ! [X6,X7,X8] :
            ( X6 = X7
            | ~ apply(X0,X7,X8)
            | ~ apply(X0,X6,X8)
            | ~ member(X8,X2)
            | ~ member(X7,X1)
            | ~ member(X6,X1) )
        | ~ injective(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f100,f101]) ).

fof(f122,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ~ injective(X0,X2,X3)
        & injective(compose_function(X1,X0,X2,X3,X4),X2,X4)
        & maps(X1,X3,X4)
        & maps(X0,X2,X3) )
   => ( ~ injective(sK12,sK14,sK15)
      & injective(compose_function(sK13,sK12,sK14,sK15,sK16),sK14,sK16)
      & maps(sK13,sK15,sK16)
      & maps(sK12,sK14,sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ( ~ injective(sK12,sK14,sK15)
    & injective(compose_function(sK13,sK12,sK14,sK15,sK16),sK14,sK16)
    & maps(sK13,sK15,sK16)
    & maps(sK12,sK14,sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16])],[f70,f122]) ).

fof(f150,plain,
    ! [X2,X0,X1,X6] :
      ( member(sK3(X0,X2,X6),X2)
      | ~ member(X6,X1)
      | ~ maps(X0,X1,X2) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f151,plain,
    ! [X2,X0,X1,X6] :
      ( apply(X0,X6,sK3(X0,X2,X6))
      | ~ member(X6,X1)
      | ~ maps(X0,X1,X2) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f156,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      | ~ apply(X0,X7,X6)
      | ~ apply(X1,X5,X7)
      | ~ member(X7,X3)
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f157,plain,
    ! [X2,X0,X1,X8,X6,X7] :
      ( X6 = X7
      | ~ apply(X0,X7,X8)
      | ~ apply(X0,X6,X8)
      | ~ member(X8,X2)
      | ~ member(X7,X1)
      | ~ member(X6,X1)
      | ~ injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | member(sK5(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f159,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | member(sK6(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f160,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | member(sK7(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f161,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f162,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f163,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | sK5(X0,X1,X2) != sK6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f181,plain,
    maps(sK13,sK15,sK16),
    inference(cnf_transformation,[],[f123]) ).

fof(f182,plain,
    injective(compose_function(sK13,sK12,sK14,sK15,sK16),sK14,sK16),
    inference(cnf_transformation,[],[f123]) ).

fof(f183,plain,
    ~ injective(sK12,sK14,sK15),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_76,plain,
    ( ~ maps(X0,X1,X2)
    | ~ member(X3,X1)
    | apply(X0,X3,sK3(X0,X2,X3)) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_77,plain,
    ( ~ maps(X0,X1,X2)
    | ~ member(X3,X1)
    | member(sK3(X0,X2,X3),X2) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_78,plain,
    ( ~ apply(X0,X1,X2)
    | ~ apply(X3,X4,X1)
    | ~ member(X1,X7)
    | ~ member(X2,X6)
    | ~ member(X4,X5)
    | apply(compose_function(X0,X3,X5,X7,X6),X4,X2) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_82,plain,
    ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_83,plain,
    ( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_84,plain,
    ( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_85,plain,
    ( member(sK7(X0,X1,X2),X2)
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_86,plain,
    ( member(sK6(X0,X1,X2),X1)
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_87,plain,
    ( member(sK5(X0,X1,X2),X1)
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_88,plain,
    ( ~ apply(X0,X1,X2)
    | ~ apply(X0,X3,X2)
    | ~ injective(X0,X4,X5)
    | ~ member(X1,X4)
    | ~ member(X2,X5)
    | ~ member(X3,X4)
    | X1 = X3 ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_105,negated_conjecture,
    ~ injective(sK12,sK14,sK15),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_106,negated_conjecture,
    injective(compose_function(sK13,sK12,sK14,sK15,sK16),sK14,sK16),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_107,negated_conjecture,
    maps(sK13,sK15,sK16),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_880,plain,
    ( ~ maps(sK13,sK15,sK16)
    | ~ member(X0,sK15)
    | member(sK3(sK13,sK16,X0),sK16) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_881,plain,
    ( ~ maps(sK13,sK15,sK16)
    | ~ member(X0,sK15)
    | apply(sK13,X0,sK3(sK13,sK16,X0)) ),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_965,plain,
    ( sK5(sK12,sK14,sK15) != sK6(sK12,sK14,sK15)
    | injective(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_966,plain,
    ( apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | injective(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_967,plain,
    ( apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | injective(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_968,plain,
    ( member(sK7(sK12,sK14,sK15),sK15)
    | injective(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_85]) ).

cnf(c_969,plain,
    ( member(sK6(sK12,sK14,sK15),sK14)
    | injective(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_86]) ).

cnf(c_970,plain,
    ( member(sK5(sK12,sK14,sK15),sK14)
    | injective(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_87]) ).

cnf(c_1039,plain,
    ( ~ member(sK7(sK12,sK14,sK15),sK15)
    | ~ maps(sK13,sK15,sK16)
    | apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_881]) ).

cnf(c_1040,plain,
    ( ~ member(sK7(sK12,sK14,sK15),sK15)
    | ~ maps(sK13,sK15,sK16)
    | member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16) ),
    inference(instantiation,[status(thm)],[c_880]) ).

cnf(c_3864,plain,
    ( ~ apply(X0,sK5(sK12,sK14,sK15),X1)
    | ~ apply(X0,sK6(sK12,sK14,sK15),X1)
    | ~ member(sK5(sK12,sK14,sK15),X2)
    | ~ member(sK6(sK12,sK14,sK15),X2)
    | ~ injective(X0,X2,X3)
    | ~ member(X1,X3)
    | sK5(sK12,sK14,sK15) = sK6(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_88]) ).

cnf(c_3869,plain,
    ( ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ apply(X0,sK7(sK12,sK14,sK15),X1)
    | ~ member(sK6(sK12,sK14,sK15),X2)
    | ~ member(sK7(sK12,sK14,sK15),X3)
    | ~ member(X1,X4)
    | apply(compose_function(X0,sK12,X2,X3,X4),sK6(sK12,sK14,sK15),X1) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_3874,plain,
    ( ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ apply(X0,sK7(sK12,sK14,sK15),X1)
    | ~ member(sK5(sK12,sK14,sK15),X2)
    | ~ member(sK7(sK12,sK14,sK15),X3)
    | ~ member(X1,X4)
    | apply(compose_function(X0,sK12,X2,X3,X4),sK5(sK12,sK14,sK15),X1) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_6090,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),X0)
    | ~ member(sK6(sK12,sK14,sK15),X1)
    | ~ member(sK7(sK12,sK14,sK15),X2)
    | apply(compose_function(sK13,sK12,X1,X2,X0),sK6(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_3869]) ).

cnf(c_10448,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),X0)
    | ~ member(sK6(sK12,sK14,sK15),X1)
    | ~ member(sK7(sK12,sK14,sK15),sK15)
    | apply(compose_function(sK13,sK12,X1,sK15,X0),sK6(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_6090]) ).

cnf(c_10463,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),X0)
    | ~ member(sK5(sK12,sK14,sK15),X1)
    | ~ member(sK7(sK12,sK14,sK15),X2)
    | apply(compose_function(sK13,sK12,X1,X2,X0),sK5(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_3874]) ).

cnf(c_13261,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16)
    | ~ member(sK6(sK12,sK14,sK15),X0)
    | ~ member(sK7(sK12,sK14,sK15),sK15)
    | apply(compose_function(sK13,sK12,X0,sK15,sK16),sK6(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_10448]) ).

cnf(c_13262,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16)
    | ~ member(sK6(sK12,sK14,sK15),sK14)
    | ~ member(sK7(sK12,sK14,sK15),sK15)
    | apply(compose_function(sK13,sK12,sK14,sK15,sK16),sK6(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_13261]) ).

cnf(c_13315,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16)
    | ~ member(sK5(sK12,sK14,sK15),X0)
    | ~ member(sK7(sK12,sK14,sK15),X1)
    | apply(compose_function(sK13,sK12,X0,X1,sK16),sK5(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_10463]) ).

cnf(c_21476,plain,
    ( ~ apply(compose_function(sK13,sK12,X0,sK15,sK16),sK5(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(compose_function(sK13,sK12,X0,sK15,sK16),sK6(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ injective(compose_function(sK13,sK12,X0,sK15,sK16),X1,X2)
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),X2)
    | ~ member(sK5(sK12,sK14,sK15),X1)
    | ~ member(sK6(sK12,sK14,sK15),X1)
    | sK5(sK12,sK14,sK15) = sK6(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_3864]) ).

cnf(c_21626,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16)
    | ~ member(sK5(sK12,sK14,sK15),X0)
    | ~ member(sK7(sK12,sK14,sK15),sK15)
    | apply(compose_function(sK13,sK12,X0,sK15,sK16),sK5(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_13315]) ).

cnf(c_21627,plain,
    ( ~ apply(sK13,sK7(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16)
    | ~ member(sK5(sK12,sK14,sK15),sK14)
    | ~ member(sK7(sK12,sK14,sK15),sK15)
    | apply(compose_function(sK13,sK12,sK14,sK15,sK16),sK5(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15))) ),
    inference(instantiation,[status(thm)],[c_21626]) ).

cnf(c_36785,plain,
    ( ~ apply(compose_function(sK13,sK12,sK14,sK15,sK16),sK5(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ apply(compose_function(sK13,sK12,sK14,sK15,sK16),sK6(sK12,sK14,sK15),sK3(sK13,sK16,sK7(sK12,sK14,sK15)))
    | ~ member(sK3(sK13,sK16,sK7(sK12,sK14,sK15)),sK16)
    | ~ injective(compose_function(sK13,sK12,sK14,sK15,sK16),sK14,sK16)
    | ~ member(sK5(sK12,sK14,sK15),sK14)
    | ~ member(sK6(sK12,sK14,sK15),sK14)
    | sK5(sK12,sK14,sK15) = sK6(sK12,sK14,sK15) ),
    inference(instantiation,[status(thm)],[c_21476]) ).

cnf(c_36786,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_36785,c_21627,c_13262,c_1039,c_1040,c_970,c_969,c_968,c_967,c_966,c_965,c_106,c_105,c_107]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET721+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n032.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 20:26:23 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.15/0.41  Running first-order theorem proving
% 0.15/0.41  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
% 72.13/10.71  % SZS status Started for theBenchmark.p
% 72.13/10.71  % SZS status Theorem for theBenchmark.p
% 72.13/10.71  
% 72.13/10.71  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 72.13/10.71  
% 72.13/10.71  ------  iProver source info
% 72.13/10.71  
% 72.13/10.71  git: date: 2024-05-02 19:28:25 +0000
% 72.13/10.71  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 72.13/10.71  git: non_committed_changes: false
% 72.13/10.71  
% 72.13/10.71  ------ Parsing...
% 72.13/10.71  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 72.13/10.71  
% 72.13/10.71  ------ Preprocessing...
% 72.13/10.71  
% 72.13/10.71  ------ Preprocessing...
% 72.13/10.71  
% 72.13/10.71  ------ Preprocessing...
% 72.13/10.71  ------ Proving...
% 72.13/10.71  ------ Problem Properties 
% 72.13/10.71  
% 72.13/10.71  
% 72.13/10.71  clauses                                 60
% 72.13/10.71  conjectures                             4
% 72.13/10.71  EPR                                     7
% 72.13/10.71  Horn                                    50
% 72.13/10.71  unary                                   8
% 72.13/10.71  binary                                  31
% 72.13/10.71  lits                                    151
% 72.13/10.71  lits eq                                 6
% 72.13/10.71  fd_pure                                 0
% 72.13/10.71  fd_pseudo                               0
% 72.13/10.71  fd_cond                                 0
% 72.13/10.71  fd_pseudo_cond                          4
% 72.13/10.71  AC symbols                              0
% 72.13/10.71  
% 72.13/10.71  ------ Input Options Time Limit: Unbounded
% 72.13/10.71  
% 72.13/10.71  
% 72.13/10.71  ------ 
% 72.13/10.71  Current options:
% 72.13/10.71  ------ 
% 72.13/10.71  
% 72.13/10.71  
% 72.13/10.71  
% 72.13/10.71  
% 72.13/10.71  ------ Proving...
% 72.13/10.71  
% 72.13/10.71  
% 72.13/10.71  % SZS status Theorem for theBenchmark.p
% 72.13/10.71  
% 72.13/10.71  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.13/10.71  
% 72.13/10.71  
%------------------------------------------------------------------------------