TSTP Solution File: SET669+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 03:01:11 EDT 2024

% Result   : Theorem 0.45s 1.13s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ( subset(X1,X0)
              & subset(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X0,X1))
                 => ( subset(identity_relation_of(X2),X3)
                   => ( subset(X2,range(X0,X1,X3))
                      & subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f7,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( subset(X0,X1)
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).

fof(f9,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( X0 = X1
          <=> ( subset(X1,X0)
              & subset(X0,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).

fof(f16,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).

fof(f20,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).

fof(f21,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).

fof(f22,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).

fof(f31,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).

fof(f32,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p32) ).

fof(f33,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ( subset(identity_relation_of(X1),X2)
               => ( range(X0,X1,X2) = X1
                  & subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_32) ).

fof(f34,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ( subset(identity_relation_of(X1),X2)
                 => ( range(X0,X1,X2) = X1
                    & subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
    inference(negated_conjecture,[],[f33]) ).

fof(f36,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ subset(X1,X0)
          | ~ subset(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f37,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ subset(X1,X0)
          | ~ subset(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f36]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( subset(X2,range(X0,X1,X3))
                    & subset(X2,domain(X0,X1,X3)) )
                  | ~ subset(identity_relation_of(X2),X3)
                  | ~ ilf_type(X3,relation_type(X0,X1)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f39,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( subset(X2,range(X0,X1,X3))
                    & subset(X2,domain(X0,X1,X3)) )
                  | ~ subset(identity_relation_of(X2),X3)
                  | ~ ilf_type(X3,relation_type(X0,X1)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f38]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f45,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f44]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( X0 = X1
          <=> ( subset(X1,X0)
              & subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f58]) ).

fof(f60,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f61]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(range(X0,X1,X2),subset_type(X1))
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f75,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( range(X0,X1,X2) != X1
                | ~ subset(X1,domain(X0,X1,X2)) )
              & subset(identity_relation_of(X1),X2)
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f76,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( range(X0,X1,X2) != X1
                | ~ subset(X1,domain(X0,X1,X2)) )
              & subset(identity_relation_of(X1),X2)
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f75]) ).

fof(f81,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f82,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f81]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0)
        & ilf_type(sK1(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ~ member(sK1(X0,X1),X1)
                & member(sK1(X0,X1),X0)
                & ilf_type(sK1(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f82,f83]) ).

fof(f90,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 = X1
              | ~ subset(X1,X0)
              | ~ subset(X0,X1) )
            & ( ( subset(X1,X0)
                & subset(X0,X1) )
              | X0 != X1 ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 = X1
              | ~ subset(X1,X0)
              | ~ subset(X0,X1) )
            & ( ( subset(X1,X0)
                & subset(X0,X1) )
              | X0 != X1 ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f90]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X1,subset_type(X0))
              | ~ ilf_type(X1,member_type(power_set(X0))) )
            & ( ilf_type(X1,member_type(power_set(X0)))
              | ~ ilf_type(X1,subset_type(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f99]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK6(X0,X1),X1)
        & member(sK6(X0,X1),X0)
        & ilf_type(sK6(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK6(X0,X1),X1)
                & member(sK6(X0,X1),X0)
                & ilf_type(sK6(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f100,f101]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f116,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ( range(X0,X1,X2) != X1
                  | ~ subset(X1,domain(X0,X1,X2)) )
                & subset(identity_relation_of(X1),X2)
                & ilf_type(X2,relation_type(X0,X1)) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ( range(sK12,X1,X2) != X1
                | ~ subset(X1,domain(sK12,X1,X2)) )
              & subset(identity_relation_of(X1),X2)
              & ilf_type(X2,relation_type(sK12,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK12,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( range(sK12,X1,X2) != X1
              | ~ subset(X1,domain(sK12,X1,X2)) )
            & subset(identity_relation_of(X1),X2)
            & ilf_type(X2,relation_type(sK12,X1)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ( sK13 != range(sK12,sK13,X2)
            | ~ subset(sK13,domain(sK12,sK13,X2)) )
          & subset(identity_relation_of(sK13),X2)
          & ilf_type(X2,relation_type(sK12,sK13)) )
      & ilf_type(sK13,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f118,plain,
    ( ? [X2] :
        ( ( sK13 != range(sK12,sK13,X2)
          | ~ subset(sK13,domain(sK12,sK13,X2)) )
        & subset(identity_relation_of(sK13),X2)
        & ilf_type(X2,relation_type(sK12,sK13)) )
   => ( ( sK13 != range(sK12,sK13,sK14)
        | ~ subset(sK13,domain(sK12,sK13,sK14)) )
      & subset(identity_relation_of(sK13),sK14)
      & ilf_type(sK14,relation_type(sK12,sK13)) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ( ( sK13 != range(sK12,sK13,sK14)
      | ~ subset(sK13,domain(sK12,sK13,sK14)) )
    & subset(identity_relation_of(sK13),sK14)
    & ilf_type(sK14,relation_type(sK12,sK13))
    & ilf_type(sK13,set_type)
    & ilf_type(sK12,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f76,f118,f117,f116]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f121,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X2,domain(X0,X1,X3))
      | ~ subset(identity_relation_of(X2),X3)
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f122,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X2,range(X0,X1,X3))
      | ~ subset(identity_relation_of(X2),X3)
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK1(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK1(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f155,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f159,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f178,plain,
    ! [X2,X0,X1] :
      ( ilf_type(range(X0,X1,X2),subset_type(X1))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f179,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f32]) ).

fof(f182,plain,
    ilf_type(sK14,relation_type(sK12,sK13)),
    inference(cnf_transformation,[],[f119]) ).

fof(f183,plain,
    subset(identity_relation_of(sK13),sK14),
    inference(cnf_transformation,[],[f119]) ).

fof(f184,plain,
    ( sK13 != range(sK12,sK13,sK14)
    | ~ subset(sK13,domain(sK12,sK13,sK14)) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_49,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_50,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X3),X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(X3,range(X1,X2,X0)) ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_51,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X3),X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(X3,domain(X1,X2,X0)) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_59,plain,
    ( ~ member(sK1(X0,X1),X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_60,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_68,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_79,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_86,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_88,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_90,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_106,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(range(X1,X2,X0),subset_type(X2)) ),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_107,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_108,negated_conjecture,
    ( range(sK12,sK13,sK14) != sK13
    | ~ subset(sK13,domain(sK12,sK13,sK14)) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_109,negated_conjecture,
    subset(identity_relation_of(sK13),sK14),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_110,negated_conjecture,
    ilf_type(sK14,relation_type(sK12,sK13)),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_167,plain,
    ~ empty(power_set(X0)),
    inference(global_subsumption_just,[status(thm)],[c_88,c_107,c_88]) ).

cnf(c_224,plain,
    ( ~ ilf_type(X1,set_type)
    | member(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_60,c_107,c_60]) ).

cnf(c_225,plain,
    ( ~ ilf_type(X0,set_type)
    | member(sK1(X1,X0),X1)
    | subset(X1,X0) ),
    inference(renaming,[status(thm)],[c_224]) ).

cnf(c_226,plain,
    ( member(sK1(X1,X0),X1)
    | subset(X1,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_225,c_107,c_225]) ).

cnf(c_227,plain,
    ( member(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_226]) ).

cnf(c_238,plain,
    ( ~ member(sK1(X0,X1),X1)
    | ~ ilf_type(X1,set_type)
    | subset(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_59,c_107,c_59]) ).

cnf(c_240,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_90,c_107,c_90]) ).

cnf(c_247,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_79,c_107,c_79]) ).

cnf(c_259,plain,
    ( ~ subset(X1,X0)
    | ~ subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_107,c_68]) ).

cnf(c_260,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | ~ ilf_type(X1,set_type)
    | X0 = X1 ),
    inference(renaming,[status(thm)],[c_259]) ).

cnf(c_271,plain,
    ( ~ member(X2,X0)
    | ~ member(X0,power_set(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_86,c_107,c_86]) ).

cnf(c_272,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(renaming,[status(thm)],[c_271]) ).

cnf(c_429,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | ilf_type(range(X1,X2,X0),subset_type(X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_106,c_107]) ).

cnf(c_434,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_260,c_107]) ).

cnf(c_435,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_272,c_107]) ).

cnf(c_437,plain,
    ( ~ member(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_238,c_107]) ).

cnf(c_439,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X3),X0)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(X3,domain(X1,X2,X0)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_51,c_107]) ).

cnf(c_448,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X3),X0)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(X3,range(X1,X2,X0)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_50,c_107]) ).

cnf(c_450,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_247,c_107]) ).

cnf(c_453,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | member(X0,X1)
    | empty(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_240,c_107]) ).

cnf(c_628,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(range(X1,X2,X0),subset_type(X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_429,c_107]) ).

cnf(c_687,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_435,c_107]) ).

cnf(c_718,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X3),X0)
    | subset(X3,domain(X1,X2,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_439,c_107,c_107]) ).

cnf(c_734,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X3),X0)
    | subset(X3,range(X1,X2,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_448,c_107,c_107]) ).

cnf(c_1310,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_450]) ).

cnf(c_1312,plain,
    ( subset(X0,X1)
    | ~ member(sK1(X0,X1),X1) ),
    inference(prop_impl_just,[status(thm)],[c_437]) ).

cnf(c_1313,plain,
    ( ~ member(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_1312]) ).

cnf(c_1314,plain,
    ( subset(X0,X1)
    | member(sK1(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_227]) ).

cnf(c_1315,plain,
    ( member(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_1314]) ).

cnf(c_1324,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(range(X1,X2,X0),subset_type(X2)) ),
    inference(prop_impl_just,[status(thm)],[c_628]) ).

cnf(c_1908,plain,
    relation_type(sK12,sK13) = sP0_iProver_def,
    definition ).

cnf(c_1909,plain,
    identity_relation_of(sK13) = sP1_iProver_def,
    definition ).

cnf(c_1910,plain,
    range(sK12,sK13,sK14) = sP2_iProver_def,
    definition ).

cnf(c_1911,plain,
    domain(sK12,sK13,sK14) = sP3_iProver_def,
    definition ).

cnf(c_1912,negated_conjecture,
    ilf_type(sK14,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_110,c_1908]) ).

cnf(c_1913,negated_conjecture,
    subset(sP1_iProver_def,sK14),
    inference(demodulation,[status(thm)],[c_109,c_1909]) ).

cnf(c_1914,negated_conjecture,
    ( sP2_iProver_def != sK13
    | ~ subset(sK13,sP3_iProver_def) ),
    inference(demodulation,[status(thm)],[c_108,c_1911,c_1910]) ).

cnf(c_2934,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1))
    | empty(power_set(X1)) ),
    inference(superposition,[status(thm)],[c_1310,c_453]) ).

cnf(c_2935,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2934,c_167]) ).

cnf(c_3130,plain,
    ( ~ ilf_type(sK14,relation_type(sK12,sK13))
    | ~ subset(identity_relation_of(X0),sK14)
    | subset(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_1911,c_718]) ).

cnf(c_3132,plain,
    ( ~ subset(identity_relation_of(X0),sK14)
    | ~ ilf_type(sK14,sP0_iProver_def)
    | subset(X0,sP3_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_3130,c_1908]) ).

cnf(c_3133,plain,
    ( ~ subset(identity_relation_of(X0),sK14)
    | subset(X0,sP3_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3132,c_1912]) ).

cnf(c_3173,plain,
    ( ~ ilf_type(sK14,relation_type(sK12,sK13))
    | ilf_type(sP2_iProver_def,subset_type(sK13)) ),
    inference(superposition,[status(thm)],[c_1910,c_1324]) ).

cnf(c_3175,plain,
    ( ~ ilf_type(sK14,sP0_iProver_def)
    | ilf_type(sP2_iProver_def,subset_type(sK13)) ),
    inference(light_normalisation,[status(thm)],[c_3173,c_1908]) ).

cnf(c_3176,plain,
    ilf_type(sP2_iProver_def,subset_type(sK13)),
    inference(forward_subsumption_resolution,[status(thm)],[c_3175,c_1912]) ).

cnf(c_3181,plain,
    member(sP2_iProver_def,power_set(sK13)),
    inference(superposition,[status(thm)],[c_3176,c_2935]) ).

cnf(c_3191,plain,
    ( ~ subset(sP1_iProver_def,sK14)
    | subset(sK13,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_1909,c_3133]) ).

cnf(c_3192,plain,
    subset(sK13,sP3_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_3191,c_1913]) ).

cnf(c_3195,plain,
    sK13 != sP2_iProver_def,
    inference(backward_subsumption_resolution,[status(thm)],[c_1914,c_3192]) ).

cnf(c_3240,plain,
    ( ~ ilf_type(sK14,relation_type(sK12,sK13))
    | ~ subset(identity_relation_of(X0),sK14)
    | subset(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_1910,c_734]) ).

cnf(c_3242,plain,
    ( ~ subset(identity_relation_of(X0),sK14)
    | ~ ilf_type(sK14,sP0_iProver_def)
    | subset(X0,sP2_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_3240,c_1908]) ).

cnf(c_3243,plain,
    ( ~ subset(identity_relation_of(X0),sK14)
    | subset(X0,sP2_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3242,c_1912]) ).

cnf(c_3347,plain,
    ( ~ subset(sP1_iProver_def,sK14)
    | subset(sK13,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_1909,c_3243]) ).

cnf(c_3348,plain,
    subset(sK13,sP2_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_3347,c_1913]) ).

cnf(c_3356,plain,
    ( ~ subset(sP2_iProver_def,sK13)
    | sK13 = sP2_iProver_def ),
    inference(superposition,[status(thm)],[c_3348,c_434]) ).

cnf(c_3357,plain,
    ~ subset(sP2_iProver_def,sK13),
    inference(forward_subsumption_resolution,[status(thm)],[c_3356,c_3195]) ).

cnf(c_4214,plain,
    ( ~ member(X0,sP2_iProver_def)
    | member(X0,sK13) ),
    inference(superposition,[status(thm)],[c_3181,c_687]) ).

cnf(c_4383,plain,
    ( member(sK1(sP2_iProver_def,X0),sK13)
    | subset(sP2_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_1315,c_4214]) ).

cnf(c_5348,plain,
    subset(sP2_iProver_def,sK13),
    inference(superposition,[status(thm)],[c_4383,c_1313]) ).

cnf(c_5351,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_5348,c_3357]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11  % Command  : run_iprover %s %d THM
% 0.12/0.32  % Computer : n008.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu May  2 20:28:27 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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
% 0.45/1.13  % SZS status Started for theBenchmark.p
% 0.45/1.13  % SZS status Theorem for theBenchmark.p
% 0.45/1.13  
% 0.45/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.13  
% 0.45/1.13  ------  iProver source info
% 0.45/1.13  
% 0.45/1.13  git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.13  git: non_committed_changes: false
% 0.45/1.13  
% 0.45/1.13  ------ Parsing...
% 0.45/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.45/1.13  
% 0.45/1.13  ------ 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 
% 0.45/1.13  
% 0.45/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.45/1.13  
% 0.45/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.45/1.13  ------ Proving...
% 0.45/1.13  ------ Problem Properties 
% 0.45/1.13  
% 0.45/1.13  
% 0.45/1.13  clauses                                 48
% 0.45/1.13  conjectures                             3
% 0.45/1.13  EPR                                     12
% 0.45/1.13  Horn                                    41
% 0.45/1.13  unary                                   13
% 0.45/1.13  binary                                  26
% 0.45/1.13  lits                                    94
% 0.45/1.13  lits eq                                 11
% 0.45/1.13  fd_pure                                 0
% 0.45/1.13  fd_pseudo                               0
% 0.45/1.13  fd_cond                                 0
% 0.45/1.13  fd_pseudo_cond                          2
% 0.45/1.13  AC symbols                              0
% 0.45/1.13  
% 0.45/1.13  ------ Schedule dynamic 5 is on 
% 0.45/1.13  
% 0.45/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.13  
% 0.45/1.13  
% 0.45/1.13  ------ 
% 0.45/1.13  Current options:
% 0.45/1.13  ------ 
% 0.45/1.13  
% 0.45/1.13  
% 0.45/1.13  
% 0.45/1.13  
% 0.45/1.13  ------ Proving...
% 0.45/1.13  
% 0.45/1.13  
% 0.45/1.13  % SZS status Theorem for theBenchmark.p
% 0.45/1.13  
% 0.45/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.13  
% 0.45/1.13  
%------------------------------------------------------------------------------