TSTP Solution File: SET770+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 03:01:28 EDT 2024

% Result   : Theorem 20.34s 3.63s
% Output   : CNFRefutation 20.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  105 (  21 unt;   0 def)
%            Number of atoms       :  379 (  10 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  451 ( 177   ~; 171   |;  70   &)
%                                         (   8 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  221 (   3 sgn 134   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> ~ ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).

fof(f14,axiom,
    ! [X0,X6] :
      ( equivalence(X6,X0)
    <=> ( ! [X2,X4,X5] :
            ( ( member(X5,X0)
              & member(X4,X0)
              & member(X2,X0) )
           => ( ( apply(X6,X4,X5)
                & apply(X6,X2,X4) )
             => apply(X6,X2,X5) ) )
        & ! [X2,X4] :
            ( ( member(X4,X0)
              & member(X2,X0) )
           => ( apply(X6,X2,X4)
             => apply(X6,X4,X2) ) )
        & ! [X2] :
            ( member(X2,X0)
           => apply(X6,X2,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).

fof(f15,axiom,
    ! [X6,X3,X0,X2] :
      ( member(X2,equivalence_class(X0,X3,X6))
    <=> ( apply(X6,X0,X2)
        & member(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).

fof(f17,conjecture,
    ! [X3,X6,X0,X1] :
      ( ( member(X1,X3)
        & member(X0,X3)
        & equivalence(X6,X3) )
     => ( disjoint(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
        | equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII06) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X6,X0,X1] :
        ( ( member(X1,X3)
          & member(X0,X3)
          & equivalence(X6,X3) )
       => ( disjoint(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
          | equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X4,X0)
              & member(X3,X0)
              & member(X2,X0) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X2,X3) )
             => apply(X1,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X0)
              & member(X5,X0) )
           => ( apply(X1,X5,X6)
             => apply(X1,X6,X5) ) )
        & ! [X7] :
            ( member(X7,X0)
           => apply(X1,X7,X7) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( member(X3,equivalence_class(X2,X1,X0))
    <=> ( apply(X0,X2,X3)
        & member(X3,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f32,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( member(X3,X0)
          & member(X2,X0)
          & equivalence(X1,X0) )
       => ( disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
          | equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) ) ),
    inference(rectify,[],[f18]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
     => ( ! [X2,X3,X4] :
            ( ( member(X4,X0)
              & member(X3,X0)
              & member(X2,X0) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X2,X3) )
             => apply(X1,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X0)
              & member(X5,X0) )
           => ( apply(X1,X5,X6)
             => apply(X1,X6,X5) ) )
        & ! [X7] :
            ( member(X7,X0)
           => apply(X1,X7,X7) ) ) ),
    inference(unused_predicate_definition_removal,[],[f29]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
     => disjoint(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f37]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( apply(X1,X2,X4)
            | ~ apply(X1,X3,X4)
            | ~ apply(X1,X2,X3)
            | ~ member(X4,X0)
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5,X6] :
            ( apply(X1,X6,X5)
            | ~ apply(X1,X5,X6)
            | ~ member(X6,X0)
            | ~ member(X5,X0) )
        & ! [X7] :
            ( apply(X1,X7,X7)
            | ~ member(X7,X0) ) )
      | ~ equivalence(X1,X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( apply(X1,X2,X4)
            | ~ apply(X1,X3,X4)
            | ~ apply(X1,X2,X3)
            | ~ member(X4,X0)
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5,X6] :
            ( apply(X1,X6,X5)
            | ~ apply(X1,X5,X6)
            | ~ member(X6,X0)
            | ~ member(X5,X0) )
        & ! [X7] :
            ( apply(X1,X7,X7)
            | ~ member(X7,X0) ) )
      | ~ equivalence(X1,X0) ),
    inference(flattening,[],[f41]) ).

fof(f43,plain,
    ? [X0,X1,X2,X3] :
      ( ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
      & ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
      & member(X3,X0)
      & member(X2,X0)
      & equivalence(X1,X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f44,plain,
    ? [X0,X1,X2,X3] :
      ( ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
      & ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
      & member(X3,X0)
      & member(X2,X0)
      & equivalence(X1,X0) ),
    inference(flattening,[],[f43]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f45]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f46,f47]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) )
     => ( member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | ( member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f40,f67]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X2,X1,X0))
        | ~ apply(X0,X2,X3)
        | ~ member(X3,X1) )
      & ( ( apply(X0,X2,X3)
          & member(X3,X1) )
        | ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X2,X1,X0))
        | ~ apply(X0,X2,X3)
        | ~ member(X3,X1) )
      & ( ( apply(X0,X2,X3)
          & member(X3,X1) )
        | ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
    inference(flattening,[],[f69]) ).

fof(f71,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ disjoint(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
        & ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
        & member(X3,X0)
        & member(X2,X0)
        & equivalence(X1,X0) )
   => ( ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
      & ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
      & member(sK7,sK4)
      & member(sK6,sK4)
      & equivalence(sK5,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ( ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
    & ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
    & member(sK7,sK4)
    & member(sK6,sK4)
    & equivalence(sK5,sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f44,f71]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f103,plain,
    ! [X0,X1,X6,X5] :
      ( apply(X1,X6,X5)
      | ~ apply(X1,X5,X6)
      | ~ member(X6,X0)
      | ~ member(X5,X0)
      | ~ equivalence(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f104,plain,
    ! [X2,X3,X0,X1,X4] :
      ( apply(X1,X2,X4)
      | ~ apply(X1,X3,X4)
      | ~ apply(X1,X2,X3)
      | ~ member(X4,X0)
      | ~ member(X3,X0)
      | ~ member(X2,X0)
      | ~ equivalence(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f105,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,equivalence_class(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f106,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,X2,X3)
      | ~ member(X3,equivalence_class(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f107,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,equivalence_class(X2,X1,X0))
      | ~ apply(X0,X2,X3)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f108,plain,
    equivalence(sK5,sK4),
    inference(cnf_transformation,[],[f72]) ).

fof(f109,plain,
    member(sK6,sK4),
    inference(cnf_transformation,[],[f72]) ).

fof(f110,plain,
    member(sK7,sK4),
    inference(cnf_transformation,[],[f72]) ).

fof(f111,plain,
    ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
    inference(cnf_transformation,[],[f72]) ).

fof(f112,plain,
    ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_76,plain,
    ( member(sK3(X0,X1),X1)
    | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f101]) ).

cnf(c_77,plain,
    ( member(sK3(X0,X1),X0)
    | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_78,plain,
    ( ~ apply(X0,X1,X2)
    | ~ apply(X0,X3,X1)
    | ~ member(X1,X4)
    | ~ member(X2,X4)
    | ~ member(X3,X4)
    | ~ equivalence(X0,X4)
    | apply(X0,X3,X2) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_79,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X1,X3)
    | ~ member(X2,X3)
    | ~ equivalence(X0,X3)
    | apply(X0,X2,X1) ),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_81,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X2,X3)
    | member(X2,equivalence_class(X1,X3,X0)) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_82,plain,
    ( ~ member(X0,equivalence_class(X1,X2,X3))
    | apply(X3,X1,X0) ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_83,plain,
    ( ~ member(X0,equivalence_class(X1,X2,X3))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_84,negated_conjecture,
    ~ disjoint(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_85,negated_conjecture,
    ~ equal_set(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_86,negated_conjecture,
    member(sK7,sK4),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_87,negated_conjecture,
    member(sK6,sK4),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_88,negated_conjecture,
    equivalence(sK5,sK4),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_165,plain,
    ( member(sK3(X0,X1),X0)
    | disjoint(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_77]) ).

cnf(c_167,plain,
    ( disjoint(X0,X1)
    | member(sK3(X0,X1),X1) ),
    inference(prop_impl_just,[status(thm)],[c_76]) ).

cnf(c_168,plain,
    ( member(sK3(X0,X1),X1)
    | disjoint(X0,X1) ),
    inference(renaming,[status(thm)],[c_167]) ).

cnf(c_596,plain,
    ( equivalence_class(sK6,sK4,sK5) != X0
    | equivalence_class(sK7,sK4,sK5) != X1
    | ~ subset(X0,X1)
    | ~ subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_85]) ).

cnf(c_597,plain,
    ( ~ subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))
    | ~ subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
    inference(unflattening,[status(thm)],[c_596]) ).

cnf(c_606,plain,
    ( equivalence_class(sK6,sK4,sK5) != X0
    | equivalence_class(sK7,sK4,sK5) != X1
    | member(sK3(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_165,c_84]) ).

cnf(c_607,plain,
    member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5)),
    inference(unflattening,[status(thm)],[c_606]) ).

cnf(c_611,plain,
    ( equivalence_class(sK6,sK4,sK5) != X0
    | equivalence_class(sK7,sK4,sK5) != X1
    | member(sK3(X0,X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_168,c_84]) ).

cnf(c_612,plain,
    member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5)),
    inference(unflattening,[status(thm)],[c_611]) ).

cnf(c_618,plain,
    ( X0 != sK5
    | X1 != sK4
    | ~ apply(X0,X2,X3)
    | ~ apply(X0,X4,X2)
    | ~ member(X2,X1)
    | ~ member(X3,X1)
    | ~ member(X4,X1)
    | apply(X0,X4,X3) ),
    inference(resolution_lifted,[status(thm)],[c_78,c_88]) ).

cnf(c_619,plain,
    ( ~ apply(sK5,X0,X1)
    | ~ apply(sK5,X2,X0)
    | ~ member(X0,sK4)
    | ~ member(X1,sK4)
    | ~ member(X2,sK4)
    | apply(sK5,X2,X1) ),
    inference(unflattening,[status(thm)],[c_618]) ).

cnf(c_638,plain,
    ( X0 != sK5
    | X1 != sK4
    | ~ apply(X0,X2,X3)
    | ~ member(X2,X1)
    | ~ member(X3,X1)
    | apply(X0,X3,X2) ),
    inference(resolution_lifted,[status(thm)],[c_79,c_88]) ).

cnf(c_639,plain,
    ( ~ apply(sK5,X0,X1)
    | ~ member(X0,sK4)
    | ~ member(X1,sK4)
    | apply(sK5,X1,X0) ),
    inference(unflattening,[status(thm)],[c_638]) ).

cnf(c_1113,negated_conjecture,
    member(sK6,sK4),
    inference(demodulation,[status(thm)],[c_87]) ).

cnf(c_1114,negated_conjecture,
    member(sK7,sK4),
    inference(demodulation,[status(thm)],[c_86]) ).

cnf(c_2051,plain,
    ( ~ apply(sK5,X0,sK7)
    | ~ apply(sK5,sK7,X1)
    | ~ member(X0,sK4)
    | ~ member(X1,sK4)
    | ~ member(sK7,sK4)
    | apply(sK5,X0,X1) ),
    inference(instantiation,[status(thm)],[c_619]) ).

cnf(c_2052,plain,
    ( ~ apply(sK5,X0,sK6)
    | ~ apply(sK5,sK6,X1)
    | ~ member(X0,sK4)
    | ~ member(X1,sK4)
    | ~ member(sK6,sK4)
    | apply(sK5,X0,X1) ),
    inference(instantiation,[status(thm)],[c_619]) ).

cnf(c_2093,plain,
    ( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
    | subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_2094,plain,
    ( member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
    | subset(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_2117,plain,
    member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4),
    inference(superposition,[status(thm)],[c_607,c_83]) ).

cnf(c_2258,plain,
    apply(sK5,sK6,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))),
    inference(superposition,[status(thm)],[c_607,c_82]) ).

cnf(c_2259,plain,
    apply(sK5,sK7,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))),
    inference(superposition,[status(thm)],[c_612,c_82]) ).

cnf(c_2379,plain,
    ( ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
    | ~ member(sK6,sK4)
    | apply(sK5,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK6) ),
    inference(superposition,[status(thm)],[c_2258,c_639]) ).

cnf(c_2380,plain,
    apply(sK5,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK6),
    inference(forward_subsumption_resolution,[status(thm)],[c_2379,c_1113,c_2117]) ).

cnf(c_2386,plain,
    ( ~ apply(sK5,X0,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
    | ~ member(sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
    | ~ member(X0,sK4)
    | ~ member(sK6,sK4)
    | apply(sK5,X0,sK6) ),
    inference(superposition,[status(thm)],[c_2380,c_619]) ).

cnf(c_2388,plain,
    ( ~ apply(sK5,X0,sK3(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
    | ~ member(X0,sK4)
    | apply(sK5,X0,sK6) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2386,c_1113,c_2117]) ).

cnf(c_2921,plain,
    ( ~ member(sK7,sK4)
    | apply(sK5,sK7,sK6) ),
    inference(superposition,[status(thm)],[c_2259,c_2388]) ).

cnf(c_2922,plain,
    apply(sK5,sK7,sK6),
    inference(forward_subsumption_resolution,[status(thm)],[c_2921,c_1114]) ).

cnf(c_2930,plain,
    ( ~ member(sK6,sK4)
    | ~ member(sK7,sK4)
    | apply(sK5,sK6,sK7) ),
    inference(superposition,[status(thm)],[c_2922,c_639]) ).

cnf(c_2931,plain,
    apply(sK5,sK6,sK7),
    inference(forward_subsumption_resolution,[status(thm)],[c_2930,c_1114,c_1113]) ).

cnf(c_3409,plain,
    ( member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
    | subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_3410,plain,
    ( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
    | subset(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_5023,plain,
    ( ~ apply(sK5,sK7,X0)
    | ~ apply(sK5,sK6,sK7)
    | ~ member(X0,sK4)
    | ~ member(sK6,sK4)
    | ~ member(sK7,sK4)
    | apply(sK5,sK6,X0) ),
    inference(instantiation,[status(thm)],[c_2051]) ).

cnf(c_5027,plain,
    ( ~ apply(sK5,sK6,X0)
    | ~ apply(sK5,sK7,sK6)
    | ~ member(X0,sK4)
    | ~ member(sK6,sK4)
    | ~ member(sK7,sK4)
    | apply(sK5,sK7,X0) ),
    inference(instantiation,[status(thm)],[c_2052]) ).

cnf(c_7457,plain,
    ( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
    | apply(sK5,sK6,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_7458,plain,
    ( ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK6,sK4,sK5))
    | member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_14597,plain,
    ( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
    | apply(sK5,sK7,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_14598,plain,
    ( ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK7,sK4,sK5))
    | member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_19405,plain,
    ( ~ apply(sK5,X0,X1)
    | ~ member(X1,X2)
    | member(X1,equivalence_class(X0,X2,sK5)) ),
    inference(instantiation,[status(thm)],[c_81]) ).

cnf(c_42928,plain,
    ( ~ apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
    | ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
    | member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),equivalence_class(sK7,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_19405]) ).

cnf(c_42929,plain,
    ( ~ apply(sK5,sK6,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
    | ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
    | member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),equivalence_class(sK6,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_19405]) ).

cnf(c_57936,plain,
    ( ~ apply(sK5,sK6,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)))
    | ~ member(sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5)),sK4)
    | ~ apply(sK5,sK7,sK6)
    | ~ member(sK6,sK4)
    | ~ member(sK7,sK4)
    | apply(sK5,sK7,sK0(equivalence_class(sK6,sK4,sK5),equivalence_class(sK7,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_5027]) ).

cnf(c_58032,plain,
    ( ~ apply(sK5,sK7,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)))
    | ~ member(sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5)),sK4)
    | ~ apply(sK5,sK6,sK7)
    | ~ member(sK6,sK4)
    | ~ member(sK7,sK4)
    | apply(sK5,sK6,sK0(equivalence_class(sK7,sK4,sK5),equivalence_class(sK6,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_5023]) ).

cnf(c_60453,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_58032,c_57936,c_42929,c_42928,c_14597,c_14598,c_7457,c_7458,c_3409,c_3410,c_2931,c_2922,c_2094,c_2093,c_597,c_86,c_87]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n027.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 20:59:20 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  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
% 20.34/3.63  % SZS status Started for theBenchmark.p
% 20.34/3.63  % SZS status Theorem for theBenchmark.p
% 20.34/3.63  
% 20.34/3.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.34/3.63  
% 20.34/3.63  ------  iProver source info
% 20.34/3.63  
% 20.34/3.63  git: date: 2024-05-02 19:28:25 +0000
% 20.34/3.63  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.34/3.63  git: non_committed_changes: false
% 20.34/3.63  
% 20.34/3.63  ------ Parsing...
% 20.34/3.63  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 20.34/3.63  
% 20.34/3.63  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 20.34/3.63  
% 20.34/3.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 20.34/3.63  
% 20.34/3.63  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 20.34/3.63  ------ Proving...
% 20.34/3.63  ------ Problem Properties 
% 20.34/3.63  
% 20.34/3.63  
% 20.34/3.63  clauses                                 37
% 20.34/3.63  conjectures                             2
% 20.34/3.63  EPR                                     7
% 20.34/3.63  Horn                                    32
% 20.34/3.63  unary                                   8
% 20.34/3.63  binary                                  19
% 20.34/3.63  lits                                    80
% 20.34/3.63  lits eq                                 3
% 20.34/3.63  fd_pure                                 0
% 20.34/3.63  fd_pseudo                               0
% 20.34/3.63  fd_cond                                 0
% 20.34/3.63  fd_pseudo_cond                          2
% 20.34/3.63  AC symbols                              0
% 20.34/3.63  
% 20.34/3.63  ------ Schedule dynamic 5 is on 
% 20.34/3.63  
% 20.34/3.63  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.34/3.63  
% 20.34/3.63  
% 20.34/3.63  ------ 
% 20.34/3.63  Current options:
% 20.34/3.63  ------ 
% 20.34/3.63  
% 20.34/3.63  
% 20.34/3.63  
% 20.34/3.63  
% 20.34/3.63  ------ Proving...
% 20.34/3.63  
% 20.34/3.63  
% 20.34/3.63  % SZS status Theorem for theBenchmark.p
% 20.34/3.63  
% 20.34/3.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.34/3.63  
% 20.34/3.63  
%------------------------------------------------------------------------------