TSTP Solution File: SET768+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET768+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 15:09:32 EDT 2023

% Result   : Theorem 49.26s 7.29s
% Output   : CNFRefutation 49.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   87 (   7 unt;   0 def)
%            Number of atoms       :  374 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  464 ( 177   ~; 180   |;  73   &)
%                                         (  10 <=>;  22  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :  204 (   4 sgn; 126   !;  23   ?)

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

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

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/sandbox/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/sandbox/benchmark/theBenchmark.p',equivalence_class) ).

fof(f17,conjecture,
    ! [X3,X6,X0,X1] :
      ( ( member(X1,X3)
        & member(X0,X3)
        & equivalence(X6,X3) )
     => ( equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
      <=> apply(X6,X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII04) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X6,X0,X1] :
        ( ( member(X1,X3)
          & member(X0,X3)
          & equivalence(X6,X3) )
       => ( equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
        <=> apply(X6,X0,X1) ) ),
    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) )
       => ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
        <=> apply(X1,X2,X3) ) ),
    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] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f36,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(f37,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,[],[f36]) ).

fof(f38,plain,
    ? [X0,X1,X2,X3] :
      ( ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
      <~> apply(X1,X2,X3) )
      & member(X3,X0)
      & member(X2,X0)
      & equivalence(X1,X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f39,plain,
    ? [X0,X1,X2,X3] :
      ( ( equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1))
      <~> apply(X1,X2,X3) )
      & member(X3,X0)
      & member(X2,X0)
      & equivalence(X1,X0) ),
    inference(flattening,[],[f38]) ).

fof(f40,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,[],[f34]) ).

fof(f41,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,[],[f40]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,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])],[f41,f42]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( equal_set(X0,X1)
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | ~ equal_set(X0,X1) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( equal_set(X0,X1)
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | ~ equal_set(X0,X1) ) ),
    inference(flattening,[],[f44]) ).

fof(f64,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(f65,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,[],[f64]) ).

fof(f66,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ apply(X1,X2,X3)
        | ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
      & ( apply(X1,X2,X3)
        | equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
      & member(X3,X0)
      & member(X2,X0)
      & equivalence(X1,X0) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f67,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ apply(X1,X2,X3)
        | ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
      & ( apply(X1,X2,X3)
        | equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
      & member(X3,X0)
      & member(X2,X0)
      & equivalence(X1,X0) ),
    inference(flattening,[],[f66]) ).

fof(f68,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ apply(X1,X2,X3)
          | ~ equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
        & ( apply(X1,X2,X3)
          | equal_set(equivalence_class(X2,X0,X1),equivalence_class(X3,X0,X1)) )
        & member(X3,X0)
        & member(X2,X0)
        & equivalence(X1,X0) )
   => ( ( ~ apply(sK4,sK5,sK6)
        | ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
      & ( apply(sK4,sK5,sK6)
        | equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
      & member(sK6,sK3)
      & member(sK5,sK3)
      & equivalence(sK4,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ( ( ~ apply(sK4,sK5,sK6)
      | ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
    & ( apply(sK4,sK5,sK6)
      | equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) )
    & member(sK6,sK3)
    & member(sK5,sK3)
    & equivalence(sK4,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f67,f68]) ).

fof(f70,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f99,plain,
    ! [X0,X1,X7] :
      ( apply(X1,X7,X7)
      | ~ member(X7,X0)
      | ~ equivalence(X1,X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f100,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,[],[f37]) ).

fof(f101,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,[],[f37]) ).

fof(f102,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,equivalence_class(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f103,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,X2,X3)
      | ~ member(X3,equivalence_class(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f104,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,equivalence_class(X2,X1,X0))
      | ~ apply(X0,X2,X3)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f105,plain,
    equivalence(sK4,sK3),
    inference(cnf_transformation,[],[f69]) ).

fof(f106,plain,
    member(sK5,sK3),
    inference(cnf_transformation,[],[f69]) ).

fof(f107,plain,
    member(sK6,sK3),
    inference(cnf_transformation,[],[f69]) ).

fof(f108,plain,
    ( apply(sK4,sK5,sK6)
    | equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f109,plain,
    ( ~ apply(sK4,sK5,sK6)
    | ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_53,plain,
    ( ~ equal_set(X0,X1)
    | subset(X1,X0) ),
    inference(cnf_transformation,[],[f74]) ).

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,[],[f101]) ).

cnf(c_79,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X1,X3)
    | ~ member(X2,X3)
    | ~ equivalence(X0,X3)
    | apply(X0,X2,X1) ),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_80,plain,
    ( ~ member(X0,X1)
    | ~ equivalence(X2,X1)
    | apply(X2,X0,X0) ),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_81,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X2,X3)
    | member(X2,equivalence_class(X1,X3,X0)) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_82,plain,
    ( ~ member(X0,equivalence_class(X1,X2,X3))
    | apply(X3,X1,X0) ),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_83,plain,
    ( ~ member(X0,equivalence_class(X1,X2,X3))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_84,negated_conjecture,
    ( ~ equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))
    | ~ apply(sK4,sK5,sK6) ),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_85,negated_conjecture,
    ( equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))
    | apply(sK4,sK5,sK6) ),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_86,negated_conjecture,
    member(sK6,sK3),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_87,negated_conjecture,
    member(sK5,sK3),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_88,negated_conjecture,
    equivalence(sK4,sK3),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_592,plain,
    ( ~ subset(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))
    | ~ subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))
    | equal_set(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_595,plain,
    ( ~ apply(sK4,sK5,sK6)
    | ~ member(sK5,X0)
    | ~ member(sK6,X0)
    | ~ equivalence(sK4,X0)
    | apply(sK4,sK6,sK5) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_598,plain,
    ( ~ apply(sK4,sK5,sK6)
    | ~ member(sK5,sK3)
    | ~ member(sK6,sK3)
    | ~ equivalence(sK4,sK3)
    | apply(sK4,sK6,sK5) ),
    inference(instantiation,[status(thm)],[c_595]) ).

cnf(c_599,plain,
    ( ~ apply(sK4,sK6,X0)
    | ~ apply(sK4,sK5,sK6)
    | ~ member(X0,X1)
    | ~ member(sK5,X1)
    | ~ member(sK6,X1)
    | ~ equivalence(sK4,X1)
    | apply(sK4,sK5,X0) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_1613,plain,
    ( subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))
    | apply(sK4,sK5,sK6) ),
    inference(superposition,[status(thm)],[c_85,c_53]) ).

cnf(c_1741,plain,
    ( ~ equivalence(X0,sK3)
    | apply(X0,sK6,sK6) ),
    inference(superposition,[status(thm)],[c_86,c_80]) ).

cnf(c_1931,plain,
    ( ~ subset(equivalence_class(X0,X1,X2),X3)
    | ~ apply(X2,X0,X4)
    | ~ member(X4,X1)
    | member(X4,X3) ),
    inference(superposition,[status(thm)],[c_81,c_51]) ).

cnf(c_2016,plain,
    ( ~ apply(sK4,sK6,X0)
    | ~ member(X0,sK3)
    | member(X0,equivalence_class(sK5,sK3,sK4))
    | apply(sK4,sK5,sK6) ),
    inference(superposition,[status(thm)],[c_1613,c_1931]) ).

cnf(c_2109,plain,
    ( ~ apply(sK4,sK6,X0)
    | ~ member(X0,sK3)
    | apply(sK4,sK5,X0)
    | apply(sK4,sK5,sK6) ),
    inference(superposition,[status(thm)],[c_2016,c_82]) ).

cnf(c_3044,plain,
    ( ~ member(sK6,sK3)
    | ~ equivalence(sK4,sK3)
    | apply(sK4,sK5,sK6) ),
    inference(superposition,[status(thm)],[c_1741,c_2109]) ).

cnf(c_6191,plain,
    ( member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
    | subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_6192,plain,
    ( ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
    | subset(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_6227,plain,
    ( ~ apply(sK4,X0,X1)
    | ~ apply(sK4,sK6,X0)
    | ~ member(X0,X2)
    | ~ member(X1,X2)
    | ~ member(sK6,X2)
    | ~ equivalence(sK4,X2)
    | apply(sK4,sK6,X1) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_6231,plain,
    ( ~ member(X0,equivalence_class(sK6,X1,sK4))
    | apply(sK4,sK6,X0) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_7813,plain,
    ( member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
    | subset(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_7814,plain,
    ( ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
    | subset(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_11206,plain,
    ( ~ apply(sK4,sK5,X0)
    | ~ apply(sK4,sK6,sK5)
    | ~ member(X0,X1)
    | ~ member(sK5,X1)
    | ~ member(sK6,X1)
    | ~ equivalence(sK4,X1)
    | apply(sK4,sK6,X0) ),
    inference(instantiation,[status(thm)],[c_6227]) ).

cnf(c_13918,plain,
    ( ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
    | member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),sK3) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_13919,plain,
    ( ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK6,sK3,sK4))
    | apply(sK4,sK6,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_6231]) ).

cnf(c_16690,plain,
    ( ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
    | apply(sK4,sK5,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_16691,plain,
    ( ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK5,sK3,sK4))
    | member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),sK3) ),
    inference(instantiation,[status(thm)],[c_83]) ).

cnf(c_26292,plain,
    ( ~ apply(sK4,sK6,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)))
    | ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),X0)
    | ~ apply(sK4,sK5,sK6)
    | ~ member(sK5,X0)
    | ~ member(sK6,X0)
    | ~ equivalence(sK4,X0)
    | apply(sK4,sK5,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_599]) ).

cnf(c_26293,plain,
    ( ~ apply(sK4,sK6,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)))
    | ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),sK3)
    | ~ apply(sK4,sK5,sK6)
    | ~ member(sK5,sK3)
    | ~ member(sK6,sK3)
    | ~ equivalence(sK4,sK3)
    | apply(sK4,sK5,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_26292]) ).

cnf(c_27577,plain,
    ( ~ apply(sK4,sK5,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)))
    | ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),X0)
    | ~ apply(sK4,sK6,sK5)
    | ~ member(sK5,X0)
    | ~ member(sK6,X0)
    | ~ equivalence(sK4,X0)
    | apply(sK4,sK6,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_11206]) ).

cnf(c_27578,plain,
    ( ~ apply(sK4,sK5,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)))
    | ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),sK3)
    | ~ apply(sK4,sK6,sK5)
    | ~ member(sK5,sK3)
    | ~ member(sK6,sK3)
    | ~ equivalence(sK4,sK3)
    | apply(sK4,sK6,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_27577]) ).

cnf(c_27626,plain,
    ( ~ apply(sK4,sK5,sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)))
    | ~ member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),sK3)
    | member(sK0(equivalence_class(sK6,sK3,sK4),equivalence_class(sK5,sK3,sK4)),equivalence_class(sK5,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_81]) ).

cnf(c_69971,plain,
    ( ~ apply(sK4,sK6,sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)))
    | ~ member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),sK3)
    | member(sK0(equivalence_class(sK5,sK3,sK4),equivalence_class(sK6,sK3,sK4)),equivalence_class(sK6,sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_81]) ).

cnf(c_69972,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_69971,c_27626,c_27578,c_26293,c_16690,c_16691,c_13919,c_13918,c_7813,c_7814,c_6191,c_6192,c_3044,c_598,c_592,c_84,c_86,c_87,c_88]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET768+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n002.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 : Sat Aug 26 10:21:18 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 49.26/7.29  % SZS status Started for theBenchmark.p
% 49.26/7.29  % SZS status Theorem for theBenchmark.p
% 49.26/7.29  
% 49.26/7.29  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 49.26/7.29  
% 49.26/7.29  ------  iProver source info
% 49.26/7.29  
% 49.26/7.29  git: date: 2023-05-31 18:12:56 +0000
% 49.26/7.29  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 49.26/7.29  git: non_committed_changes: false
% 49.26/7.29  git: last_make_outside_of_git: false
% 49.26/7.29  
% 49.26/7.29  ------ Parsing...
% 49.26/7.29  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 49.26/7.29  
% 49.26/7.29  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 49.26/7.29  
% 49.26/7.29  ------ Preprocessing...
% 49.26/7.29  
% 49.26/7.29  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 49.26/7.29  ------ Proving...
% 49.26/7.29  ------ Problem Properties 
% 49.26/7.29  
% 49.26/7.29  
% 49.26/7.29  clauses                                 40
% 49.26/7.29  conjectures                             5
% 49.26/7.29  EPR                                     11
% 49.26/7.29  Horn                                    34
% 49.26/7.29  unary                                   7
% 49.26/7.29  binary                                  21
% 49.26/7.29  lits                                    91
% 49.26/7.29  lits eq                                 3
% 49.26/7.29  fd_pure                                 0
% 49.26/7.29  fd_pseudo                               0
% 49.26/7.29  fd_cond                                 0
% 49.26/7.29  fd_pseudo_cond                          2
% 49.26/7.29  AC symbols                              0
% 49.26/7.29  
% 49.26/7.29  ------ Input Options Time Limit: Unbounded
% 49.26/7.29  
% 49.26/7.29  
% 49.26/7.29  ------ 
% 49.26/7.29  Current options:
% 49.26/7.29  ------ 
% 49.26/7.29  
% 49.26/7.29  
% 49.26/7.29  
% 49.26/7.29  
% 49.26/7.29  ------ Proving...
% 49.26/7.29  
% 49.26/7.29  
% 49.26/7.29  % SZS status Theorem for theBenchmark.p
% 49.26/7.29  
% 49.26/7.29  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.26/7.29  
% 49.26/7.30  
%------------------------------------------------------------------------------