TSTP Solution File: SET697+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET697+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 03:01:16 EDT 2024

% Result   : Theorem 49.49s 7.73s
% Output   : CNFRefutation 49.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  129 (  10 unt;   0 def)
%            Number of atoms       :  401 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  450 ( 178   ~; 180   |;  65   &)
%                                         (  15 <=>;  10  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  259 (  11 sgn 132   !;  26   ?)

% 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(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).

fof(f10,axiom,
    ! [X2,X0] :
      ( member(X2,sum(X0))
    <=> ? [X4] :
          ( member(X2,X4)
          & member(X4,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).

fof(f11,axiom,
    ! [X2,X0] :
      ( member(X2,product(X0))
    <=> ! [X4] :
          ( member(X4,X0)
         => member(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).

fof(f12,conjecture,
    ! [X0,X1,X3] :
      ( ( subset(X1,X3)
        & subset(X0,X3) )
     => ( subset(X0,X1)
      <=> equal_set(intersection(X0,difference(X3,X1)),empty_set) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI31) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X3] :
        ( ( subset(X1,X3)
          & subset(X0,X3) )
       => ( subset(X0,X1)
        <=> equal_set(intersection(X0,difference(X3,X1)),empty_set) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f17,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( member(X0,sum(X1))
    <=> ? [X2] :
          ( member(X0,X2)
          & member(X2,X1) ) ),
    inference(rectify,[],[f10]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X0,X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f23,plain,
    ~ ! [X0,X1,X2] :
        ( ( subset(X1,X2)
          & subset(X0,X2) )
       => ( subset(X0,X1)
        <=> equal_set(intersection(X0,difference(X2,X1)),empty_set) ) ),
    inference(rectify,[],[f13]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
    <=> ! [X2] :
          ( member(X0,X2)
          | ~ member(X2,X1) ) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( ( subset(X0,X1)
      <~> equal_set(intersection(X0,difference(X2,X1)),empty_set) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f27,plain,
    ? [X0,X1,X2] :
      ( ( subset(X0,X1)
      <~> equal_set(intersection(X0,difference(X2,X1)),empty_set) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(flattening,[],[f26]) ).

fof(f28,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,[],[f24]) ).

fof(f29,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,[],[f28]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,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])],[f29,f30]) ).

fof(f32,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(f33,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,[],[f32]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f35]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f39]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ? [X2] :
            ( member(X0,X2)
            & member(X2,X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ? [X3] :
            ( member(X0,X3)
            & member(X3,X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(rectify,[],[f44]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X0,X3)
          & member(X3,X1) )
     => ( member(X0,sK1(X0,X1))
        & member(sK1(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ( member(X0,sK1(X0,X1))
          & member(sK1(X0,X1),X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f45,f46]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ( member(X0,product(X1))
        | ? [X2] :
            ( ~ member(X0,X2)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( member(X0,X2)
            | ~ member(X2,X1) )
        | ~ member(X0,product(X1)) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ( member(X0,product(X1))
        | ? [X2] :
            ( ~ member(X0,X2)
            & member(X2,X1) ) )
      & ( ! [X3] :
            ( member(X0,X3)
            | ~ member(X3,X1) )
        | ~ member(X0,product(X1)) ) ),
    inference(rectify,[],[f48]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X0,X2)
          & member(X2,X1) )
     => ( ~ member(X0,sK2(X0,X1))
        & member(sK2(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( member(X0,product(X1))
        | ( ~ member(X0,sK2(X0,X1))
          & member(sK2(X0,X1),X1) ) )
      & ( ! [X3] :
            ( member(X0,X3)
            | ~ member(X3,X1) )
        | ~ member(X0,product(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f50]) ).

fof(f52,plain,
    ? [X0,X1,X2] :
      ( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
        | ~ subset(X0,X1) )
      & ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
        | subset(X0,X1) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
        | ~ subset(X0,X1) )
      & ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
        | subset(X0,X1) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(flattening,[],[f52]) ).

fof(f54,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
          | ~ subset(X0,X1) )
        & ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
          | subset(X0,X1) )
        & subset(X1,X2)
        & subset(X0,X2) )
   => ( ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
        | ~ subset(sK3,sK4) )
      & ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
        | subset(sK3,sK4) )
      & subset(sK4,sK5)
      & subset(sK3,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ( ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
      | ~ subset(sK3,sK4) )
    & ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
      | subset(sK3,sK4) )
    & subset(sK4,sK5)
    & subset(sK3,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f53,f54]) ).

fof(f56,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f70,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f17]) ).

fof(f72,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X1)
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( member(X0,sum(X1))
      | ~ member(X0,X2)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f82,plain,
    ! [X3,X0,X1] :
      ( member(X0,X3)
      | ~ member(X3,X1)
      | ~ member(X0,product(X1)) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
      | member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f85,plain,
    subset(sK3,sK5),
    inference(cnf_transformation,[],[f55]) ).

fof(f87,plain,
    ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
    | subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f88,plain,
    ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
    | ~ subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_53,plain,
    ( ~ equal_set(X0,X1)
    | subset(X1,X0) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_54,plain,
    ( ~ equal_set(X0,X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_58,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_59,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_63,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_64,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_65,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_72,plain,
    ( ~ member(X0,X1)
    | ~ member(X1,X2)
    | member(X0,sum(X2)) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_74,plain,
    ( ~ member(X0,sum(X1))
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_76,plain,
    ( member(sK2(X0,X1),X1)
    | member(X0,product(X1)) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_77,plain,
    ( ~ member(X0,product(X1))
    | ~ member(X2,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_78,negated_conjecture,
    ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
    | ~ subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_79,negated_conjecture,
    ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
    | subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_81,negated_conjecture,
    subset(sK3,sK5),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_133,plain,
    ( member(sK0(sK3,sK4),sK3)
    | subset(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_385,plain,
    ( ~ member(X0,intersection(X1,difference(X2,X3)))
    | member(X0,difference(X2,X3)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_405,plain,
    ( subset(intersection(sK3,difference(sK5,sK4)),empty_set)
    | subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_54,c_79]) ).

cnf(c_416,plain,
    subset(empty_set,X0),
    inference(resolution,[status(thm)],[c_63,c_50]) ).

cnf(c_523,plain,
    ( ~ subset(X0,X1)
    | member(sK0(X0,X2),X1)
    | subset(X0,X2) ),
    inference(resolution,[status(thm)],[c_51,c_50]) ).

cnf(c_554,plain,
    ( ~ subset(intersection(sK3,difference(sK5,sK4)),empty_set)
    | ~ subset(empty_set,intersection(sK3,difference(sK5,sK4)))
    | ~ subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_52,c_78]) ).

cnf(c_558,plain,
    ( ~ subset(intersection(sK3,difference(sK5,sK4)),empty_set)
    | ~ subset(sK3,sK4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_554,c_416]) ).

cnf(c_605,plain,
    ( member(sK2(X0,intersection(X1,X2)),X2)
    | member(X0,product(intersection(X1,X2))) ),
    inference(resolution,[status(thm)],[c_76,c_58]) ).

cnf(c_606,plain,
    ( member(sK2(X0,intersection(X1,X2)),X1)
    | member(X0,product(intersection(X1,X2))) ),
    inference(resolution,[status(thm)],[c_76,c_59]) ).

cnf(c_1060,plain,
    ( ~ member(X0,sum(intersection(X1,X2)))
    | member(sK1(X0,intersection(X1,X2)),X2) ),
    inference(resolution,[status(thm)],[c_74,c_58]) ).

cnf(c_1061,plain,
    ( ~ member(X0,sum(intersection(X1,X2)))
    | member(sK1(X0,intersection(X1,X2)),X1) ),
    inference(resolution,[status(thm)],[c_74,c_59]) ).

cnf(c_1402,plain,
    ( member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
    | subset(intersection(sK3,difference(sK5,sK4)),empty_set) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1749,plain,
    ( ~ subset(intersection(X0,X1),X2)
    | ~ member(X3,X0)
    | ~ member(X3,X1)
    | member(X3,X2) ),
    inference(resolution,[status(thm)],[c_57,c_51]) ).

cnf(c_1787,plain,
    ( subset(empty_set,intersection(sK3,difference(sK5,sK4)))
    | subset(sK3,sK4) ),
    inference(superposition,[status(thm)],[c_79,c_53]) ).

cnf(c_1792,plain,
    ( ~ subset(intersection(sK3,difference(sK5,sK4)),empty_set)
    | equal_set(empty_set,intersection(sK3,difference(sK5,sK4)))
    | subset(sK3,sK4) ),
    inference(superposition,[status(thm)],[c_1787,c_52]) ).

cnf(c_1793,plain,
    ( equal_set(empty_set,intersection(sK3,difference(sK5,sK4)))
    | subset(sK3,sK4) ),
    inference(global_subsumption_just,[status(thm)],[c_1792,c_405,c_1792]) ).

cnf(c_1855,plain,
    ( subset(intersection(sK3,difference(sK5,sK4)),empty_set)
    | subset(sK3,sK4) ),
    inference(superposition,[status(thm)],[c_1793,c_53]) ).

cnf(c_2044,plain,
    ( ~ subset(intersection(X0,X1),X2)
    | ~ member(X3,X0)
    | ~ member(X3,X1)
    | member(X3,X2) ),
    inference(superposition,[status(thm)],[c_57,c_51]) ).

cnf(c_2773,plain,
    ( ~ member(X0,difference(sK5,sK4))
    | ~ member(X0,sK3)
    | member(X0,empty_set)
    | subset(sK3,sK4) ),
    inference(superposition,[status(thm)],[c_1855,c_2044]) ).

cnf(c_2775,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,difference(sK5,sK4))
    | subset(sK3,sK4) ),
    inference(global_subsumption_just,[status(thm)],[c_2773,c_63,c_2773]) ).

cnf(c_2776,plain,
    ( ~ member(X0,difference(sK5,sK4))
    | ~ member(X0,sK3)
    | subset(sK3,sK4) ),
    inference(renaming,[status(thm)],[c_2775]) ).

cnf(c_2828,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,sK5)
    | member(X0,sK4)
    | subset(sK3,sK4) ),
    inference(superposition,[status(thm)],[c_64,c_2776]) ).

cnf(c_2834,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,sK5)
    | member(X0,sK4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2828,c_51]) ).

cnf(c_4198,plain,
    ( ~ subset(X0,empty_set)
    | subset(X0,X1) ),
    inference(resolution,[status(thm)],[c_523,c_63]) ).

cnf(c_4674,plain,
    ( subset(intersection(sK3,difference(sK5,sK4)),X0)
    | subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_4198,c_405]) ).

cnf(c_5915,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
    | member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),difference(sK5,sK4)) ),
    inference(instantiation,[status(thm)],[c_385]) ).

cnf(c_11769,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),difference(sK5,sK4))
    | ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK4) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_12186,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
    | member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK3) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_18170,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
    | ~ member(X0,sK0(intersection(sK3,difference(sK5,sK4)),empty_set))
    | member(X0,sum(intersection(sK3,difference(sK5,sK4)))) ),
    inference(instantiation,[status(thm)],[c_72]) ).

cnf(c_18172,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
    | ~ member(X0,product(intersection(sK3,difference(sK5,sK4))))
    | member(X0,sK0(intersection(sK3,difference(sK5,sK4)),empty_set)) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_18595,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK3)
    | ~ subset(sK3,X0)
    | member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_21961,plain,
    ( ~ member(X0,difference(sK5,sK4))
    | ~ member(X0,sK3)
    | member(X0,X1)
    | subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_1749,c_4674]) ).

cnf(c_24499,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,difference(sK5,sK4))
    | subset(sK3,sK4) ),
    inference(global_subsumption_just,[status(thm)],[c_21961,c_2776]) ).

cnf(c_24500,plain,
    ( ~ member(X0,difference(sK5,sK4))
    | ~ member(X0,sK3)
    | subset(sK3,sK4) ),
    inference(renaming,[status(thm)],[c_24499]) ).

cnf(c_24583,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,sK5)
    | member(X0,sK4)
    | subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_24500,c_64]) ).

cnf(c_24590,plain,
    ( ~ member(sK2(X0,intersection(X1,difference(sK5,sK4))),sK3)
    | member(X0,product(intersection(X1,difference(sK5,sK4))))
    | subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_24500,c_605]) ).

cnf(c_24606,plain,
    ( ~ member(sK1(X0,intersection(X1,difference(sK5,sK4))),sK3)
    | ~ member(X0,sum(intersection(X1,difference(sK5,sK4))))
    | subset(sK3,sK4) ),
    inference(resolution,[status(thm)],[c_24500,c_1060]) ).

cnf(c_24828,plain,
    ( member(X0,sK4)
    | ~ member(X0,sK5)
    | ~ member(X0,sK3) ),
    inference(global_subsumption_just,[status(thm)],[c_24583,c_2834]) ).

cnf(c_24829,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,sK5)
    | member(X0,sK4) ),
    inference(renaming,[status(thm)],[c_24828]) ).

cnf(c_24856,plain,
    ( ~ member(sK0(X0,sK4),sK3)
    | ~ member(sK0(X0,sK4),sK5)
    | subset(X0,sK4) ),
    inference(resolution,[status(thm)],[c_24829,c_49]) ).

cnf(c_29896,plain,
    ( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK3)
    | ~ subset(sK3,sK4)
    | member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK4) ),
    inference(instantiation,[status(thm)],[c_18595]) ).

cnf(c_31171,plain,
    ( member(X0,product(intersection(X1,difference(sK5,sK4))))
    | ~ member(sK2(X0,intersection(X1,difference(sK5,sK4))),sK3) ),
    inference(global_subsumption_just,[status(thm)],[c_24590,c_558,c_1402,c_5915,c_11769,c_12186,c_24590,c_29896]) ).

cnf(c_31172,plain,
    ( ~ member(sK2(X0,intersection(X1,difference(sK5,sK4))),sK3)
    | member(X0,product(intersection(X1,difference(sK5,sK4)))) ),
    inference(renaming,[status(thm)],[c_31171]) ).

cnf(c_31221,plain,
    member(X0,product(intersection(sK3,difference(sK5,sK4)))),
    inference(resolution,[status(thm)],[c_31172,c_606]) ).

cnf(c_32042,plain,
    ( ~ member(X0,sum(intersection(X1,difference(sK5,sK4))))
    | ~ member(sK1(X0,intersection(X1,difference(sK5,sK4))),sK3) ),
    inference(global_subsumption_just,[status(thm)],[c_24606,c_558,c_1402,c_5915,c_11769,c_12186,c_24606,c_29896]) ).

cnf(c_32043,plain,
    ( ~ member(sK1(X0,intersection(X1,difference(sK5,sK4))),sK3)
    | ~ member(X0,sum(intersection(X1,difference(sK5,sK4)))) ),
    inference(renaming,[status(thm)],[c_32042]) ).

cnf(c_32055,plain,
    ~ member(X0,sum(intersection(sK3,difference(sK5,sK4)))),
    inference(resolution,[status(thm)],[c_32043,c_1061]) ).

cnf(c_47022,plain,
    ( ~ member(sK0(X0,sK4),sK3)
    | ~ subset(X0,sK5)
    | subset(X0,sK4) ),
    inference(resolution,[status(thm)],[c_24856,c_523]) ).

cnf(c_47023,plain,
    ( ~ member(sK0(sK3,sK4),sK3)
    | ~ subset(sK3,sK5)
    | subset(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_47022]) ).

cnf(c_47024,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_47023,c_32055,c_31221,c_18172,c_18170,c_1402,c_558,c_133,c_81]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET697+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n026.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 : Thu May  2 20:55:51 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 49.49/7.73  % SZS status Started for theBenchmark.p
% 49.49/7.73  % SZS status Theorem for theBenchmark.p
% 49.49/7.73  
% 49.49/7.73  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 49.49/7.73  
% 49.49/7.73  ------  iProver source info
% 49.49/7.73  
% 49.49/7.73  git: date: 2024-05-02 19:28:25 +0000
% 49.49/7.73  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 49.49/7.73  git: non_committed_changes: false
% 49.49/7.73  
% 49.49/7.73  ------ Parsing...
% 49.49/7.73  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 49.49/7.73  
% 49.49/7.73  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 49.49/7.73  
% 49.49/7.73  ------ Preprocessing...
% 49.49/7.73  
% 49.49/7.73  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 49.49/7.73  ------ Proving...
% 49.49/7.73  ------ Problem Properties 
% 49.49/7.73  
% 49.49/7.73  
% 49.49/7.73  clauses                                 33
% 49.49/7.73  conjectures                             4
% 49.49/7.73  EPR                                     7
% 49.49/7.73  Horn                                    27
% 49.49/7.73  unary                                   6
% 49.49/7.73  binary                                  19
% 49.49/7.73  lits                                    68
% 49.49/7.73  lits eq                                 3
% 49.49/7.73  fd_pure                                 0
% 49.49/7.73  fd_pseudo                               0
% 49.49/7.73  fd_cond                                 0
% 49.49/7.73  fd_pseudo_cond                          2
% 49.49/7.73  AC symbols                              0
% 49.49/7.73  
% 49.49/7.73  ------ Input Options Time Limit: Unbounded
% 49.49/7.73  
% 49.49/7.73  
% 49.49/7.73  ------ 
% 49.49/7.73  Current options:
% 49.49/7.73  ------ 
% 49.49/7.73  
% 49.49/7.73  
% 49.49/7.73  
% 49.49/7.73  
% 49.49/7.73  ------ Proving...
% 49.49/7.73  
% 49.49/7.73  
% 49.49/7.73  % SZS status Theorem for theBenchmark.p
% 49.49/7.73  
% 49.49/7.73  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.49/7.74  
% 49.49/7.74  
%------------------------------------------------------------------------------