TSTP Solution File: SET690+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET690+4 : 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 03:01:15 EDT 2024

% Result   : Theorem 124.42s 17.27s
% Output   : CNFRefutation 124.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   90 (   2 unt;   0 def)
%            Number of atoms       :  255 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  274 ( 109   ~; 124   |;  27   &)
%                                         (  10 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  151 (   8 sgn  87   !;  12   ?)

% 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(f5,axiom,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

fof(f12,conjecture,
    ! [X0,X1,X5] :
      ( equal_set(union(intersection(X0,X1),X5),intersection(X0,union(X1,X5)))
    <=> subset(X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI12) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X5] :
        ( equal_set(union(intersection(X0,X1),X5),intersection(X0,union(X1,X5)))
      <=> subset(X5,X0) ),
    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(f16,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

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

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

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

fof(f27,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(f28,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,[],[f27]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,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])],[f28,f29]) ).

fof(f31,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(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(flattening,[],[f31]) ).

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

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f36]) ).

fof(f51,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(X2,X0)
        | ~ equal_set(union(intersection(X0,X1),X2),intersection(X0,union(X1,X2))) )
      & ( subset(X2,X0)
        | equal_set(union(intersection(X0,X1),X2),intersection(X0,union(X1,X2))) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f52,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(X2,X0)
          | ~ equal_set(union(intersection(X0,X1),X2),intersection(X0,union(X1,X2))) )
        & ( subset(X2,X0)
          | equal_set(union(intersection(X0,X1),X2),intersection(X0,union(X1,X2))) ) )
   => ( ( ~ subset(sK5,sK3)
        | ~ equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) )
      & ( subset(sK5,sK3)
        | equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ( ( ~ subset(sK5,sK3)
      | ~ equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) )
    & ( subset(sK5,sK3)
      | equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f51,f52]) ).

fof(f54,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f83,plain,
    ( subset(sK5,sK3)
    | equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f84,plain,
    ( ~ subset(sK5,sK3)
    | ~ equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_53,plain,
    ( ~ equal_set(X0,X1)
    | subset(X1,X0) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_54,plain,
    ( ~ equal_set(X0,X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_58,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_59,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_60,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_61,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_62,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_78,negated_conjecture,
    ( ~ equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5)))
    | ~ subset(sK5,sK3) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_79,negated_conjecture,
    ( equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5)))
    | subset(sK5,sK3) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_212,plain,
    ( ~ subset(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5))
    | ~ subset(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5)))
    | equal_set(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_242,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),intersection(sK3,union(sK4,sK5)))
    | subset(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_243,plain,
    ( member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(intersection(sK3,sK4),sK5))
    | subset(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_398,plain,
    ( subset(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5)))
    | subset(sK5,sK3) ),
    inference(resolution,[status(thm)],[c_54,c_79]) ).

cnf(c_528,plain,
    ( ~ subset(union(X0,X1),X2)
    | ~ member(X3,X1)
    | member(X3,X2) ),
    inference(resolution,[status(thm)],[c_51,c_60]) ).

cnf(c_1597,plain,
    ( subset(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5))
    | subset(sK5,sK3) ),
    inference(superposition,[status(thm)],[c_79,c_53]) ).

cnf(c_1609,plain,
    ( ~ subset(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5)))
    | equal_set(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5))
    | subset(sK5,sK3) ),
    inference(superposition,[status(thm)],[c_1597,c_52]) ).

cnf(c_1610,plain,
    ( equal_set(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5))
    | subset(sK5,sK3) ),
    inference(global_subsumption_just,[status(thm)],[c_1609,c_398,c_1609]) ).

cnf(c_1622,plain,
    ( subset(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5)))
    | subset(sK5,sK3) ),
    inference(superposition,[status(thm)],[c_1610,c_53]) ).

cnf(c_1773,plain,
    ( ~ subset(union(X0,X1),X2)
    | ~ member(X3,X1)
    | member(X3,X2) ),
    inference(superposition,[status(thm)],[c_60,c_51]) ).

cnf(c_2099,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),union(intersection(sK3,sK4),sK5))
    | subset(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_2100,plain,
    ( member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),intersection(sK3,union(sK4,sK5)))
    | subset(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_3388,plain,
    ( ~ member(X0,sK5)
    | member(X0,intersection(sK3,union(sK4,sK5)))
    | subset(sK5,sK3) ),
    inference(superposition,[status(thm)],[c_1622,c_1773]) ).

cnf(c_3449,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3)
    | subset(sK5,sK3) ),
    inference(superposition,[status(thm)],[c_3388,c_59]) ).

cnf(c_3457,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3449,c_51]) ).

cnf(c_5165,plain,
    ( ~ member(X0,sK5)
    | member(X0,intersection(sK3,union(sK4,sK5)))
    | subset(sK5,sK3) ),
    inference(resolution,[status(thm)],[c_528,c_398]) ).

cnf(c_5778,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3)
    | subset(sK5,sK3) ),
    inference(resolution,[status(thm)],[c_5165,c_59]) ).

cnf(c_5949,plain,
    ( member(X0,sK3)
    | ~ member(X0,sK5) ),
    inference(global_subsumption_just,[status(thm)],[c_5778,c_3457]) ).

cnf(c_5950,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3) ),
    inference(renaming,[status(thm)],[c_5949]) ).

cnf(c_5959,plain,
    ( ~ member(sK0(X0,sK3),sK5)
    | subset(X0,sK3) ),
    inference(resolution,[status(thm)],[c_5950,c_49]) ).

cnf(c_8506,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(intersection(sK3,sK4),sK5))
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),intersection(sK3,sK4))
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK5) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_12573,plain,
    subset(sK5,sK3),
    inference(resolution,[status(thm)],[c_5959,c_50]) ).

cnf(c_13408,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK5)
    | ~ subset(sK5,X0)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_13409,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK5)
    | ~ subset(sK5,sK3)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK3) ),
    inference(instantiation,[status(thm)],[c_13408]) ).

cnf(c_15489,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),sK5)
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),union(intersection(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_15518,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),intersection(sK3,sK4))
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),union(intersection(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_19125,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(sK4,sK5))
    | ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK3)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),intersection(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_19535,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),sK3)
    | ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),sK4)
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),intersection(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_102874,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),intersection(sK3,union(sK4,sK5)))
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),union(sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_102883,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),intersection(sK3,union(sK4,sK5)))
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),sK3) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_103436,plain,
    ( ~ member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),union(sK4,sK5))
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),sK5)
    | member(sK0(intersection(sK3,union(sK4,sK5)),union(intersection(sK3,sK4),sK5)),sK4) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_110976,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),intersection(sK3,sK4))
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK3) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_110977,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),intersection(sK3,sK4))
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK4) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_111060,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),X0)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_111061,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),X0)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(X1,X0)) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_193648,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK5)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_111061]) ).

cnf(c_193650,plain,
    ( ~ member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),sK4)
    | member(sK0(union(intersection(sK3,sK4),sK5),intersection(sK3,union(sK4,sK5))),union(sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_111060]) ).

cnf(c_193651,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_193650,c_193648,c_110976,c_110977,c_103436,c_102883,c_102874,c_19535,c_19125,c_15518,c_15489,c_13409,c_12573,c_8506,c_2099,c_2100,c_242,c_243,c_212,c_78]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET690+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 20:37:58 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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
% 124.42/17.27  % SZS status Started for theBenchmark.p
% 124.42/17.27  % SZS status Theorem for theBenchmark.p
% 124.42/17.27  
% 124.42/17.27  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 124.42/17.27  
% 124.42/17.27  ------  iProver source info
% 124.42/17.27  
% 124.42/17.27  git: date: 2024-05-02 19:28:25 +0000
% 124.42/17.27  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 124.42/17.27  git: non_committed_changes: false
% 124.42/17.27  
% 124.42/17.27  ------ Parsing...
% 124.42/17.27  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 124.42/17.27  
% 124.42/17.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 124.42/17.27  
% 124.42/17.27  ------ Preprocessing...
% 124.42/17.27  
% 124.42/17.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 124.42/17.27  ------ Proving...
% 124.42/17.27  ------ Problem Properties 
% 124.42/17.27  
% 124.42/17.27  
% 124.42/17.27  clauses                                 31
% 124.42/17.27  conjectures                             2
% 124.42/17.27  EPR                                     5
% 124.42/17.27  Horn                                    25
% 124.42/17.27  unary                                   4
% 124.42/17.27  binary                                  19
% 124.42/17.27  lits                                    66
% 124.42/17.27  lits eq                                 3
% 124.42/17.27  fd_pure                                 0
% 124.42/17.27  fd_pseudo                               0
% 124.42/17.27  fd_cond                                 0
% 124.42/17.27  fd_pseudo_cond                          2
% 124.42/17.27  AC symbols                              0
% 124.42/17.27  
% 124.42/17.27  ------ Input Options Time Limit: Unbounded
% 124.42/17.27  
% 124.42/17.27  
% 124.42/17.27  ------ 
% 124.42/17.27  Current options:
% 124.42/17.27  ------ 
% 124.42/17.27  
% 124.42/17.27  
% 124.42/17.27  
% 124.42/17.27  
% 124.42/17.27  ------ Proving...
% 124.42/17.27  
% 124.42/17.27  
% 124.42/17.27  % SZS status Theorem for theBenchmark.p
% 124.42/17.27  
% 124.42/17.27  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 124.42/17.27  
% 124.42/17.28  
%------------------------------------------------------------------------------