TSTP Solution File: SET634+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET634+3 : 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 03:01:03 EDT 2024

% Result   : Theorem 7.66s 1.64s
% Output   : CNFRefutation 7.66s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

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

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( ~ member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f5,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

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

fof(f8,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f9,conjecture,
    ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_and_intersection) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
    inference(negated_conjecture,[],[f9]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( member(X2,X0)
        <~> member(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f13,plain,
    ? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),X2),
    inference(ennf_transformation,[],[f10]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK0(X0,X1),X1)
          | ~ member(sK0(X0,X1),X0) )
        & ( member(sK0(X0,X1),X1)
          | member(sK0(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ member(sK0(X0,X1),X1)
          | ~ member(sK0(X0,X1),X0) )
        & ( member(sK0(X0,X1),X1)
          | member(sK0(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(flattening,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f21]) ).

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,[],[f12]) ).

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(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),X2)
   => intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f13,f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK0(X0,X1),X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK0(X0,X1),X1)
      | ~ member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f44,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f49,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f52,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f53,plain,
    intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X0)
    | ~ member(sK0(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_50,plain,
    ( X0 = X1
    | member(sK0(X0,X1),X0)
    | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_51,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_52,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_53,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_55,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_56,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_57,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_60,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_63,plain,
    ( ~ member(sK2(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_64,plain,
    ( member(sK2(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_65,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_66,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_67,negated_conjecture,
    intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_387,plain,
    difference(sK4,sK5) = sP0_iProver_def,
    definition ).

cnf(c_388,plain,
    intersection(sK3,sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_389,plain,
    intersection(sK3,sK4) = sP2_iProver_def,
    definition ).

cnf(c_390,plain,
    difference(sP2_iProver_def,sK5) = sP3_iProver_def,
    definition ).

cnf(c_391,negated_conjecture,
    sP1_iProver_def != sP3_iProver_def,
    inference(demodulation,[status(thm)],[c_67,c_389,c_390,c_387,c_388]) ).

cnf(c_392,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_394,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_631,plain,
    intersection(sP0_iProver_def,sK3) = sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_388,c_60]) ).

cnf(c_640,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X2,X1)) ),
    inference(superposition,[status(thm)],[c_60,c_51]) ).

cnf(c_663,plain,
    ( ~ member(X0,sP2_iProver_def)
    | member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_389,c_52]) ).

cnf(c_664,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_631,c_52]) ).

cnf(c_681,plain,
    ( ~ member(X0,sP2_iProver_def)
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_389,c_53]) ).

cnf(c_682,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_631,c_53]) ).

cnf(c_695,plain,
    ( member(sK2(difference(X0,X1),X2),X0)
    | subset(difference(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_64,c_56]) ).

cnf(c_696,plain,
    ( ~ member(X0,sP0_iProver_def)
    | member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_387,c_56]) ).

cnf(c_697,plain,
    ( ~ member(X0,sP3_iProver_def)
    | member(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_390,c_56]) ).

cnf(c_740,plain,
    ( member(sK2(sP1_iProver_def,X0),sP0_iProver_def)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_64,c_682]) ).

cnf(c_756,plain,
    ( member(sK2(sP3_iProver_def,X0),sP2_iProver_def)
    | subset(sP3_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_64,c_697]) ).

cnf(c_781,plain,
    ( ~ member(X0,sK4)
    | member(X0,sK5)
    | member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_387,c_54]) ).

cnf(c_782,plain,
    ( ~ member(X0,sP2_iProver_def)
    | member(X0,sK5)
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_390,c_54]) ).

cnf(c_784,plain,
    ( ~ member(sK2(X0,difference(X1,X2)),X1)
    | member(sK2(X0,difference(X1,X2)),X2)
    | subset(X0,difference(X1,X2)) ),
    inference(superposition,[status(thm)],[c_54,c_63]) ).

cnf(c_802,plain,
    ( ~ member(X0,sK5)
    | ~ member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_387,c_55]) ).

cnf(c_803,plain,
    ( ~ member(X0,sK5)
    | ~ member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_390,c_55]) ).

cnf(c_841,plain,
    ( sP1_iProver_def != X0
    | sP3_iProver_def != X0
    | sP1_iProver_def = sP3_iProver_def ),
    inference(instantiation,[status(thm)],[c_394]) ).

cnf(c_877,plain,
    ( X0 = sP1_iProver_def
    | member(sK0(X0,sP1_iProver_def),X0)
    | member(sK0(X0,sP1_iProver_def),sK3) ),
    inference(superposition,[status(thm)],[c_50,c_664]) ).

cnf(c_1007,plain,
    ( sP1_iProver_def != sP1_iProver_def
    | sP3_iProver_def != sP1_iProver_def
    | sP1_iProver_def = sP3_iProver_def ),
    inference(instantiation,[status(thm)],[c_841]) ).

cnf(c_1008,plain,
    sP1_iProver_def = sP1_iProver_def,
    inference(instantiation,[status(thm)],[c_392]) ).

cnf(c_1016,plain,
    ( member(sK2(sP1_iProver_def,X0),sK4)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_740,c_696]) ).

cnf(c_1045,plain,
    ( member(sK2(sP3_iProver_def,X0),sK4)
    | subset(sP3_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_756,c_663]) ).

cnf(c_1076,plain,
    ( ~ member(sK2(sP1_iProver_def,X0),sK5)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_740,c_802]) ).

cnf(c_1136,plain,
    ( ~ member(sK0(sP3_iProver_def,X0),sK5)
    | X0 = sP3_iProver_def
    | member(sK0(sP3_iProver_def,X0),X0) ),
    inference(superposition,[status(thm)],[c_50,c_803]) ).

cnf(c_1155,plain,
    ( sP3_iProver_def = sP1_iProver_def
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP1_iProver_def)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP3_iProver_def) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1156,plain,
    ( ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sP1_iProver_def)
    | ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sP3_iProver_def)
    | sP3_iProver_def = sP1_iProver_def ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1172,plain,
    ( ~ subset(sK4,X0)
    | member(sK2(sP1_iProver_def,X1),X0)
    | subset(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_1016,c_65]) ).

cnf(c_1185,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,sK4)
    | member(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_389,c_640]) ).

cnf(c_1186,plain,
    ( ~ member(X0,sK3)
    | ~ member(X0,sP0_iProver_def)
    | member(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_631,c_640]) ).

cnf(c_1506,plain,
    ( ~ subset(sK4,X0)
    | member(sK2(sP3_iProver_def,X1),X0)
    | subset(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_1045,c_65]) ).

cnf(c_2210,plain,
    subset(difference(X0,X1),X0),
    inference(superposition,[status(thm)],[c_695,c_63]) ).

cnf(c_2396,plain,
    ( ~ subset(X0,difference(X0,X1))
    | difference(X0,X1) = X0 ),
    inference(superposition,[status(thm)],[c_2210,c_57]) ).

cnf(c_2655,plain,
    ( member(sK2(X0,difference(X0,X1)),X1)
    | subset(X0,difference(X0,X1)) ),
    inference(superposition,[status(thm)],[c_64,c_784]) ).

cnf(c_2735,plain,
    ( ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sP1_iProver_def)
    | ~ subset(sP1_iProver_def,X0)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),X0) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_3354,plain,
    ( ~ subset(sK4,X0)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_1172,c_63]) ).

cnf(c_3897,plain,
    ( ~ subset(sK4,X0)
    | subset(sP3_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_1506,c_63]) ).

cnf(c_5088,plain,
    subset(sP1_iProver_def,difference(sP1_iProver_def,sK5)),
    inference(superposition,[status(thm)],[c_2655,c_1076]) ).

cnf(c_5292,plain,
    difference(sP1_iProver_def,sK5) = sP1_iProver_def,
    inference(superposition,[status(thm)],[c_5088,c_2396]) ).

cnf(c_5324,plain,
    ( ~ member(X0,sK5)
    | ~ member(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_5292,c_55]) ).

cnf(c_6608,plain,
    ( sP1_iProver_def = sP3_iProver_def
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sK3)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_877,c_697]) ).

cnf(c_6615,plain,
    ( member(sK0(sP3_iProver_def,sP1_iProver_def),sK3)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP2_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6608,c_391]) ).

cnf(c_6888,plain,
    member(sK0(sP3_iProver_def,sP1_iProver_def),sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_6615,c_681]) ).

cnf(c_6889,plain,
    ( ~ subset(sK3,X0)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_6888,c_65]) ).

cnf(c_6890,plain,
    ( ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sP0_iProver_def)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_6888,c_1186]) ).

cnf(c_6891,plain,
    ( ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sK4)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_6888,c_1185]) ).

cnf(c_6933,plain,
    ( ~ subset(sK3,sP2_iProver_def)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sK4) ),
    inference(superposition,[status(thm)],[c_6889,c_663]) ).

cnf(c_7069,plain,
    ( ~ subset(sK4,X0)
    | ~ subset(sK3,sP2_iProver_def)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_6933,c_65]) ).

cnf(c_8442,plain,
    ( ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sP3_iProver_def)
    | ~ subset(sP3_iProver_def,X0)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),X0) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_9062,plain,
    ( ~ subset(sK4,X0)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_7069,c_391,c_1007,c_1008,c_1155,c_2735,c_3354,c_3897,c_8442]) ).

cnf(c_9079,plain,
    ( ~ subset(sK4,sK4)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sK5)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_9062,c_781]) ).

cnf(c_9091,plain,
    ( ~ subset(sK4,sK4)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_9062,c_6891]) ).

cnf(c_9098,plain,
    member(sK0(sP3_iProver_def,sP1_iProver_def),sP2_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_9091,c_66]) ).

cnf(c_9124,plain,
    ( member(sK0(sP3_iProver_def,sP1_iProver_def),sK5)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9079,c_66]) ).

cnf(c_9317,plain,
    ( member(sK0(sP3_iProver_def,sP1_iProver_def),sK5)
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_9098,c_782]) ).

cnf(c_10833,plain,
    member(sK0(sP3_iProver_def,sP1_iProver_def),sK5),
    inference(global_subsumption_just,[status(thm)],[c_9124,c_391,c_1007,c_1008,c_1156,c_6890,c_9124,c_9317]) ).

cnf(c_10836,plain,
    ( sP1_iProver_def = sP3_iProver_def
    | member(sK0(sP3_iProver_def,sP1_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_10833,c_1136]) ).

cnf(c_10837,plain,
    member(sK0(sP3_iProver_def,sP1_iProver_def),sP1_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_10836,c_391]) ).

cnf(c_10842,plain,
    ~ member(sK0(sP3_iProver_def,sP1_iProver_def),sK5),
    inference(superposition,[status(thm)],[c_10837,c_5324]) ).

cnf(c_10845,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_10842,c_10833]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET634+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n026.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:54:36 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.43  Running first-order theorem proving
% 0.17/0.43  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
% 7.66/1.64  % SZS status Started for theBenchmark.p
% 7.66/1.64  % SZS status Theorem for theBenchmark.p
% 7.66/1.64  
% 7.66/1.64  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.66/1.64  
% 7.66/1.64  ------  iProver source info
% 7.66/1.64  
% 7.66/1.64  git: date: 2024-05-02 19:28:25 +0000
% 7.66/1.64  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.66/1.64  git: non_committed_changes: false
% 7.66/1.64  
% 7.66/1.64  ------ Parsing...
% 7.66/1.64  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.66/1.64  
% 7.66/1.64  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.66/1.64  
% 7.66/1.64  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.66/1.64  
% 7.66/1.64  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.66/1.64  ------ Proving...
% 7.66/1.64  ------ Problem Properties 
% 7.66/1.64  
% 7.66/1.64  
% 7.66/1.64  clauses                                 21
% 7.66/1.64  conjectures                             1
% 7.66/1.64  EPR                                     4
% 7.66/1.64  Horn                                    17
% 7.66/1.64  unary                                   7
% 7.66/1.64  binary                                  6
% 7.66/1.64  lits                                    43
% 7.66/1.64  lits eq                                 11
% 7.66/1.64  fd_pure                                 0
% 7.66/1.64  fd_pseudo                               0
% 7.66/1.64  fd_cond                                 0
% 7.66/1.64  fd_pseudo_cond                          5
% 7.66/1.64  AC symbols                              0
% 7.66/1.64  
% 7.66/1.64  ------ Schedule dynamic 5 is on 
% 7.66/1.64  
% 7.66/1.64  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.66/1.64  
% 7.66/1.64  
% 7.66/1.64  ------ 
% 7.66/1.64  Current options:
% 7.66/1.64  ------ 
% 7.66/1.64  
% 7.66/1.64  
% 7.66/1.64  
% 7.66/1.64  
% 7.66/1.64  ------ Proving...
% 7.66/1.64  
% 7.66/1.64  
% 7.66/1.64  % SZS status Theorem for theBenchmark.p
% 7.66/1.64  
% 7.66/1.64  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.66/1.64  
% 7.66/1.64  
%------------------------------------------------------------------------------