TSTP Solution File: SET169+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET169+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 : Mon Jun 24 14:33:44 EDT 2024

% Result   : Theorem 14.01s 2.71s
% Output   : CNFRefutation 14.01s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

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

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

fof(f5,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f7,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f9,conjecture,
    ! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_distributes_over_union) ).

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

fof(f11,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f12,plain,
    ? [X0,X1,X2] : intersection(X0,union(X1,X2)) != union(intersection(X0,X1),intersection(X0,X2)),
    inference(ennf_transformation,[],[f10]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f13]) ).

fof(f15,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(f16,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,[],[f15]) ).

fof(f19,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,[],[f11]) ).

fof(f20,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,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,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])],[f20,f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK1(X0,X1),X1)
          | ~ member(sK1(X0,X1),X0) )
        & ( member(sK1(X0,X1),X1)
          | member(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK1(X0,X1),X1)
            | ~ member(sK1(X0,X1),X0) )
          & ( member(sK1(X0,X1),X1)
            | member(sK1(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).

fof(f27,plain,
    ( ? [X0,X1,X2] : intersection(X0,union(X1,X2)) != union(intersection(X0,X1),intersection(X0,X2))
   => intersection(sK2,union(sK3,sK4)) != union(intersection(sK2,sK3),intersection(sK2,sK4)) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    intersection(sK2,union(sK3,sK4)) != union(intersection(sK2,sK3),intersection(sK2,sK4)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f27]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f39,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f40,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f43,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f48,plain,
    intersection(sK2,union(sK3,sK4)) != union(intersection(sK2,sK3),intersection(sK2,sK4)),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_49,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_51,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_52,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_53,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_54,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_59,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_62,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_63,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_64,plain,
    ( ~ member(sK1(X0,X1),X0)
    | ~ member(sK1(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_65,plain,
    ( X0 = X1
    | member(sK1(X0,X1),X0)
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_66,negated_conjecture,
    union(intersection(sK2,sK3),intersection(sK2,sK4)) != intersection(sK2,union(sK3,sK4)),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_67,plain,
    subset(sK2,sK2),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_341,plain,
    intersection(sK2,sK3) = sP0_iProver_def,
    definition ).

cnf(c_342,plain,
    intersection(sK2,sK4) = sP1_iProver_def,
    definition ).

cnf(c_343,plain,
    union(sP0_iProver_def,sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_344,plain,
    union(sK3,sK4) = sP3_iProver_def,
    definition ).

cnf(c_345,plain,
    intersection(sK2,sP3_iProver_def) = sP4_iProver_def,
    definition ).

cnf(c_346,negated_conjecture,
    sP2_iProver_def != sP4_iProver_def,
    inference(demodulation,[status(thm)],[c_66,c_344,c_345,c_342,c_341,c_343]) ).

cnf(c_347,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_349,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_351,plain,
    ( X0 != X1
    | X2 != X3
    | ~ member(X1,X3)
    | member(X0,X2) ),
    theory(equality) ).

cnf(c_569,plain,
    intersection(sP3_iProver_def,sK2) = sP4_iProver_def,
    inference(demodulation,[status(thm)],[c_345,c_59]) ).

cnf(c_578,plain,
    ( ~ member(X0,sK4)
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_344,c_49]) ).

cnf(c_579,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_343,c_49]) ).

cnf(c_592,plain,
    ( ~ member(X0,sK3)
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_344,c_50]) ).

cnf(c_607,plain,
    ( ~ member(X0,sP0_iProver_def)
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_341,c_53]) ).

cnf(c_608,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_342,c_53]) ).

cnf(c_609,plain,
    ( ~ member(X0,sP4_iProver_def)
    | member(X0,sK2) ),
    inference(superposition,[status(thm)],[c_569,c_53]) ).

cnf(c_713,plain,
    ( ~ member(X0,sP3_iProver_def)
    | member(X0,sK3)
    | member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_344,c_51]) ).

cnf(c_714,plain,
    ( ~ member(X0,sP2_iProver_def)
    | member(X0,sP0_iProver_def)
    | member(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_343,c_51]) ).

cnf(c_734,plain,
    ( ~ member(X0,sP0_iProver_def)
    | member(X0,sK2) ),
    inference(superposition,[status(thm)],[c_341,c_54]) ).

cnf(c_735,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sK2) ),
    inference(superposition,[status(thm)],[c_342,c_54]) ).

cnf(c_736,plain,
    ( ~ member(X0,sP4_iProver_def)
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_569,c_54]) ).

cnf(c_768,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def)
    | ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def)
    | sP2_iProver_def = sP4_iProver_def ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_769,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_845,plain,
    sP2_iProver_def = sP2_iProver_def,
    inference(instantiation,[status(thm)],[c_347]) ).

cnf(c_846,plain,
    ( X0 != X1
    | sP2_iProver_def != X1
    | sP2_iProver_def = X0 ),
    inference(instantiation,[status(thm)],[c_349]) ).

cnf(c_924,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X2,X1)) ),
    inference(superposition,[status(thm)],[c_59,c_52]) ).

cnf(c_966,plain,
    ( X0 = sP4_iProver_def
    | member(sK1(X0,sP4_iProver_def),X0)
    | member(sK1(X0,sP4_iProver_def),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_65,c_736]) ).

cnf(c_967,plain,
    ( X0 = sP4_iProver_def
    | member(sK1(X0,sP4_iProver_def),X0)
    | member(sK1(X0,sP4_iProver_def),sK2) ),
    inference(superposition,[status(thm)],[c_65,c_609]) ).

cnf(c_1879,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),union(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1892,plain,
    ( X0 != sK1(sP2_iProver_def,sP4_iProver_def)
    | X1 != X2
    | ~ member(sK1(sP2_iProver_def,sP4_iProver_def),X2)
    | member(X0,X1) ),
    inference(instantiation,[status(thm)],[c_351]) ).

cnf(c_2250,plain,
    sK1(sP2_iProver_def,sP4_iProver_def) = sK1(sP2_iProver_def,sP4_iProver_def),
    inference(instantiation,[status(thm)],[c_347]) ).

cnf(c_2948,plain,
    ( X0 != sP2_iProver_def
    | sP2_iProver_def != sP2_iProver_def
    | sP2_iProver_def = X0 ),
    inference(instantiation,[status(thm)],[c_846]) ).

cnf(c_4816,plain,
    ( sK1(sP2_iProver_def,sP4_iProver_def) != sK1(sP2_iProver_def,sP4_iProver_def)
    | sP2_iProver_def != X0
    | ~ member(sK1(sP2_iProver_def,sP4_iProver_def),X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def) ),
    inference(instantiation,[status(thm)],[c_1892]) ).

cnf(c_9123,plain,
    ( union(sP0_iProver_def,sP1_iProver_def) != sP2_iProver_def
    | sP2_iProver_def != sP2_iProver_def
    | sP2_iProver_def = union(sP0_iProver_def,sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_2948]) ).

cnf(c_11201,plain,
    intersection(sP3_iProver_def,sK2) = sP4_iProver_def,
    inference(demodulation,[status(thm)],[c_345,c_59]) ).

cnf(c_11299,plain,
    ( ~ member(X0,sP4_iProver_def)
    | member(X0,sK2) ),
    inference(superposition,[status(thm)],[c_11201,c_53]) ).

cnf(c_11547,plain,
    ( ~ member(X0,sP2_iProver_def)
    | member(X0,sP0_iProver_def)
    | member(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_343,c_51]) ).

cnf(c_11849,plain,
    ( X0 = sP4_iProver_def
    | member(sK1(X0,sP4_iProver_def),X0)
    | member(sK1(X0,sP4_iProver_def),sK2) ),
    inference(superposition,[status(thm)],[c_65,c_11299]) ).

cnf(c_13372,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_967,c_714]) ).

cnf(c_13426,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13372,c_346]) ).

cnf(c_13596,plain,
    member(sK1(sP2_iProver_def,sP4_iProver_def),sK2),
    inference(forward_subsumption_resolution,[status(thm)],[c_13426,c_735,c_734]) ).

cnf(c_13597,plain,
    ( ~ subset(sK2,X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_13596,c_62]) ).

cnf(c_13600,plain,
    ( ~ subset(sK2,sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sK2) ),
    inference(instantiation,[status(thm)],[c_13597]) ).

cnf(c_34720,plain,
    ( sK1(sP2_iProver_def,sP4_iProver_def) != sK1(sP2_iProver_def,sP4_iProver_def)
    | sP2_iProver_def != union(sP0_iProver_def,sP1_iProver_def)
    | ~ member(sK1(sP2_iProver_def,sP4_iProver_def),union(sP0_iProver_def,sP1_iProver_def))
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def) ),
    inference(instantiation,[status(thm)],[c_4816]) ).

cnf(c_35836,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),union(sP0_iProver_def,sP1_iProver_def)) ),
    inference(instantiation,[status(thm)],[c_1879]) ).

cnf(c_46162,plain,
    ( ~ member(X0,sK2)
    | ~ member(X0,sK3)
    | member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_341,c_924]) ).

cnf(c_46163,plain,
    ( ~ member(X0,sK2)
    | ~ member(X0,sK4)
    | member(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_342,c_924]) ).

cnf(c_46164,plain,
    ( ~ member(X0,sK2)
    | ~ member(X0,sP3_iProver_def)
    | member(X0,sP4_iProver_def) ),
    inference(superposition,[status(thm)],[c_569,c_924]) ).

cnf(c_58138,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_11849,c_11547]) ).

cnf(c_58187,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_58138,c_346]) ).

cnf(c_59431,plain,
    member(sK1(sP2_iProver_def,sP4_iProver_def),sK2),
    inference(global_subsumption_just,[status(thm)],[c_58187,c_67,c_13600]) ).

cnf(c_59433,plain,
    ( ~ subset(sK2,X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_59431,c_62]) ).

cnf(c_60314,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_966,c_714]) ).

cnf(c_60357,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP3_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60314,c_346]) ).

cnf(c_60645,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def)
    | ~ subset(sK2,sP2_iProver_def)
    | sP2_iProver_def = sP4_iProver_def ),
    inference(superposition,[status(thm)],[c_59433,c_64]) ).

cnf(c_60704,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def)
    | ~ subset(sK2,sP2_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60645,c_346]) ).

cnf(c_60986,plain,
    ( ~ subset(sP3_iProver_def,X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_60357,c_62]) ).

cnf(c_60988,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sK3)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sK4)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_60357,c_713]) ).

cnf(c_61090,plain,
    ( ~ subset(sP3_iProver_def,X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),X0)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_60986,c_579]) ).

cnf(c_61293,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sK3)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sK4) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_60988,c_608,c_607]) ).

cnf(c_61301,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sK3)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_61293,c_46163]) ).

cnf(c_61303,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sK3)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_61293,c_578]) ).

cnf(c_61312,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sK3)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61301,c_13596]) ).

cnf(c_61368,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_61312,c_46162]) ).

cnf(c_61379,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_61368,c_13596]) ).

cnf(c_61390,plain,
    ( member(sK1(sP2_iProver_def,sP4_iProver_def),sP0_iProver_def)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_61379,c_579]) ).

cnf(c_62197,plain,
    ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_60704,c_343,c_346,c_768,c_845,c_2250,c_9123,c_34720,c_35836,c_61390]) ).

cnf(c_63182,plain,
    member(sK1(sP2_iProver_def,sP4_iProver_def),sP2_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_61090,c_346,c_769,c_62197]) ).

cnf(c_63185,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def)
    | sP2_iProver_def = sP4_iProver_def ),
    inference(superposition,[status(thm)],[c_63182,c_64]) ).

cnf(c_63189,plain,
    ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_63185,c_346]) ).

cnf(c_65732,plain,
    member(sK1(sP2_iProver_def,sP4_iProver_def),sP3_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_61303,c_592]) ).

cnf(c_65734,plain,
    ( ~ member(sK1(sP2_iProver_def,sP4_iProver_def),sK2)
    | member(sK1(sP2_iProver_def,sP4_iProver_def),sP4_iProver_def) ),
    inference(superposition,[status(thm)],[c_65732,c_46164]) ).

cnf(c_65738,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_65734,c_63189,c_13596]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET169+3 : TPTP v8.2.0. Released v2.2.0.
% 0.00/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 12:51:54 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.01/2.71  % SZS status Started for theBenchmark.p
% 14.01/2.71  % SZS status Theorem for theBenchmark.p
% 14.01/2.71  
% 14.01/2.71  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 14.01/2.71  
% 14.01/2.71  ------  iProver source info
% 14.01/2.71  
% 14.01/2.71  git: date: 2024-06-12 09:56:46 +0000
% 14.01/2.71  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 14.01/2.71  git: non_committed_changes: false
% 14.01/2.71  
% 14.01/2.71  ------ Parsing...
% 14.01/2.71  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 14.01/2.71  
% 14.01/2.71  ------ 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 
% 14.01/2.71  
% 14.01/2.71  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 14.01/2.71  
% 14.01/2.71  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 14.01/2.71  ------ Proving...
% 14.01/2.71  ------ Problem Properties 
% 14.01/2.71  
% 14.01/2.71  
% 14.01/2.71  clauses                                 21
% 14.01/2.71  conjectures                             1
% 14.01/2.71  EPR                                     4
% 14.01/2.71  Horn                                    18
% 14.01/2.71  unary                                   9
% 14.01/2.71  binary                                  6
% 14.01/2.71  lits                                    39
% 14.01/2.71  lits eq                                 11
% 14.01/2.71  fd_pure                                 0
% 14.01/2.71  fd_pseudo                               0
% 14.01/2.71  fd_cond                                 0
% 14.01/2.71  fd_pseudo_cond                          3
% 14.01/2.71  AC symbols                              0
% 14.01/2.71  
% 14.01/2.71  ------ Schedule dynamic 5 is on 
% 14.01/2.71  
% 14.01/2.71  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.01/2.71  
% 14.01/2.71  
% 14.01/2.71  ------ 
% 14.01/2.71  Current options:
% 14.01/2.71  ------ 
% 14.01/2.71  
% 14.01/2.71  
% 14.01/2.71  
% 14.01/2.71  
% 14.01/2.71  ------ Proving...
% 14.01/2.71  
% 14.01/2.71  
% 14.01/2.71  % SZS status Theorem for theBenchmark.p
% 14.01/2.71  
% 14.01/2.71  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.01/2.71  
% 14.01/2.72  
%------------------------------------------------------------------------------