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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:55:44 PM UTC 2026

% Result   : Theorem 43.88s 7.01s
% Output   : CNFRefutation 43.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   83 (   9 unt;   0 def)
%            Number of atoms       :  283 (  18 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  331 ( 131   ~; 133   |;  52   &)
%                                         (   6 <=>;   8  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  168 (   0 sgn 151   !;  17   ?;  55   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( X2 = set_difference(X0,X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => subset_complement(X0,X1) = set_difference(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] :
              ( in(X2,X1)
              & in(X2,X0) ) )
      & ~ ( ! [X2] :
              ~ ( in(X2,X1)
                & in(X2,X0) )
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).

fof(f23,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => ! [X2] :
          ( element(X2,powerset(X0))
         => ( disjoint(X1,X2)
          <=> subset(X1,subset_complement(X0,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).

fof(f24,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(X0))
       => ! [X2] :
            ( element(X2,powerset(X0))
           => ( disjoint(X1,X2)
            <=> subset(X1,subset_complement(X0,X2)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f23]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X3] :
              ( in(X3,X1)
              & in(X3,X0) ) )
      & ~ ( ! [X2] :
              ~ ( in(X2,X1)
                & in(X2,X0) )
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | subset_complement(X0,X1) = set_difference(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(X3,X0) ) )
      & ( ? [X2] :
            ( in(X2,X1)
            & in(X2,X0) )
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f40,plain,
    ? [X0,X1] :
      ( element(X1,powerset(X0))
      & ? [X2] :
          ( element(X2,powerset(X0))
          & ( disjoint(X1,X2)
          <~> subset(X1,subset_complement(X0,X2)) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) ) )
      & ( ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) )
        | subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f32]) ).

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

fof(f46,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) ) )
      & ( ( in(sK0(X0,X1),X0)
          & ~ in(sK0(X0,X1),X1) )
        | subset(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f45]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) != X2
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ( ~ in(X3,X1)
                & in(X3,X0) ) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) ) )
        | X2 = set_difference(X0,X1) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) != X2
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ( ~ in(X3,X1)
                & in(X3,X0) ) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) ) )
        | X2 = set_difference(X0,X1) ) ),
    inference(flattening,[],[f47]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) != X2
        | ! [X4] :
            ( ( ~ in(X4,X2)
              | ( ~ in(X4,X1)
                & in(X4,X0) ) )
            & ( in(X4,X1)
              | ~ in(X4,X0)
              | in(X4,X2) ) ) )
      & ( ? [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & in(X3,X0) ) )
            & ( ~ in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) ) )
        | X2 = set_difference(X0,X1) ) ),
    inference(rectify,[],[f48]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) != X2
        | ! [X4] :
            ( ( ~ in(X4,X2)
              | ( ~ in(X4,X1)
                & in(X4,X0) ) )
            & ( in(X4,X1)
              | ~ in(X4,X0)
              | in(X4,X2) ) ) )
      & ( ( ( in(sK1(X0,X1,X2),X2)
            | ( ~ in(sK1(X0,X1,X2),X1)
              & in(sK1(X0,X1,X2),X0) ) )
          & ( ~ in(sK1(X0,X1,X2),X2)
            | in(sK1(X0,X1,X2),X1)
            | ~ in(sK1(X0,X1,X2),X0) ) )
        | X2 = set_difference(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f49]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(X3,X0) ) )
      & ( ( in(sK7(X0,X1),X1)
          & in(sK7(X0,X1),X0) )
        | disjoint(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f39]) ).

fof(f57,plain,
    ? [X0,X1] :
      ( element(X1,powerset(X0))
      & ? [X2] :
          ( element(X2,powerset(X0))
          & ( disjoint(X1,X2)
            | subset(X1,subset_complement(X0,X2)) )
          & ( ~ disjoint(X1,X2)
            | ~ subset(X1,subset_complement(X0,X2)) ) ) ),
    inference(nnf_transformation,[],[f40]) ).

fof(f58,plain,
    ? [X0,X1] :
      ( element(X1,powerset(X0))
      & ? [X2] :
          ( element(X2,powerset(X0))
          & ( disjoint(X1,X2)
            | subset(X1,subset_complement(X0,X2)) )
          & ( ~ disjoint(X1,X2)
            | ~ subset(X1,subset_complement(X0,X2)) ) ) ),
    inference(flattening,[],[f57]) ).

fof(f59,plain,
    ( element(sK9,powerset(sK8))
    & element(sK10,powerset(sK8))
    & ( disjoint(sK9,sK10)
      | subset(sK9,subset_complement(sK8,sK10)) )
    & ( ~ disjoint(sK9,sK10)
      | ~ subset(sK9,subset_complement(sK8,sK10)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f58]) ).

fof(f61,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( in(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ in(sK0(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f64,plain,
    ! [X2,X0,X1,X4] :
      ( set_difference(X0,X1) != X2
      | ~ in(X4,X2)
      | ~ in(X4,X1) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f66,plain,
    ! [X2,X0,X1,X4] :
      ( set_difference(X0,X1) != X2
      | in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | set_difference(X0,X1) = subset_complement(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f76,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X0))
      | ~ in(X2,X1)
      | in(X2,X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f86,plain,
    ! [X3,X0,X1] :
      ( ~ disjoint(X0,X1)
      | ~ in(X3,X1)
      | ~ in(X3,X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( in(sK7(X0,X1),X1)
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( in(sK7(X0,X1),X0)
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f89,plain,
    element(sK9,powerset(sK8)),
    inference(cnf_transformation,[],[f59]) ).

fof(f90,plain,
    element(sK10,powerset(sK8)),
    inference(cnf_transformation,[],[f59]) ).

fof(f91,plain,
    ( disjoint(sK9,sK10)
    | subset(sK9,subset_complement(sK8,sK10)) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f92,plain,
    ( ~ disjoint(sK9,sK10)
    | ~ subset(sK9,subset_complement(sK8,sK10)) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f97,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,set_difference(X0,X1)) ),
    inference(equality_resolution,[],[f66]) ).

fof(f99,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f64]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | ~ in(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f63]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | in(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X2)
      | ~ subset(X1,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X2)
      | in(X0,set_difference(X1,X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f97]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ in(X0,X2)
      | ~ in(X0,set_difference(X1,X2)) ),
    inference(cnf_transformation,[],[f99]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i] :
      ( ( set_difference(X1,X0) = subset_complement(X1,X0) )
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f70]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X2,X1)
      | ~ in(X2,X0)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f76]) ).

tcf(c_75,plain,
    ! [X0: $i,X1: $i] :
      ( disjoint(X0,X1)
      | in(sK7(X0,X1),X0) ),
    inference(cnf_transformation,[],[f88]) ).

tcf(c_76,plain,
    ! [X0: $i,X1: $i] :
      ( disjoint(X0,X1)
      | in(sK7(X0,X1),X1) ),
    inference(cnf_transformation,[],[f87]) ).

tcf(c_77,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ disjoint(X2,X1)
      | ~ in(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

tcf(c_78,negated_conjecture,
    ( ~ disjoint(sK9,sK10)
    | ~ subset(sK9,subset_complement(sK8,sK10)) ),
    inference(cnf_transformation,[],[f92]) ).

tcf(c_79,negated_conjecture,
    ( disjoint(sK9,sK10)
    | subset(sK9,subset_complement(sK8,sK10)) ),
    inference(cnf_transformation,[],[f91]) ).

tcf(c_80,negated_conjecture,
    element(sK10,powerset(sK8)),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_81,negated_conjecture,
    element(sK9,powerset(sK8)),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_100,plain,
    ( ~ subset(sK9,subset_complement(sK8,sK10))
    | ~ disjoint(sK9,sK10) ),
    inference(prop_impl_just,[status(thm)],[c_78]) ).

tcf(c_101,plain,
    ( ~ disjoint(sK9,sK10)
    | ~ subset(sK9,subset_complement(sK8,sK10)) ),
    inference(renaming,[status(thm)],[c_100]) ).

tcf(c_152,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | in(sK0(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_51]) ).

tcf(c_253,plain,
    ! [X0: $i,X1: $i] :
      ( in(sK0(X0,X1),X0)
      | ~ disjoint(sK9,sK10)
      | ( X0 != sK9 )
      | ( subset_complement(sK8,sK10) != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_152,c_101]) ).

tcf(c_254,plain,
    ( in(sK0(sK9,subset_complement(sK8,sK10)),sK9)
    | ~ disjoint(sK9,sK10) ),
    inference(unflattening,[status(thm)],[c_253]) ).

tcf(c_640,plain,
    ( disjoint(sK9,sK10)
    | in(sK7(sK9,sK10),sK9) ),
    inference(instantiation,[status(thm)],[c_75]) ).

tcf(c_641,plain,
    ( disjoint(sK9,sK10)
    | in(sK7(sK9,sK10),sK10) ),
    inference(instantiation,[status(thm)],[c_76]) ).

tcf(c_646,plain,
    ! [X0: $i] :
      ( ~ disjoint(sK9,sK10)
      | ~ in(X0,sK10)
      | ~ in(X0,sK9) ),
    inference(instantiation,[status(thm)],[c_77]) ).

tcf(c_690,plain,
    ( ~ disjoint(sK9,sK10)
    | ~ in(sK0(sK9,subset_complement(sK8,sK10)),sK10)
    | ~ in(sK0(sK9,subset_complement(sK8,sK10)),sK9) ),
    inference(instantiation,[status(thm)],[c_646]) ).

tcf(c_777,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( disjoint(X0,set_difference(X1,X2))
      | ~ in(sK7(X0,set_difference(X1,X2)),X2) ),
    inference(superposition,[status(thm)],[c_76,c_58]) ).

tcf(c_842,plain,
    ! [X0: $i] :
      ( in(X0,sK8)
      | ~ in(X0,sK9) ),
    inference(superposition,[status(thm)],[c_81,c_65]) ).

tcf(c_869,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subset(X0,set_difference(X1,X2))
      | in(sK0(X0,set_difference(X1,X2)),X2)
      | ~ in(sK0(X0,set_difference(X1,X2)),X1) ),
    inference(superposition,[status(thm)],[c_56,c_50]) ).

tcf(c_945,plain,
    set_difference(sK8,sK10) = subset_complement(sK8,sK10),
    inference(superposition,[status(thm)],[c_80,c_59]) ).

tcf(c_1453,plain,
    ! [X0: $i,X1: $i] : disjoint(X0,set_difference(X1,X0)),
    inference(superposition,[status(thm)],[c_75,c_777]) ).

tcf(c_1788,plain,
    ! [X0: $i] :
      ( in(sK7(sK9,sK10),X0)
      | ~ subset(sK9,X0)
      | ~ in(sK7(sK9,sK10),sK9) ),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_1929,plain,
    ! [X0: $i] :
      ( subset(sK9,X0)
      | in(sK0(sK9,X0),sK8) ),
    inference(superposition,[status(thm)],[c_51,c_842]) ).

tcf(c_2916,plain,
    ! [X0: $i] :
      ( subset(X0,set_difference(sK8,sK10))
      | in(sK0(X0,set_difference(sK8,sK10)),sK10)
      | ~ in(sK0(X0,subset_complement(sK8,sK10)),sK8) ),
    inference(superposition,[status(thm)],[c_945,c_869]) ).

tcf(c_2942,plain,
    ! [X0: $i] :
      ( subset(X0,subset_complement(sK8,sK10))
      | in(sK0(X0,subset_complement(sK8,sK10)),sK10)
      | ~ in(sK0(X0,subset_complement(sK8,sK10)),sK8) ),
    inference(light_normalisation,[status(thm)],[c_2916,c_945]) ).

tcf(c_5299,plain,
    ! [X0: $i,X1: $i] :
      ( ~ disjoint(sK10,X1)
      | ~ in(X0,sK10)
      | ~ in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_77]) ).

tcf(c_7691,plain,
    ( in(sK7(sK9,sK10),subset_complement(sK8,sK10))
    | ~ subset(sK9,subset_complement(sK8,sK10))
    | ~ in(sK7(sK9,sK10),sK9) ),
    inference(instantiation,[status(thm)],[c_1788]) ).

tcf(c_8989,plain,
    disjoint(sK10,subset_complement(sK8,sK10)),
    inference(superposition,[status(thm)],[c_945,c_1453]) ).

tcf(c_10933,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( disjoint(X2,X0)
      | in(sK7(X2,X0),X1)
      | ~ subset(X0,X1) ),
    inference(superposition,[status(thm)],[c_76,c_52]) ).

tcf(c_10947,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( disjoint(X0,X1)
      | ~ disjoint(X2,X0)
      | ~ in(sK7(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_75,c_77]) ).

tcf(c_12649,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( disjoint(X2,X0)
      | ~ disjoint(X1,X2)
      | ~ subset(X0,X1) ),
    inference(superposition,[status(thm)],[c_10933,c_10947]) ).

tcf(c_26878,plain,
    ( ~ disjoint(sK10,subset_complement(sK8,sK10))
    | ~ in(sK7(sK9,sK10),sK10)
    | ~ in(sK7(sK9,sK10),subset_complement(sK8,sK10)) ),
    inference(instantiation,[status(thm)],[c_5299]) ).

tcf(c_27048,plain,
    ! [X0: $i] :
      ( disjoint(sK9,sK10)
      | disjoint(X0,sK9)
      | ~ disjoint(subset_complement(sK8,sK10),X0) ),
    inference(superposition,[status(thm)],[c_79,c_12649]) ).

tcf(c_27054,plain,
    disjoint(sK9,sK10),
    inference(global_subsumption_just,[status(thm)],[c_27048,c_79,c_641,c_640,c_7691,c_8989,c_26878]) ).

tcf(c_33058,plain,
    ( subset(sK9,subset_complement(sK8,sK10))
    | in(sK0(sK9,subset_complement(sK8,sK10)),sK10) ),
    inference(superposition,[status(thm)],[c_1929,c_2942]) ).

tcf(c_33072,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_33058,c_27054,c_690,c_254,c_78]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU170+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39  % Computer : n009.cluster.edu
% 0.14/0.39  % Model    : x86_64 x86_64
% 0.14/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39  % Memory   : 8046.5625MB
% 0.14/0.39  % OS       : Linux 6.8.0-71-generic
% 0.14/0.39  % CPULimit : 300
% 0.14/0.39  % WCLimit  : 300
% 0.14/0.39  % DateTime : Thu Sep 24 13:01:44 UTC 2026
% 0.14/0.39  % CPUTime  : 
% 0.14/0.39  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.45  Running first-order theorem proving
% 0.14/0.45  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.47  
% 0.14/0.47  % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47  
% 0.14/0.47  % Detected problem language: tptp
% 0.23/0.50  % Proving...
% 43.88/7.01  % SZS status Started for theBenchmark.p
% 43.88/7.01  % SZS status Theorem for theBenchmark.p
% 43.88/7.01  
% 43.88/7.01  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 43.88/7.01  
% 43.88/7.01  % ------  iProver source info
% 43.88/7.01  
% 43.88/7.01  % git: date: 2026-07-19 20:42:38 +0200
% 43.88/7.01  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 43.88/7.01  % git: non_committed_changes: false
% 43.88/7.01  
% 43.88/7.01  % ------ Parsing...
% 43.88/7.01  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 43.88/7.01  
% 43.88/7.01  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 43.88/7.01  
% 43.88/7.01  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 0 0s scvd_e  snvd_s sp: 0 0s snvd_e % 
% 43.88/7.01  
% 43.88/7.01  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 43.88/7.01  % ------ Proving...
% 43.88/7.01  % ------ Problem Properties 
% 43.88/7.01  
% 43.88/7.01  % 
% 43.88/7.01  % clauses                               37
% 43.88/7.01  % conjectures                           4
% 43.88/7.01  % EPR                                   11
% 43.88/7.01  % Horn                                  28
% 43.88/7.01  % unary                                 12
% 43.88/7.01  % binary                                17
% 43.88/7.01  % lits                                  71
% 43.88/7.01  % lits eq                               9
% 43.88/7.01  % fd_pure                               0
% 43.88/7.01  % fd_pseudo                             0
% 43.88/7.01  % fd_cond                               1
% 43.88/7.01  % fd_pseudo_cond                        4
% 43.88/7.01  % AC symbols                            0
% 43.88/7.01  
% 43.88/7.01  % ------ Input Options Time Limit: Unbounded
% 43.88/7.01  
% 43.88/7.01  
% 43.88/7.01  % ------ 
% 43.88/7.01  % Current options:
% 43.88/7.01  % ------ 
% 43.88/7.01  
% 43.88/7.01  
% 43.88/7.01  % 
% 43.88/7.01  
% 43.88/7.01  % ------ Proving...
% 43.88/7.01  % 
% 43.88/7.01  
% 43.88/7.01  % SZS status Theorem for theBenchmark.p
% 43.88/7.01  
% 43.88/7.01  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 43.88/7.01  
% 43.88/7.01  
%------------------------------------------------------------------------------