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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU136+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n014.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 02:55:32 PM UTC 2026

% Result   : Theorem 6.35s 8.36s
% Output   : CNFRefutation 6.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   64 (  13 unt;   0 def)
%            Number of atoms       :  244 (  44 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  291 ( 111   ~; 130   |;  43   &)
%                                         (   5 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :  134 (   0 sgn 124   !;  10   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( X2 = set_union2(X0,X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( X2 = set_difference(X0,X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(f42,conjecture,
    ! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).

fof(f43,negated_conjecture,
    ~ ! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
    inference(negated_conjecture,[status(cth)],[f42]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) )
      | X0 = X1 ),
    inference(ennf_transformation,[],[f33]) ).

fof(f72,plain,
    ? [X0,X1] : set_difference(X0,X1) != set_difference(set_union2(X0,X1),X1),
    inference(ennf_transformation,[],[f43]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) ) ),
    inference(flattening,[],[f84]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) ) ),
    inference(rectify,[],[f85]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f86]) ).

fof(f95,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,[],[f9]) ).

fof(f96,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,[],[f95]) ).

fof(f97,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,[],[f96]) ).

fof(f98,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(sK4(X0,X1,X2),X2)
            | ( ~ in(sK4(X0,X1,X2),X1)
              & in(sK4(X0,X1,X2),X0) ) )
          & ( ~ in(sK4(X0,X1,X2),X2)
            | in(sK4(X0,X1,X2),X1)
            | ~ in(sK4(X0,X1,X2),X0) ) )
        | X2 = set_difference(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f97]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( in(X2,X0)
            | in(X2,X1) )
          & ( ~ in(X2,X0)
            | ~ in(X2,X1) ) )
      | X0 = X1 ),
    inference(nnf_transformation,[],[f68]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ( ( in(sK7(X0,X1),X0)
          | in(sK7(X0,X1),X1) )
        & ( ~ in(sK7(X0,X1),X0)
          | ~ in(sK7(X0,X1),X1) ) )
      | X0 = X1 ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f103]) ).

fof(f107,plain,
    set_difference(sK9,sK10) != set_difference(set_union2(sK9,sK10),sK10),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f72]) ).

fof(f110,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f117,plain,
    ! [X2,X0,X1,X4] :
      ( set_union2(X0,X1) != X2
      | ~ in(X4,X2)
      | in(X4,X1)
      | in(X4,X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f118,plain,
    ! [X2,X0,X1,X4] :
      ( set_union2(X0,X1) != X2
      | ~ in(X4,X1)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f132,plain,
    ! [X2,X0,X1,X4] :
      ( set_difference(X0,X1) != X2
      | ~ in(X4,X2)
      | ~ in(X4,X1) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f133,plain,
    ! [X2,X0,X1,X4] :
      ( set_difference(X0,X1) != X2
      | ~ in(X4,X2)
      | in(X4,X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f134,plain,
    ! [X2,X0,X1,X4] :
      ( set_difference(X0,X1) != X2
      | in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( in(sK7(X0,X1),X0)
      | in(sK7(X0,X1),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f104]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ~ in(sK7(X0,X1),X0)
      | ~ in(sK7(X0,X1),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f104]) ).

fof(f172,plain,
    set_difference(sK9,sK10) != set_difference(set_union2(sK9,sK10),sK10),
    inference(cnf_transformation,[],[f107]) ).

fof(f185,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X1)
      | in(X4,set_union2(X0,X1)) ),
    inference(equality_resolution,[],[f118]) ).

fof(f186,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_union2(X0,X1))
      | in(X4,X1)
      | in(X4,X0) ),
    inference(equality_resolution,[],[f117]) ).

fof(f190,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,set_difference(X0,X1)) ),
    inference(equality_resolution,[],[f134]) ).

fof(f191,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | in(X4,X0) ),
    inference(equality_resolution,[],[f133]) ).

fof(f192,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_difference(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f132]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f110]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,set_union2(X2,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f185]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X2)
      | in(X0,X1)
      | ~ in(X0,set_union2(X1,X2)) ),
    inference(cnf_transformation,[],[f186]) ).

tcf(c_75,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X2)
      | in(X0,set_difference(X1,X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f190]) ).

tcf(c_76,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X0,X1)
      | ~ in(X0,set_difference(X1,X2)) ),
    inference(cnf_transformation,[],[f191]) ).

tcf(c_77,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ in(X0,X2)
      | ~ in(X0,set_difference(X1,X2)) ),
    inference(cnf_transformation,[],[f192]) ).

tcf(c_99,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ in(sK7(X0,X1),X1)
      | ~ in(sK7(X0,X1),X0) ),
    inference(cnf_transformation,[],[f160]) ).

tcf(c_100,plain,
    ! [X0: $i,X1: $i] :
      ( in(sK7(X0,X1),X1)
      | in(sK7(X0,X1),X0)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f159]) ).

tcf(c_112,negated_conjecture,
    set_difference(set_union2(sK9,sK10),sK10) != set_difference(sK9,sK10),
    inference(cnf_transformation,[],[f172]) ).

tcf(c_631,plain,
    set_difference(set_union2(sK10,sK9),sK10) != set_difference(sK9,sK10),
    inference(demodulation,[status(thm)],[c_112,c_50]) ).

tcf(c_2236,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
    | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10))
    | ( set_difference(set_union2(sK10,sK9),sK10) = set_difference(sK9,sK10) ) ),
    inference(instantiation,[status(thm)],[c_100]) ).

tcf(c_2238,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
    | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10))
    | ( set_difference(set_union2(sK10,sK9),sK10) = set_difference(sK9,sK10) ) ),
    inference(instantiation,[status(thm)],[c_100]) ).

tcf(c_2239,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
    | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10)) ),
    inference(global_subsumption_just,[status(thm)],[c_2238,c_631,c_2236]) ).

tcf(c_2258,plain,
    ( ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK10)
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10)) ),
    inference(instantiation,[status(thm)],[c_77]) ).

tcf(c_2259,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_union2(sK10,sK9))
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10)) ),
    inference(instantiation,[status(thm)],[c_76]) ).

tcf(c_2260,plain,
    ( ( set_difference(set_union2(sK10,sK9),sK10) = set_difference(sK9,sK10) )
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10)) ),
    inference(instantiation,[status(thm)],[c_99]) ).

tcf(c_2261,plain,
    ( ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10))
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
    inference(global_subsumption_just,[status(thm)],[c_2260,c_631,c_2260]) ).

tcf(c_2262,plain,
    ( ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10)) ),
    inference(renaming,[status(thm)],[c_2261]) ).

tcf(c_2302,plain,
    ( ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK10)
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
    inference(instantiation,[status(thm)],[c_77]) ).

tcf(c_2303,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK9)
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
    inference(instantiation,[status(thm)],[c_76]) ).

tcf(c_2304,plain,
    ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK10),
    inference(global_subsumption_just,[status(thm)],[c_2302,c_631,c_2236,c_2258,c_2302]) ).

tcf(c_2682,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK10)
    | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK9)
    | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_union2(sK10,sK9)) ),
    inference(instantiation,[status(thm)],[c_62]) ).

tcf(c_2683,plain,
    in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK9),
    inference(global_subsumption_just,[status(thm)],[c_2682,c_2239,c_2259,c_2303,c_2304,c_2682]) ).

tcf(c_2840,plain,
    ! [X0: $i] :
      ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),X0)
      | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,X0))
      | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK9) ),
    inference(instantiation,[status(thm)],[c_75]) ).

tcf(c_2844,plain,
    ! [X0: $i] :
      ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_union2(X0,sK9))
      | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK9) ),
    inference(instantiation,[status(thm)],[c_61]) ).

tcf(c_2868,plain,
    ! [X0: $i] :
      ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),X0)
      | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_2840,c_631,c_2236,c_2239,c_2259,c_2258,c_2303,c_2302,c_2682,c_2840]) ).

tcf(c_3186,plain,
    ! [X0: $i,X1: $i] :
      ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),X1)
      | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(X0,sK9),X1))
      | ~ in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_union2(X0,sK9)) ),
    inference(instantiation,[status(thm)],[c_75]) ).

tcf(c_3218,plain,
    ! [X0: $i,X1: $i] :
      ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),X1)
      | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(X0,sK9),X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_3186,c_2683,c_2844,c_3186]) ).

tcf(c_3288,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK10)
    | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
    inference(instantiation,[status(thm)],[c_2868]) ).

tcf(c_7193,plain,
    ( in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),sK10)
    | in(sK7(set_difference(set_union2(sK10,sK9),sK10),set_difference(sK9,sK10)),set_difference(set_union2(sK10,sK9),sK10)) ),
    inference(instantiation,[status(thm)],[c_3218]) ).

tcf(c_7194,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_7193,c_3288,c_2304,c_2262]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU136+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.39  % Computer : n014.cluster.edu
% 0.12/5.39  % Model    : x86_64 x86_64
% 0.12/5.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39  % Memory   : 8046.5625MB
% 0.12/5.39  % OS       : Linux 6.8.0-71-generic
% 0.12/5.39  % CPULimit : 300
% 0.12/5.39  % WCLimit  : 300
% 0.12/5.39  % DateTime : Thu Sep 24 12:53:38 UTC 2026
% 0.16/5.40  % CPUTime  : 
% 0.16/5.40  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.44  Running first-order theorem proving
% 0.16/5.44  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.45  
% 0.16/5.45  % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45  
% 0.16/5.45  % Detected problem language: tptp
% 0.16/5.47  % Proving...
% 6.35/8.36  % SZS status Started for theBenchmark.p
% 6.35/8.36  % SZS status Theorem for theBenchmark.p
% 6.35/8.36  
% 6.35/8.36  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.35/8.36  
% 6.35/8.36  % ------  iProver source info
% 6.35/8.36  
% 6.35/8.36  % git: date: 2026-07-19 20:42:38 +0200
% 6.35/8.36  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.35/8.36  % git: non_committed_changes: false
% 6.35/8.36  
% 6.35/8.36  % ------ Parsing...
% 6.35/8.36  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 6.35/8.36  
% 6.35/8.36  % ------ Preprocessing... sup_sim: 1  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 % 
% 6.35/8.36  
% 6.35/8.36  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 6.35/8.36  
% 6.35/8.36  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 6.35/8.36  % ------ Proving...
% 6.35/8.36  % ------ Problem Properties 
% 6.35/8.36  
% 6.35/8.36  % 
% 6.35/8.36  % clauses                               68
% 6.35/8.36  % conjectures                           0
% 6.35/8.36  % EPR                                   16
% 6.35/8.36  % Horn                                  54
% 6.35/8.36  % unary                                 19
% 6.35/8.36  % binary                                28
% 6.35/8.36  % lits                                  141
% 6.35/8.36  % lits eq                               32
% 6.35/8.36  % fd_pure                               0
% 6.35/8.36  % fd_pseudo                             0
% 6.35/8.36  % fd_cond                               3
% 6.35/8.36  % fd_pseudo_cond                        13
% 6.35/8.36  % AC symbols                            0
% 6.35/8.36  
% 6.35/8.36  % ------ Input Options Time Limit: Unbounded
% 6.35/8.36  
% 6.35/8.36  
% 6.35/8.36  % ------ 
% 6.35/8.36  % Current options:
% 6.35/8.36  % ------ 
% 6.35/8.36  
% 6.35/8.36  
% 6.35/8.36  % 
% 6.35/8.36  
% 6.35/8.36  % ------ Proving...
% 6.35/8.36  % 
% 6.35/8.36  
% 6.35/8.36  % SZS status Theorem for theBenchmark.p
% 6.35/8.36  
% 6.35/8.36  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.35/8.36  
% 6.35/8.36  
%------------------------------------------------------------------------------