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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SET358+4 : TPTP v9.3.1. Released v2.2.0.
% 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 02:47:09 PM UTC 2026

% Result   : Theorem 3.97s 1.75s
% Output   : CNFRefutation 3.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   71 (   7 unt;   0 def)
%            Number of atoms       :  181 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  194 (  84   ~;  87   |;  15   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  104 (   0 sgn  98   !;   6   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( member(X0,sum(X1))
    <=> ? [X2] :
          ( member(X0,X2)
          & member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).

fof(f12,conjecture,
    ! [X0,X1] : equal_set(union(sum(X0),sum(X1)),sum(union(X0,X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI37) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1] : equal_set(union(sum(X0),sum(X1)),sum(union(X0,X1))),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
     => subset(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

fof(f16,plain,
    ? [X0,X1] : ~ equal_set(union(sum(X0),sum(X1)),sum(union(X0,X1))),
    inference(ennf_transformation,[],[f13]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(flattening,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X0)
          & ~ member(X2,X1) )
      | subset(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f20,plain,
    ~ equal_set(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( ~ member(X0,union(X1,X2))
        | member(X0,X2)
        | member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & ~ member(X0,X1) )
        | member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( ~ member(X0,union(X1,X2))
        | member(X0,X2)
        | member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & ~ member(X0,X1) )
        | member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ~ member(X0,sum(X1))
        | ? [X2] :
            ( member(X0,X2)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) )
        | member(X0,sum(X1)) ) ),
    inference(nnf_transformation,[],[f10]) ).

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

fof(f25,plain,
    ! [X0,X1] :
      ( ( ~ member(X0,sum(X1))
        | ( member(X0,sK2(X0,X1))
          & member(sK2(X0,X1),X1) ) )
      & ( ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) )
        | member(X0,sum(X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( member(sK3(X0,X1),X0)
        & ~ member(sK3(X0,X1),X1) )
      | subset(X0,X1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f19]) ).

fof(f27,plain,
    ~ equal_set(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),
    inference(cnf_transformation,[],[f20]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X2)
      | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ member(X0,sum(X1))
      | member(X0,sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ member(X0,sum(X1))
      | member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X2)
      | ~ member(X2,X1)
      | member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

tcf(c_49,negated_conjecture,
    ~ equal_set(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),
    inference(cnf_transformation,[],[f27]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,union(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f28]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_54,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,sum(X2))
      | ~ member(X1,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( member(sK2(X0,X1),X1)
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f33]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i] :
      ( member(X0,sK2(X0,X1))
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f32]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | ~ member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f36]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f35]) ).

tcf(c_111,plain,
    ( ~ subset(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1)))
    | ~ subset(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))) ),
    inference(resolution,[status(thm)],[c_49,c_53]) ).

tcf(c_160,plain,
    ( subset(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1)))
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_57]) ).

tcf(c_161,plain,
    ( subset(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1)))
    | member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),union(sum(sK0),sum(sK1))) ),
    inference(instantiation,[status(thm)],[c_58]) ).

tcf(c_162,plain,
    ( subset(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1)))
    | member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_58]) ).

tcf(c_163,plain,
    ( subset(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1)))
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sum(sK0),sum(sK1))) ),
    inference(instantiation,[status(thm)],[c_57]) ).

tcf(c_170,plain,
    ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)))
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_56]) ).

tcf(c_171,plain,
    ( member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),union(sK0,sK1))
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_180,plain,
    ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(sK1))
    | member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(sK0))
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),union(sum(sK0),sum(sK1))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_181,plain,
    ! [X0: $i] :
      ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(X0))
      | ~ member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),X0)
      | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_186,plain,
    ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(sK0))
    | ~ member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),sK0)
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_181]) ).

tcf(c_193,plain,
    ( member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),sK1)
    | member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),sK0)
    | ~ member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),union(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_296,plain,
    ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0))
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(sK0)) ),
    inference(instantiation,[status(thm)],[c_56]) ).

tcf(c_297,plain,
    ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),sK0)
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(sK0)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_367,plain,
    ! [X0: $i] :
      ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),X0))
      | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(X0)) ),
    inference(instantiation,[status(thm)],[c_56]) ).

tcf(c_368,plain,
    ! [X0: $i] :
      ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),X0),X0)
      | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(X0)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_370,plain,
    ! [X0: $i] :
      ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(X0))
      | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),X0)
      | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_431,plain,
    ! [X0: $i] :
      ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),union(sK0,X0))
      | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),sK0) ),
    inference(instantiation,[status(thm)],[c_50]) ).

tcf(c_491,plain,
    ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(sK1))
    | ~ member(sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1)),sK1)
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sK2(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sK0,sK1))) ),
    inference(instantiation,[status(thm)],[c_181]) ).

tcf(c_636,plain,
    ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1))
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(sK1)) ),
    inference(instantiation,[status(thm)],[c_367]) ).

tcf(c_638,plain,
    ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),sK1)
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(sK1)) ),
    inference(instantiation,[status(thm)],[c_368]) ).

tcf(c_847,plain,
    ! [X0: $i] :
      ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),union(X0,sK1))
      | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),sK1) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_850,plain,
    ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),union(sK0,sK1))
    | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),sK1) ),
    inference(instantiation,[status(thm)],[c_847]) ).

tcf(c_860,plain,
    ! [X0: $i] :
      ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(X0))
      | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),X0)
      | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_1199,plain,
    ! [X0: $i,X1: $i] :
      ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(X1,sum(X0)))
      | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(X0)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_1200,plain,
    ! [X0: $i,X1: $i] :
      ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sum(X0),X1))
      | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(X0)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

tcf(c_3825,plain,
    ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sum(sK0),sum(sK1)))
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(sK1)) ),
    inference(instantiation,[status(thm)],[c_1199]) ).

tcf(c_3967,plain,
    ( member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),union(sum(sK0),sum(sK1)))
    | ~ member(sK3(sum(union(sK0,sK1)),union(sum(sK0),sum(sK1))),sum(sK0)) ),
    inference(instantiation,[status(thm)],[c_1200]) ).

tcf(c_6219,plain,
    ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(union(sK0,sK1)))
    | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),union(sK0,sK1))
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0)) ),
    inference(instantiation,[status(thm)],[c_370]) ).

tcf(c_8668,plain,
    ( member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),union(sK0,sK1))
    | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK0),sK0) ),
    inference(instantiation,[status(thm)],[c_431]) ).

tcf(c_10090,plain,
    ! [X0: $i] :
      ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(union(X0,sK1)))
      | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),union(X0,sK1))
      | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1)) ),
    inference(instantiation,[status(thm)],[c_860]) ).

tcf(c_10091,plain,
    ( member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sum(union(sK0,sK1)))
    | ~ member(sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1),union(sK0,sK1))
    | ~ member(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK2(sK3(union(sum(sK0),sum(sK1)),sum(union(sK0,sK1))),sK1)) ),
    inference(instantiation,[status(thm)],[c_10090]) ).

tcf(c_10092,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_10091,c_8668,c_6219,c_3967,c_3825,c_850,c_636,c_638,c_491,c_296,c_297,c_193,c_186,c_180,c_170,c_171,c_162,c_163,c_161,c_160,c_111]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SET358+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36  % Computer : n014.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Thu Sep 24 10:42:02 UTC 2026
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40  Running first-order theorem proving
% 0.13/0.40  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
% 0.13/0.41  
% 0.13/0.41  % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41  
% 0.13/0.41  % Detected problem language: tptp
% 0.13/0.43  % Proving...
% 3.97/1.75  % SZS status Started for theBenchmark.p
% 3.97/1.75  % SZS status Theorem for theBenchmark.p
% 3.97/1.75  
% 3.97/1.75  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.97/1.75  
% 3.97/1.75  % ------  iProver source info
% 3.97/1.75  
% 3.97/1.75  % git: date: 2026-07-19 20:42:38 +0200
% 3.97/1.75  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.97/1.75  % git: non_committed_changes: false
% 3.97/1.75  
% 3.97/1.75  % ------ Parsing...
% 3.97/1.75  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.97/1.75  
% 3.97/1.75  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e % 
% 3.97/1.75  
% 3.97/1.75  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.97/1.75  % ------ Proving...
% 3.97/1.75  % ------ Problem Properties 
% 3.97/1.75  
% 3.97/1.75  % 
% 3.97/1.75  % clauses                               9
% 3.97/1.75  % conjectures                           0
% 3.97/1.75  % EPR                                   0
% 3.97/1.75  % Horn                                  7
% 3.97/1.75  % unary                                 0
% 3.97/1.75  % binary                                7
% 3.97/1.75  % lits                                  20
% 3.97/1.75  % lits eq                               0
% 3.97/1.75  % fd_pure                               0
% 3.97/1.75  % fd_pseudo                             0
% 3.97/1.75  % fd_cond                               0
% 3.97/1.75  % fd_pseudo_cond                        0
% 3.97/1.75  % AC symbols                            0
% 3.97/1.75  
% 3.97/1.75  % ------ Schedule dynamic 5 is on 
% 3.97/1.75  
% 3.97/1.75  % ------ no conjectures: strip conj schedule 
% 3.97/1.75  
% 3.97/1.75  % ------ no equalities: superposition off 
% 3.97/1.75  
% 3.97/1.75  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.97/1.75  
% 3.97/1.75  
% 3.97/1.75  % ------ 
% 3.97/1.75  % Current options:
% 3.97/1.75  % ------ 
% 3.97/1.75  
% 3.97/1.75  
% 3.97/1.75  % 
% 3.97/1.75  
% 3.97/1.75  % ------ Proving...
% 3.97/1.75  % 
% 3.97/1.75  
% 3.97/1.75  % SZS status Theorem for theBenchmark.p
% 3.97/1.75  
% 3.97/1.75  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/1.75  
% 3.97/1.75  
%------------------------------------------------------------------------------