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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : KRS175+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n004.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 01:54:20 PM UTC 2026

% Result   : Theorem 1.25s 1.18s
% Output   : CNFRefutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   94 (  16 unt;   0 def)
%            Number of atoms       :  375 ( 111 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  477 ( 196   ~; 237   |;  32   &)
%                                         (  10 <=>;   0  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   65 (   0 sgn  56   !;   9   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [X0] :
      ( ~ cowlNothing(X0)
      & cowlThing(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

fof(f9,axiom,
    ! [X0] :
      ( xsd_string(X0)
    <=> ~ xsd_integer(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f10,axiom,
    ! [X0] :
      ( cA(X0)
    <=> X0 = ia ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f11,axiom,
    ! [X0] :
      ( cA_and_B(X0)
    <=> ( cB(X0)
        | cA(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f12,axiom,
    ! [X0] :
      ( cB(X0)
    <=> X0 = ib ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f15,conjecture,
    ( cowlThing(ib)
    & cowlThing(ia)
    & ! [X0] :
        ( cA_and_B(X0)
      <=> ( X0 = ia
          | X0 = ib ) )
    & ! [X0] :
        ( xsd_string(X0)
      <=> ~ xsd_integer(X0) )
    & ! [X0] :
        ( ~ cowlNothing(X0)
        & cowlThing(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).

fof(f16,negated_conjecture,
    ~ ( cowlThing(ib)
      & cowlThing(ia)
      & ! [X0] :
          ( cA_and_B(X0)
        <=> ( X0 = ia
            | X0 = ib ) )
      & ! [X0] :
          ( xsd_string(X0)
        <=> ~ xsd_integer(X0) )
      & ! [X0] :
          ( ~ cowlNothing(X0)
          & cowlThing(X0) ) ),
    inference(negated_conjecture,[status(cth)],[f15]) ).

fof(f17,plain,
    ~ ( cowlThing(ib)
      & cowlThing(ia)
      & ! [X2] :
          ( cA_and_B(X2)
        <=> ( ia = X2
            | ib = X2 ) )
      & ! [X1] :
          ( xsd_string(X1)
        <=> ~ xsd_integer(X1) )
      & ! [X0] :
          ( ~ cowlNothing(X0)
          & cowlThing(X0) ) ),
    inference(rectify,[],[f16]) ).

fof(f32,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ? [X2] :
        ( cA_and_B(X2)
      <~> ( ia = X2
          | ib = X2 ) )
    | ? [X1] :
        ( xsd_string(X1)
      <~> ~ xsd_integer(X1) )
    | ? [X0] :
        ( cowlNothing(X0)
        | ~ cowlThing(X0) ) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f33,plain,
    ! [X0] :
      ( ( ~ xsd_string(X0)
        | ~ xsd_integer(X0) )
      & ( xsd_integer(X0)
        | xsd_string(X0) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f34,plain,
    ! [X0] :
      ( ( ~ cA(X0)
        | X0 = ia )
      & ( ia != X0
        | cA(X0) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f35,plain,
    ! [X0] :
      ( ( ~ cA_and_B(X0)
        | cB(X0)
        | cA(X0) )
      & ( ( ~ cB(X0)
          & ~ cA(X0) )
        | cA_and_B(X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f36,plain,
    ! [X0] :
      ( ( ~ cA_and_B(X0)
        | cB(X0)
        | cA(X0) )
      & ( ( ~ cB(X0)
          & ~ cA(X0) )
        | cA_and_B(X0) ) ),
    inference(flattening,[],[f35]) ).

fof(f37,plain,
    ! [X0] :
      ( ( ~ cB(X0)
        | X0 = ib )
      & ( ib != X0
        | cB(X0) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f38,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ? [X2] :
        ( ( cA_and_B(X2)
          | ia = X2
          | ib = X2 )
        & ( ~ cA_and_B(X2)
          | ( ia != X2
            & ib != X2 ) ) )
    | ? [X1] :
        ( ( xsd_string(X1)
          | ~ xsd_integer(X1) )
        & ( ~ xsd_string(X1)
          | xsd_integer(X1) ) )
    | ? [X0] :
        ( cowlNothing(X0)
        | ~ cowlThing(X0) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f39,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ? [X2] :
        ( ( cA_and_B(X2)
          | ia = X2
          | ib = X2 )
        & ( ~ cA_and_B(X2)
          | ( ia != X2
            & ib != X2 ) ) )
    | ? [X1] :
        ( ( xsd_string(X1)
          | ~ xsd_integer(X1) )
        & ( ~ xsd_string(X1)
          | xsd_integer(X1) ) )
    | ? [X0] :
        ( cowlNothing(X0)
        | ~ cowlThing(X0) ) ),
    inference(flattening,[],[f38]) ).

fof(f40,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ( ( cA_and_B(sK2)
        | ia = sK2
        | ib = sK2 )
      & ( ~ cA_and_B(sK2)
        | ( ia != sK2
          & ib != sK2 ) ) )
    | ( ( xsd_string(sK1)
        | ~ xsd_integer(sK1) )
      & ( ~ xsd_string(sK1)
        | xsd_integer(sK1) ) )
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f39]) ).

fof(f48,plain,
    ! [X0] : ~ cowlNothing(X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f49,plain,
    ! [X0] : cowlThing(X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ xsd_string(X0)
      | ~ xsd_integer(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f51,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | xsd_string(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ cA(X0)
      | ia = X0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f53,plain,
    ! [X0] :
      ( ia != X0
      | cA(X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f54,plain,
    ! [X0] :
      ( ~ cA_and_B(X0)
      | cB(X0)
      | cA(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ cB(X0)
      | cA_and_B(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ cA(X0)
      | cA_and_B(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ cB(X0)
      | ib = X0 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f58,plain,
    ! [X0] :
      ( ib != X0
      | cB(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f61,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | cA_and_B(sK2)
    | ia = sK2
    | ib = sK2
    | xsd_string(sK1)
    | ~ xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f62,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ~ cA_and_B(sK2)
    | ia != sK2
    | xsd_string(sK1)
    | ~ xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f63,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ~ cA_and_B(sK2)
    | ib != sK2
    | xsd_string(sK1)
    | ~ xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f64,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | cA_and_B(sK2)
    | ia = sK2
    | ib = sK2
    | ~ xsd_string(sK1)
    | xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f65,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ~ cA_and_B(sK2)
    | ia != sK2
    | ~ xsd_string(sK1)
    | xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f66,plain,
    ( ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ~ cA_and_B(sK2)
    | ib != sK2
    | ~ xsd_string(sK1)
    | xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cowlThing(sK0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f74,plain,
    cA(ia),
    inference(equality_resolution,[],[f53]) ).

fof(f75,plain,
    cB(ib),
    inference(equality_resolution,[],[f58]) ).

tcf(c_49,plain,
    ! [X0: $i] : cowlThing(X0),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_50,plain,
    ! [X0: $i] : ~ cowlNothing(X0),
    inference(cnf_transformation,[],[f48]) ).

tcf(c_51,plain,
    ! [X0: $i] :
      ( xsd_integer(X0)
      | xsd_string(X0) ),
    inference(cnf_transformation,[],[f51]) ).

tcf(c_52,plain,
    ! [X0: $i] :
      ( ~ xsd_integer(X0)
      | ~ xsd_string(X0) ),
    inference(cnf_transformation,[],[f50]) ).

tcf(c_53,plain,
    cA(ia),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_54,plain,
    ! [X0: $i] :
      ( ( X0 = ia )
      | ~ cA(X0) ),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_55,plain,
    ! [X0: $i] :
      ( cA_and_B(X0)
      | ~ cA(X0) ),
    inference(cnf_transformation,[],[f56]) ).

tcf(c_56,plain,
    ! [X0: $i] :
      ( cA_and_B(X0)
      | ~ cB(X0) ),
    inference(cnf_transformation,[],[f55]) ).

tcf(c_57,plain,
    ! [X0: $i] :
      ( cB(X0)
      | cA(X0)
      | ~ cA_and_B(X0) ),
    inference(cnf_transformation,[],[f54]) ).

tcf(c_58,plain,
    cB(ib),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_59,plain,
    ! [X0: $i] :
      ( ( X0 = ib )
      | ~ cB(X0) ),
    inference(cnf_transformation,[],[f57]) ).

tcf(c_62,negated_conjecture,
    ( xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cA_and_B(sK2)
    | ~ xsd_string(sK1)
    | ~ cowlThing(sK0)
    | ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ( ib != sK2 ) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_63,negated_conjecture,
    ( xsd_integer(sK1)
    | cowlNothing(sK0)
    | ~ cA_and_B(sK2)
    | ~ xsd_string(sK1)
    | ~ cowlThing(sK0)
    | ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ( ia != sK2 ) ),
    inference(cnf_transformation,[],[f65]) ).

tcf(c_64,negated_conjecture,
    ( cA_and_B(sK2)
    | xsd_integer(sK1)
    | cowlNothing(sK0)
    | ( ib = sK2 )
    | ( ia = sK2 )
    | ~ xsd_string(sK1)
    | ~ cowlThing(sK0)
    | ~ cowlThing(ib)
    | ~ cowlThing(ia) ),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_65,negated_conjecture,
    ( xsd_string(sK1)
    | cowlNothing(sK0)
    | ~ cA_and_B(sK2)
    | ~ xsd_integer(sK1)
    | ~ cowlThing(sK0)
    | ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ( ib != sK2 ) ),
    inference(cnf_transformation,[],[f63]) ).

tcf(c_66,negated_conjecture,
    ( xsd_string(sK1)
    | cowlNothing(sK0)
    | ~ cA_and_B(sK2)
    | ~ xsd_integer(sK1)
    | ~ cowlThing(sK0)
    | ~ cowlThing(ib)
    | ~ cowlThing(ia)
    | ( ia != sK2 ) ),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_67,negated_conjecture,
    ( cA_and_B(sK2)
    | xsd_string(sK1)
    | cowlNothing(sK0)
    | ( ib = sK2 )
    | ( ia = sK2 )
    | ~ xsd_integer(sK1)
    | ~ cowlThing(sK0)
    | ~ cowlThing(ib)
    | ~ cowlThing(ia) ),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_105,plain,
    ( xsd_integer(sK1)
    | ~ cA_and_B(sK2)
    | ~ xsd_string(sK1)
    | ( ib != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_62,c_50,c_49,c_49,c_49]) ).

tcf(c_110,plain,
    ( xsd_integer(sK1)
    | ~ cA_and_B(sK2)
    | ( ib != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_105,c_51]) ).

tcf(c_120,plain,
    ( xsd_integer(sK1)
    | ~ cA_and_B(sK2)
    | ~ xsd_string(sK1)
    | ( ia != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63,c_50,c_49,c_49,c_49]) ).

tcf(c_125,plain,
    ( xsd_integer(sK1)
    | ~ cA_and_B(sK2)
    | ( ia != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_120,c_51]) ).

tcf(c_135,plain,
    ( xsd_string(sK1)
    | ~ cA_and_B(sK2)
    | ~ xsd_integer(sK1)
    | ( ib != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_65,c_50,c_49,c_49,c_49]) ).

tcf(c_140,plain,
    ( xsd_string(sK1)
    | ~ cA_and_B(sK2)
    | ( ib != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_135,c_51]) ).

tcf(c_150,plain,
    ( xsd_string(sK1)
    | ~ cA_and_B(sK2)
    | ~ xsd_integer(sK1)
    | ( ia != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66,c_50,c_49,c_49,c_49]) ).

tcf(c_155,plain,
    ( xsd_string(sK1)
    | ~ cA_and_B(sK2)
    | ( ia != sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_150,c_51]) ).

tcf(c_165,plain,
    ( cA_and_B(sK2)
    | xsd_integer(sK1)
    | ( ib = sK2 )
    | ( ia = sK2 )
    | ~ xsd_string(sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_64,c_50,c_49,c_49,c_49]) ).

tcf(c_171,plain,
    ( cA_and_B(sK2)
    | xsd_integer(sK1)
    | ( ib = sK2 )
    | ( ia = sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_165,c_51]) ).

tcf(c_184,plain,
    ( cA_and_B(sK2)
    | xsd_string(sK1)
    | ( ib = sK2 )
    | ( ia = sK2 )
    | ~ xsd_integer(sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_67,c_50,c_49,c_49,c_49]) ).

tcf(c_190,plain,
    ( cA_and_B(sK2)
    | xsd_string(sK1)
    | ( ib = sK2 )
    | ( ia = sK2 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_184,c_51]) ).

tcf(c_213,plain,
    ! [X0: $i,X1: $i] :
      ( cB(X0)
      | ( X1 = ia )
      | ~ cA_and_B(X0)
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_57,c_54]) ).

tcf(c_214,plain,
    ! [X0: $i] :
      ( cB(X0)
      | ( X0 = ia )
      | ~ cA_and_B(X0) ),
    inference(unflattening,[status(thm)],[c_213]) ).

tcf(c_225,plain,
    ! [X0: $i] :
      ( cA_and_B(X0)
      | ( X0 != ia ) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_55]) ).

tcf(c_226,plain,
    cA_and_B(ia),
    inference(unflattening,[status(thm)],[c_225]) ).

tcf(c_236,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = ib )
      | ( X0 = ia )
      | ~ cA_and_B(X0)
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_214,c_59]) ).

tcf(c_237,plain,
    ! [X0: $i] :
      ( ( X0 = ib )
      | ( X0 = ia )
      | ~ cA_and_B(X0) ),
    inference(unflattening,[status(thm)],[c_236]) ).

tcf(c_238,plain,
    ( ( sK2 = ib )
    | ( sK2 = ia )
    | ~ cA_and_B(sK2) ),
    inference(instantiation,[status(thm)],[c_237]) ).

tcf(c_252,plain,
    ! [X0: $i] :
      ( cA_and_B(X0)
      | ( X0 != ib ) ),
    inference(resolution_lifted,[status(thm)],[c_56,c_58]) ).

tcf(c_253,plain,
    cA_and_B(ib),
    inference(unflattening,[status(thm)],[c_252]) ).

tcf(c_263,plain,
    ! [X0: $i] :
      ( cA_and_B(sK2)
      | ( ib = sK2 )
      | ( ia = sK2 )
      | ~ xsd_integer(X0)
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_190]) ).

tcf(c_264,plain,
    ( cA_and_B(sK2)
    | ( ib = sK2 )
    | ( ia = sK2 )
    | ~ xsd_integer(sK1) ),
    inference(unflattening,[status(thm)],[c_263]) ).

tcf(c_265,plain,
    ( cA_and_B(sK2)
    | ( ib = sK2 )
    | ( ia = sK2 ) ),
    inference(global_subsumption_just,[status(thm)],[c_264,c_171,c_264]) ).

tcf(c_276,plain,
    ! [X0: $i] :
      ( ~ cA_and_B(sK2)
      | ~ xsd_integer(X0)
      | ( ia != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_155]) ).

tcf(c_277,plain,
    ( ~ cA_and_B(sK2)
    | ~ xsd_integer(sK1)
    | ( ia != sK2 ) ),
    inference(unflattening,[status(thm)],[c_276]) ).

tcf(c_278,plain,
    ( ~ cA_and_B(sK2)
    | ( ia != sK2 ) ),
    inference(global_subsumption_just,[status(thm)],[c_277,c_125,c_277]) ).

tcf(c_286,plain,
    ! [X0: $i] :
      ( ~ cA_and_B(sK2)
      | ~ xsd_integer(X0)
      | ( ib != sK2 )
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_140]) ).

tcf(c_287,plain,
    ( ~ cA_and_B(sK2)
    | ~ xsd_integer(sK1)
    | ( ib != sK2 ) ),
    inference(unflattening,[status(thm)],[c_286]) ).

tcf(c_288,plain,
    ( ~ cA_and_B(sK2)
    | ( ib != sK2 ) ),
    inference(global_subsumption_just,[status(thm)],[c_287,c_110,c_287]) ).

tcf(c_330,plain,
    ia != sK2,
    inference(resolution_lifted,[status(thm)],[c_278,c_226]) ).

tcf(c_335,plain,
    ib != sK2,
    inference(resolution_lifted,[status(thm)],[c_288,c_253]) ).

tcf(c_352,plain,
    ! [X0: $i] : X0 = X0,
    theory(equality) ).

tcf(c_353,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = X0 )
      | ( X2 != X1 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_355,plain,
    ! [X0: $i] :
      ( ( ib = sK2 )
      | ( sK2 != X0 )
      | ( ib != X0 ) ),
    inference(instantiation,[status(thm)],[c_353]) ).

tcf(c_356,plain,
    ! [X0: $i] :
      ( ( ia = sK2 )
      | ( sK2 != X0 )
      | ( ia != X0 ) ),
    inference(instantiation,[status(thm)],[c_353]) ).

tcf(c_357,plain,
    ( ( ib = sK2 )
    | ( sK2 != ib )
    | ( ib != ib ) ),
    inference(instantiation,[status(thm)],[c_355]) ).

tcf(c_358,plain,
    ib = ib,
    inference(instantiation,[status(thm)],[c_352]) ).

tcf(c_360,plain,
    ( ( ia = sK2 )
    | ( sK2 != ia )
    | ( ia != ia ) ),
    inference(instantiation,[status(thm)],[c_356]) ).

tcf(c_361,plain,
    ia = ia,
    inference(instantiation,[status(thm)],[c_352]) ).

tcf(c_362,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_361,c_360,c_358,c_357,c_335,c_330,c_265,c_238]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS175+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37  % Computer : n004.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Wed Sep 23 19:35:35 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41  Running first-order theorem proving
% 0.09/0.41  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
% 0.09/0.42  
% 0.09/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42  
% 0.09/0.43  % Detected problem language: tptp
% 0.09/0.44  % Proving...
% 1.25/1.18  % SZS status Started for theBenchmark.p
% 1.25/1.18  % SZS status Theorem for theBenchmark.p
% 1.25/1.18  
% 1.25/1.18  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.25/1.18  
% 1.25/1.18  % ------  iProver source info
% 1.25/1.18  
% 1.25/1.18  % git: date: 2026-07-19 20:42:38 +0200
% 1.25/1.18  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.25/1.18  % git: non_committed_changes: false
% 1.25/1.18  
% 1.25/1.18  % ------ Parsing...
% 1.25/1.18  % ------ Clausification by vclausify_rel  & Parsing by iProver...% ------  preprocesses with Option_epr_non_horn_eq
% 1.25/1.18  % 
% 1.25/1.18  
% 1.25/1.18  % ------ Preprocessing... sup_sim: 8  sf_s  rm: 3 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 6 0s  sf_e  pe_s  pe_e % 
% 1.25/1.18  
% 1.25/1.18  % ------ Preprocessing...% ------  preprocesses with Option_epr_non_horn_eq
% 1.25/1.18   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % ------  preprocesses with Option_epr_non_horn_eq
% 1.25/1.18  % 
% 1.25/1.18  
% 1.25/1.18  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 1.25/1.18  % ------ Proving...
% 1.25/1.18  % ------ Problem Properties 
% 1.25/1.18  
% 1.25/1.18  % 
% 1.25/1.18  % clauses                               3
% 1.25/1.18  % conjectures                           0
% 1.25/1.18  % EPR                                   3
% 1.25/1.18  % Horn                                  2
% 1.25/1.18  % unary                                 2
% 1.25/1.18  % binary                                1
% 1.25/1.18  % lits                                  4
% 1.25/1.18  % lits eq                               4
% 1.25/1.18  % fd_pure                               0
% 1.25/1.18  % fd_pseudo                             0
% 1.25/1.18  % fd_cond                               0
% 1.25/1.18  % fd_pseudo_cond                        0
% 1.25/1.18  % AC symbols                            0
% 1.25/1.18  
% 1.25/1.18  % ------ Schedule EPR non Horn eq is on
% 1.25/1.18  
% 1.25/1.18  % ------ no conjectures: strip conj schedule 
% 1.25/1.18  
% 1.25/1.18  % ------ Option_epr_non_horn_eq stripped conjectures Time Limit: Unbounded
% 1.25/1.18  
% 1.25/1.18  
% 1.25/1.18  % ------ 
% 1.25/1.18  % Current options:
% 1.25/1.18  % ------ 
% 1.25/1.18  
% 1.25/1.18  
% 1.25/1.18  % 
% 1.25/1.18  
% 1.25/1.18  % ------ Proving...
% 1.25/1.18  % 
% 1.25/1.18  
% 1.25/1.18  % SZS status Theorem for theBenchmark.p
% 1.25/1.18  
% 1.25/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.25/1.18  
% 1.25/1.18  
%------------------------------------------------------------------------------