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iProver---3.9.4.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : KRS113+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 : n011.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 01:54:11 PM UTC 2026

% Result   : Unsatisfiable 2.09s 1.30s
% Output   : CNFRefutation 2.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   85 (   4 unt;   1 def)
%            Number of atoms       :  318 (  30 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  391 ( 158   ~; 144   |;  73   &)
%                                         (  12 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-1 aty)
%            Number of variables   :  183 (   0 sgn 153   !;  30   ?;  65   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f19,axiom,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X3] :
            ( cp(X3)
            & rs(X0,X3) )
        & ? [X3] :
            ( ca_Vx2(X3)
            & rr(X0,X3) )
        & ! [X1,X2] :
            ( ( rr(X0,X2)
              & rr(X0,X1) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f20,axiom,
    ! [X0] :
      ( cp(X0)
    <=> ~ ? [X1] : ra_Px1(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f21,axiom,
    ! [X0] :
      ( cpxcomp(X0)
    <=> ? [X1] : ra_Px1(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f22,axiom,
    ! [X0] :
      ( ca_Vx2(X0)
    <=> ! [X1] :
          ( rinvS(X0,X1)
         => cp(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( rinvS(X0,X1)
    <=> rs(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f24,axiom,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( rs(X0,X1)
     => rr(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(f26,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X4] :
            ( cp(X4)
            & rs(X0,X4) )
        & ? [X3] :
            ( ca_Vx2(X3)
            & rr(X0,X3) )
        & ! [X1,X2] :
            ( ( rr(X0,X2)
              & rr(X0,X1) )
           => X1 = X2 ) ) ),
    inference(rectify,[],[f19]) ).

fof(f59,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X4] :
            ( cp(X4)
            & rs(X0,X4) )
        & ? [X3] :
            ( ca_Vx2(X3)
            & rr(X0,X3) )
        & ! [X1,X2] :
            ( ~ rr(X0,X2)
            | ~ rr(X0,X1)
            | X1 = X2 ) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f60,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X4] :
            ( cp(X4)
            & rs(X0,X4) )
        & ? [X3] :
            ( ca_Vx2(X3)
            & rr(X0,X3) )
        & ! [X1,X2] :
            ( ~ rr(X0,X2)
            | ~ rr(X0,X1)
            | X1 = X2 ) ) ),
    inference(flattening,[],[f59]) ).

fof(f61,plain,
    ! [X0] :
      ( cp(X0)
    <=> ! [X1] : ~ ra_Px1(X0,X1) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f62,plain,
    ! [X0] :
      ( ca_Vx2(X0)
    <=> ! [X1] :
          ( ~ rinvS(X0,X1)
          | cp(X1) ) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ rs(X0,X1)
      | rr(X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f71,plain,
    ! [X0] :
      ( ( ~ cUnsatisfiable(X0)
        | sP0(X0) )
      & ( ~ sP0(X0)
        | cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f72,plain,
    ! [X0] :
      ( ( ~ cp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X1] : ra_Px1(X0,X1)
        | cp(X0) ) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f73,plain,
    ! [X0] :
      ( ( ~ cp(X0)
        | ! [X2] : ~ ra_Px1(X0,X2) )
      & ( ? [X1] : ra_Px1(X0,X1)
        | cp(X0) ) ),
    inference(rectify,[],[f72]) ).

fof(f74,plain,
    ! [X0] :
      ( ( ~ cp(X0)
        | ! [X2] : ~ ra_Px1(X0,X2) )
      & ( ra_Px1(X0,sK5(X0))
        | cp(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f73]) ).

fof(f75,plain,
    ! [X0] :
      ( ( ~ cpxcomp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | cpxcomp(X0) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f76,plain,
    ! [X0] :
      ( ( ~ cpxcomp(X0)
        | ? [X2] : ra_Px1(X0,X2) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | cpxcomp(X0) ) ),
    inference(rectify,[],[f75]) ).

fof(f77,plain,
    ! [X0] :
      ( ( ~ cpxcomp(X0)
        | ra_Px1(X0,sK6(X0)) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | cpxcomp(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0))],[f76]) ).

fof(f78,plain,
    ! [X0] :
      ( ( ~ ca_Vx2(X0)
        | ! [X1] :
            ( ~ rinvS(X0,X1)
            | cp(X1) ) )
      & ( ? [X1] :
            ( rinvS(X0,X1)
            & ~ cp(X1) )
        | ca_Vx2(X0) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f79,plain,
    ! [X0] :
      ( ( ~ ca_Vx2(X0)
        | ! [X2] :
            ( ~ rinvS(X0,X2)
            | cp(X2) ) )
      & ( ? [X1] :
            ( rinvS(X0,X1)
            & ~ cp(X1) )
        | ca_Vx2(X0) ) ),
    inference(rectify,[],[f78]) ).

fof(f80,plain,
    ! [X0] :
      ( ( ~ ca_Vx2(X0)
        | ! [X2] :
            ( ~ rinvS(X0,X2)
            | cp(X2) ) )
      & ( ( rinvS(X0,sK7(X0))
          & ~ cp(sK7(X0)) )
        | ca_Vx2(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f79]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( ~ rinvS(X0,X1)
        | rs(X1,X0) )
      & ( ~ rs(X1,X0)
        | rinvS(X0,X1) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f113,plain,
    ! [X2,X0] :
      ( ~ cp(X0)
      | ~ ra_Px1(X0,X2) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f115,plain,
    ! [X0] :
      ( ~ cpxcomp(X0)
      | ra_Px1(X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f117,plain,
    ! [X2,X0] :
      ( ~ ca_Vx2(X0)
      | ~ rinvS(X0,X2)
      | cp(X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ rs(X1,X0)
      | rinvS(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f122,plain,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    inference(cnf_transformation,[],[f24]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ~ rs(X0,X1)
      | rr(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

tcf(c_63,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f111]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i] :
      ( ~ cp(X0)
      | ~ ra_Px1(X0,X1) ),
    inference(cnf_transformation,[],[f113]) ).

tcf(c_67,plain,
    ! [X0: $i] :
      ( ra_Px1(X0,sK6(X0))
      | ~ cpxcomp(X0) ),
    inference(cnf_transformation,[],[f115]) ).

tcf(c_70,plain,
    ! [X0: $i,X1: $i] :
      ( cp(X1)
      | ~ ca_Vx2(X0)
      | ~ rinvS(X0,X1) ),
    inference(cnf_transformation,[],[f117]) ).

tcf(c_71,plain,
    ! [X0: $i,X1: $i] :
      ( rinvS(X1,X0)
      | ~ rs(X0,X1) ),
    inference(cnf_transformation,[],[f121]) ).

tcf(c_73,plain,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    inference(cnf_transformation,[],[f122]) ).

tcf(c_74,plain,
    ! [X0: $i,X1: $i] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

tcf(c_105,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63]) ).

tcf(c_107,plain,
    ! [X0: $i,X1: $i] :
      ( ~ rs(X0,X1)
      | rr(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_74]) ).

tcf(c_108,plain,
    ! [X0: $i,X1: $i] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(renaming,[status(thm)],[c_107]) ).

tcf(c_109,plain,
    ! [X0: $i] :
      ( ra_Px1(X0,sK6(X0))
      | ~ cpxcomp(X0) ),
    inference(prop_impl_just,[status(thm)],[c_67]) ).

tcf(c_125,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ra_Px1(X0,X1)
      | ~ cp(X0) ),
    inference(prop_impl_just,[status(thm)],[c_65]) ).

tcf(c_126,plain,
    ! [X0: $i,X1: $i] :
      ( ~ cp(X0)
      | ~ ra_Px1(X0,X1) ),
    inference(renaming,[status(thm)],[c_125]) ).

tcf(c_143,plain,
    ! [X0: $i,X1: $i] :
      ( rinvS(X1,X0)
      | ~ rs(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_71]) ).

tcf(c_503,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ cpxcomp(X1)
      | ~ cp(X0)
      | ( X0 != X1 )
      | ( sK6(X1) != X2 ) ),
    inference(resolution_lifted,[status(thm)],[c_126,c_109]) ).

tcf(c_504,plain,
    ! [X0: $i] :
      ( ~ cpxcomp(X0)
      | ~ cp(X0) ),
    inference(unflattening,[status(thm)],[c_503]) ).

tcf(c_529,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( cp(X2)
      | ~ ca_Vx2(X0)
      | ~ rs(X3,X1)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_70,c_143]) ).

tcf(c_530,plain,
    ! [X0: $i,X1: $i] :
      ( cp(X0)
      | ~ ca_Vx2(X1)
      | ~ rs(X0,X1) ),
    inference(unflattening,[status(thm)],[c_529]) ).

fof(f64,definition,
    ! [X0] :
      ( sP0(X0)
    <=> ( cpxcomp(X0)
        & ? [X4] :
            ( cp(X4)
            & rs(X0,X4) )
        & ? [X3] :
            ( ca_Vx2(X3)
            & rr(X0,X3) )
        & ! [X1,X2] :
            ( ~ rr(X0,X2)
            | ~ rr(X0,X1)
            | X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f65,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP0(X0) ),
    inference(definition_folding,[],[f60,f64]) ).

fof(f67,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ( cpxcomp(X0)
          & ? [X4] :
              ( cp(X4)
              & rs(X0,X4) )
          & ? [X3] :
              ( ca_Vx2(X3)
              & rr(X0,X3) )
          & ! [X1,X2] :
              ( ~ rr(X0,X2)
              | ~ rr(X0,X1)
              | X1 = X2 ) ) )
      & ( ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) )
        | ! [X3] :
            ( ~ ca_Vx2(X3)
            | ~ rr(X0,X3) )
        | ? [X1,X2] :
            ( rr(X0,X2)
            & rr(X0,X1)
            & X1 != X2 )
        | sP0(X0) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f68,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ( cpxcomp(X0)
          & ? [X4] :
              ( cp(X4)
              & rs(X0,X4) )
          & ? [X3] :
              ( ca_Vx2(X3)
              & rr(X0,X3) )
          & ! [X1,X2] :
              ( ~ rr(X0,X2)
              | ~ rr(X0,X1)
              | X1 = X2 ) ) )
      & ( ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) )
        | ! [X3] :
            ( ~ ca_Vx2(X3)
            | ~ rr(X0,X3) )
        | ? [X1,X2] :
            ( rr(X0,X2)
            & rr(X0,X1)
            & X1 != X2 )
        | sP0(X0) ) ),
    inference(flattening,[],[f67]) ).

fof(f69,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ( cpxcomp(X0)
          & ? [X8] :
              ( cp(X8)
              & rs(X0,X8) )
          & ? [X7] :
              ( ca_Vx2(X7)
              & rr(X0,X7) )
          & ! [X5,X6] :
              ( ~ rr(X0,X6)
              | ~ rr(X0,X5)
              | X5 = X6 ) ) )
      & ( ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) )
        | ! [X3] :
            ( ~ ca_Vx2(X3)
            | ~ rr(X0,X3) )
        | ? [X1,X2] :
            ( rr(X0,X2)
            & rr(X0,X1)
            & X1 != X2 )
        | sP0(X0) ) ),
    inference(rectify,[],[f68]) ).

fof(f70,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ( cpxcomp(X0)
          & cp(sK4(X0))
          & rs(X0,sK4(X0))
          & ca_Vx2(sK3(X0))
          & rr(X0,sK3(X0))
          & ! [X5,X6] :
              ( ~ rr(X0,X6)
              | ~ rr(X0,X5)
              | X5 = X6 ) ) )
      & ( ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) )
        | ! [X3] :
            ( ~ ca_Vx2(X3)
            | ~ rr(X0,X3) )
        | ( rr(X0,sK2(X0))
          & rr(X0,sK1(X0))
          & sK1(X0) != sK2(X0) )
        | sP0(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X7,sK3(X0)),skolemize(X8,sK4(X0))],[f69]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | cpxcomp(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | rs(X0,sK4(X0)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ca_Vx2(sK3(X0)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | rr(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f107,plain,
    ! [X0,X6,X5] :
      ( ~ sP0(X0)
      | ~ rr(X0,X6)
      | ~ rr(X0,X5)
      | X5 = X6 ),
    inference(cnf_transformation,[],[f70]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ sP0(X0)
      | ~ rr(X0,X2)
      | ~ rr(X0,X1) ),
    inference(cnf_transformation,[],[f107]) ).

tcf(c_57,plain,
    ! [X0: $i] :
      ( rr(X0,sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f106]) ).

tcf(c_58,plain,
    ! [X0: $i] :
      ( ca_Vx2(sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f105]) ).

tcf(c_59,plain,
    ! [X0: $i] :
      ( rs(X0,sK4(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f104]) ).

tcf(c_61,plain,
    ! [X0: $i] :
      ( cpxcomp(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f102]) ).

tcf(c_111,plain,
    ! [X0: $i] :
      ( ~ cUnsatisfiable(X0)
      | cpxcomp(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_61]) ).

tcf(c_112,plain,
    ! [X0: $i] :
      ( cpxcomp(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(renaming,[status(thm)],[c_111]) ).

tcf(c_117,plain,
    ! [X0: $i] :
      ( rr(X0,sK3(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_57]) ).

tcf(c_119,plain,
    ! [X0: $i] :
      ( ca_Vx2(sK3(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_58]) ).

tcf(c_121,plain,
    ! [X0: $i] :
      ( rs(X0,sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_59]) ).

tcf(c_211,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ cUnsatisfiable(X0)
      | ~ rr(X0,X2)
      | ~ rr(X0,X1) ),
    inference(bin_hyper_res,[status(thm)],[c_56,c_105]) ).

tcf(c_617,plain,
    ! [X0: $i,X1: $i] :
      ( ~ cUnsatisfiable(X0)
      | ~ cp(X1)
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_112,c_504]) ).

tcf(c_618,plain,
    ! [X0: $i] :
      ( ~ cUnsatisfiable(X0)
      | ~ cp(X0) ),
    inference(unflattening,[status(thm)],[c_617]) ).

tcf(c_727,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( cp(X2)
      | ~ cUnsatisfiable(X0)
      | ~ ca_Vx2(X1)
      | ( X0 != X2 )
      | ( sK4(X0) != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_121,c_530]) ).

tcf(c_728,plain,
    ! [X0: $i] :
      ( cp(X0)
      | ~ cUnsatisfiable(X0)
      | ~ ca_Vx2(sK4(X0)) ),
    inference(unflattening,[status(thm)],[c_727]) ).

tcf(c_730,plain,
    ! [X0: $i] :
      ( ~ ca_Vx2(sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_728,c_618,c_728]) ).

tcf(c_731,plain,
    ! [X0: $i] :
      ( ~ cUnsatisfiable(X0)
      | ~ ca_Vx2(sK4(X0)) ),
    inference(renaming,[status(thm)],[c_730]) ).

tcf(c_739,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( rr(X2,X1)
      | ~ cUnsatisfiable(X0)
      | ( X0 != X2 )
      | ( sK4(X0) != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_121,c_108]) ).

tcf(c_740,plain,
    ! [X0: $i] :
      ( rr(X0,sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(unflattening,[status(thm)],[c_739]) ).

tcf(c_1069,plain,
    ! [X0: $i,X1: $i] :
      ( ~ cUnsatisfiable(X1)
      | ~ cUnsatisfiable(X0)
      | ( sK3(X0) != sK4(X1) ) ),
    inference(resolution_lifted,[status(thm)],[c_119,c_731]) ).

tcf(c_1070,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
    | ( sK3(i2003_11_14_17_21_22376) != sK4(i2003_11_14_17_21_22376) ) ),
    inference(instantiation,[status(thm)],[c_1069]) ).

tcf(c_1809,plain,
    ! [X0: $i,X1: $i] :
      ( ( sK3(X0) = X1 )
      | ~ cUnsatisfiable(X0)
      | ~ rr(X0,X1) ),
    inference(superposition,[status(thm)],[c_117,c_211]) ).

tcf(c_1831,plain,
    ! [X0: $i] :
      ( ( sK3(X0) = sK4(X0) )
      | ~ cUnsatisfiable(X0) ),
    inference(superposition,[status(thm)],[c_740,c_1809]) ).

tcf(c_1838,plain,
    ( ( sK3(i2003_11_14_17_21_22376) = sK4(i2003_11_14_17_21_22376) )
    | ~ cUnsatisfiable(i2003_11_14_17_21_22376) ),
    inference(instantiation,[status(thm)],[c_1831]) ).

tcf(c_1839,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1838,c_1070,c_73]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS113+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38  % Computer : n011.cluster.edu
% 0.13/0.38  % Model    : x86_64 x86_64
% 0.13/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38  % Memory   : 8046.5625MB
% 0.13/0.38  % OS       : Linux 6.8.0-71-generic
% 0.13/0.38  % CPULimit : 300
% 0.13/0.38  % WCLimit  : 300
% 0.13/0.38  % DateTime : Wed Sep 23 19:25:28 UTC 2026
% 0.13/0.39  % CPUTime  : 
% 0.13/0.39  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43  Running first-order theorem proving
% 0.13/0.43  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
% 0.13/0.44  
% 0.13/0.44  % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44  
% 0.13/0.44  % Detected problem language: tptp
% 0.13/0.45  % Proving...
% 2.09/1.30  % SZS status Started for theBenchmark.p
% 2.09/1.30  % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.30  
% 2.09/1.30  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.09/1.30  
% 2.09/1.30  % ------  iProver source info
% 2.09/1.30  
% 2.09/1.30  % git: date: 2026-07-19 20:42:38 +0200
% 2.09/1.30  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.09/1.30  % git: non_committed_changes: false
% 2.09/1.30  
% 2.09/1.30  % ------ Parsing...
% 2.09/1.30  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 2.09/1.30  
% 2.09/1.30  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e % 
% 2.09/1.30  
% 2.09/1.30  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 2.09/1.30  
% 2.09/1.30  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.09/1.30  % ------ Proving...
% 2.09/1.30  % ------ Problem Properties 
% 2.09/1.30  
% 2.09/1.30  % 
% 2.09/1.30  % clauses                               12
% 2.09/1.30  % conjectures                           0
% 2.09/1.30  % EPR                                   2
% 2.09/1.30  % Horn                                  9
% 2.09/1.30  % unary                                 1
% 2.09/1.30  % binary                                6
% 2.09/1.30  % lits                                  35
% 2.09/1.30  % lits eq                               3
% 2.09/1.30  % fd_pure                               0
% 2.09/1.30  % fd_pseudo                             0
% 2.09/1.30  % fd_cond                               0
% 2.09/1.30  % fd_pseudo_cond                        1
% 2.09/1.30  % AC symbols                            0
% 2.09/1.30  
% 2.09/1.30  % ------ Schedule dynamic 5 is on 
% 2.09/1.30  
% 2.09/1.30  % ------ no conjectures: strip conj schedule 
% 2.09/1.30  
% 2.09/1.30  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.09/1.30  
% 2.09/1.30  
% 2.09/1.30  % ------ 
% 2.09/1.30  % Current options:
% 2.09/1.30  % ------ 
% 2.09/1.30  
% 2.09/1.30  
% 2.09/1.30  % 
% 2.09/1.30  
% 2.09/1.30  % ------ Proving...
% 2.09/1.30  % 
% 2.09/1.30  
% 2.09/1.30  % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.30  
% 2.09/1.30  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.09/1.30  
% 2.09/1.30  
%------------------------------------------------------------------------------