TSTP Solution File: KRS113+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS113+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 02:33:39 EDT 2024

% Result   : Unsatisfiable 0.42s 1.11s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   95 (   4 unt;   0 def)
%            Number of atoms       :  349 (  32 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  416 ( 162   ~; 143   |;  83   &)
%                                         (  16 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            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   :  204 (   4 sgn 102   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f19,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( cpxcomp(X3)
        & ? [X6] :
            ( cp(X6)
            & rs(X3,X6) )
        & ? [X6] :
            ( ca_Vx2(X6)
            & rr(X3,X6) )
        & ! [X4,X5] :
            ( ( rr(X3,X5)
              & rr(X3,X4) )
           => X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f20,axiom,
    ! [X3] :
      ( cp(X3)
    <=> ~ ? [X6] : ra_Px1(X3,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

fof(f21,axiom,
    ! [X3] :
      ( cpxcomp(X3)
    <=> ? [X4] : ra_Px1(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

fof(f22,axiom,
    ! [X3] :
      ( ca_Vx2(X3)
    <=> ! [X6] :
          ( rinvS(X3,X6)
         => cp(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f23,axiom,
    ! [X3,X6] :
      ( rinvS(X3,X6)
    <=> rs(X6,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

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

fof(f25,axiom,
    ! [X3,X6] :
      ( rs(X3,X6)
     => rr(X3,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

fof(f28,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ? [X2] :
            ( ca_Vx2(X2)
            & rr(X0,X2) )
        & ! [X3,X4] :
            ( ( rr(X0,X4)
              & rr(X0,X3) )
           => X3 = X4 ) ) ),
    inference(rectify,[],[f19]) ).

fof(f29,plain,
    ! [X0] :
      ( cp(X0)
    <=> ~ ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f20]) ).

fof(f30,plain,
    ! [X0] :
      ( cpxcomp(X0)
    <=> ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f31,plain,
    ! [X0] :
      ( ca_Vx2(X0)
    <=> ! [X1] :
          ( rinvS(X0,X1)
         => cp(X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( rinvS(X0,X1)
    <=> rs(X1,X0) ),
    inference(rectify,[],[f23]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( rs(X0,X1)
     => rr(X0,X1) ),
    inference(rectify,[],[f25]) ).

fof(f66,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ? [X2] :
            ( ca_Vx2(X2)
            & rr(X0,X2) )
        & ! [X3,X4] :
            ( X3 = X4
            | ~ rr(X0,X4)
            | ~ rr(X0,X3) ) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f67,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cpxcomp(X0)
        & ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ? [X2] :
            ( ca_Vx2(X2)
            & rr(X0,X2) )
        & ! [X3,X4] :
            ( X3 = X4
            | ~ rr(X0,X4)
            | ~ rr(X0,X3) ) ) ),
    inference(flattening,[],[f66]) ).

fof(f68,plain,
    ! [X0] :
      ( cp(X0)
    <=> ! [X1] : ~ ra_Px1(X0,X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f69,plain,
    ! [X0] :
      ( ca_Vx2(X0)
    <=> ! [X1] :
          ( cp(X1)
          | ~ rinvS(X0,X1) ) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f71,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ( cpxcomp(X0)
        & ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ? [X2] :
            ( ca_Vx2(X2)
            & rr(X0,X2) )
        & ! [X3,X4] :
            ( X3 = X4
            | ~ rr(X0,X4)
            | ~ rr(X0,X3) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f72,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP0(X0) ),
    inference(definition_folding,[],[f67,f71]) ).

fof(f74,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ~ cpxcomp(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Vx2(X2)
            | ~ rr(X0,X2) )
        | ? [X3,X4] :
            ( X3 != X4
            & rr(X0,X4)
            & rr(X0,X3) ) )
      & ( ( cpxcomp(X0)
          & ? [X1] :
              ( cp(X1)
              & rs(X0,X1) )
          & ? [X2] :
              ( ca_Vx2(X2)
              & rr(X0,X2) )
          & ! [X3,X4] :
              ( X3 = X4
              | ~ rr(X0,X4)
              | ~ rr(X0,X3) ) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f75,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ~ cpxcomp(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Vx2(X2)
            | ~ rr(X0,X2) )
        | ? [X3,X4] :
            ( X3 != X4
            & rr(X0,X4)
            & rr(X0,X3) ) )
      & ( ( cpxcomp(X0)
          & ? [X1] :
              ( cp(X1)
              & rs(X0,X1) )
          & ? [X2] :
              ( ca_Vx2(X2)
              & rr(X0,X2) )
          & ! [X3,X4] :
              ( X3 = X4
              | ~ rr(X0,X4)
              | ~ rr(X0,X3) ) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f74]) ).

fof(f76,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ~ cpxcomp(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Vx2(X2)
            | ~ rr(X0,X2) )
        | ? [X3,X4] :
            ( X3 != X4
            & rr(X0,X4)
            & rr(X0,X3) ) )
      & ( ( cpxcomp(X0)
          & ? [X5] :
              ( cp(X5)
              & rs(X0,X5) )
          & ? [X6] :
              ( ca_Vx2(X6)
              & rr(X0,X6) )
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rr(X0,X8)
              | ~ rr(X0,X7) ) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f75]) ).

fof(f77,plain,
    ! [X0] :
      ( ? [X3,X4] :
          ( X3 != X4
          & rr(X0,X4)
          & rr(X0,X3) )
     => ( sK1(X0) != sK2(X0)
        & rr(X0,sK2(X0))
        & rr(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ! [X0] :
      ( ? [X5] :
          ( cp(X5)
          & rs(X0,X5) )
     => ( cp(sK3(X0))
        & rs(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ! [X0] :
      ( ? [X6] :
          ( ca_Vx2(X6)
          & rr(X0,X6) )
     => ( ca_Vx2(sK4(X0))
        & rr(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ~ cpxcomp(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Vx2(X2)
            | ~ rr(X0,X2) )
        | ( sK1(X0) != sK2(X0)
          & rr(X0,sK2(X0))
          & rr(X0,sK1(X0)) ) )
      & ( ( cpxcomp(X0)
          & cp(sK3(X0))
          & rs(X0,sK3(X0))
          & ca_Vx2(sK4(X0))
          & rr(X0,sK4(X0))
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rr(X0,X8)
              | ~ rr(X0,X7) ) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f76,f79,f78,f77]) ).

fof(f81,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ sP0(X0) )
      & ( sP0(X0)
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f82,plain,
    ! [X0] :
      ( ( cp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | ~ cp(X0) ) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f83,plain,
    ! [X0] :
      ( ( cp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp(X0) ) ),
    inference(rectify,[],[f82]) ).

fof(f84,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
     => ra_Px1(X0,sK5(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0] :
      ( ( cp(X0)
        | ra_Px1(X0,sK5(X0)) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f83,f84]) ).

fof(f86,plain,
    ! [X0] :
      ( ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X1] : ra_Px1(X0,X1)
        | ~ cpxcomp(X0) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f87,plain,
    ! [X0] :
      ( ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X2] : ra_Px1(X0,X2)
        | ~ cpxcomp(X0) ) ),
    inference(rectify,[],[f86]) ).

fof(f88,plain,
    ! [X0] :
      ( ? [X2] : ra_Px1(X0,X2)
     => ra_Px1(X0,sK6(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0] :
      ( ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ra_Px1(X0,sK6(X0))
        | ~ cpxcomp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f87,f88]) ).

fof(f90,plain,
    ! [X0] :
      ( ( ca_Vx2(X0)
        | ? [X1] :
            ( ~ cp(X1)
            & rinvS(X0,X1) ) )
      & ( ! [X1] :
            ( cp(X1)
            | ~ rinvS(X0,X1) )
        | ~ ca_Vx2(X0) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f91,plain,
    ! [X0] :
      ( ( ca_Vx2(X0)
        | ? [X1] :
            ( ~ cp(X1)
            & rinvS(X0,X1) ) )
      & ( ! [X2] :
            ( cp(X2)
            | ~ rinvS(X0,X2) )
        | ~ ca_Vx2(X0) ) ),
    inference(rectify,[],[f90]) ).

fof(f92,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cp(X1)
          & rinvS(X0,X1) )
     => ( ~ cp(sK7(X0))
        & rinvS(X0,sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ! [X0] :
      ( ( ca_Vx2(X0)
        | ( ~ cp(sK7(X0))
          & rinvS(X0,sK7(X0)) ) )
      & ( ! [X2] :
            ( cp(X2)
            | ~ rinvS(X0,X2) )
        | ~ ca_Vx2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f91,f92]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( rinvS(X0,X1)
        | ~ rs(X1,X0) )
      & ( rs(X1,X0)
        | ~ rinvS(X0,X1) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f115,plain,
    ! [X0,X8,X7] :
      ( X7 = X8
      | ~ rr(X0,X8)
      | ~ rr(X0,X7)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f116,plain,
    ! [X0] :
      ( rr(X0,sK4(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f117,plain,
    ! [X0] :
      ( ca_Vx2(sK4(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f118,plain,
    ! [X0] :
      ( rs(X0,sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f120,plain,
    ! [X0] :
      ( cpxcomp(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f124,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f126,plain,
    ! [X2,X0] :
      ( ~ ra_Px1(X0,X2)
      | ~ cp(X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f128,plain,
    ! [X0] :
      ( ra_Px1(X0,sK6(X0))
      | ~ cpxcomp(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f130,plain,
    ! [X2,X0] :
      ( cp(X2)
      | ~ rinvS(X0,X2)
      | ~ ca_Vx2(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( rinvS(X0,X1)
      | ~ rs(X1,X0) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f135,plain,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    inference(cnf_transformation,[],[f24]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_56,plain,
    ( ~ sP0(X0)
    | cpxcomp(X0) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_58,plain,
    ( ~ sP0(X0)
    | rs(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_59,plain,
    ( ~ sP0(X0)
    | ca_Vx2(sK4(X0)) ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_60,plain,
    ( ~ sP0(X0)
    | rr(X0,sK4(X0)) ),
    inference(cnf_transformation,[],[f116]) ).

cnf(c_61,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ sP0(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f115]) ).

cnf(c_63,plain,
    ( ~ cUnsatisfiable(X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f124]) ).

cnf(c_65,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ cp(X0) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_67,plain,
    ( ~ cpxcomp(X0)
    | ra_Px1(X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f128]) ).

cnf(c_70,plain,
    ( ~ rinvS(X0,X1)
    | ~ ca_Vx2(X0)
    | cp(X1) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_71,plain,
    ( ~ rs(X0,X1)
    | rinvS(X1,X0) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_73,plain,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_74,plain,
    ( ~ rs(X0,X1)
    | rr(X0,X1) ),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_105,plain,
    ( ~ cUnsatisfiable(X0)
    | sP0(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63]) ).

cnf(c_107,plain,
    ( ~ cpxcomp(X0)
    | ra_Px1(X0,sK6(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_67]) ).

cnf(c_109,plain,
    ( cpxcomp(X0)
    | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_56]) ).

cnf(c_110,plain,
    ( ~ cUnsatisfiable(X0)
    | cpxcomp(X0) ),
    inference(renaming,[status(thm)],[c_109]) ).

cnf(c_113,plain,
    ( ~ rs(X0,X1)
    | rr(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_74]) ).

cnf(c_115,plain,
    ( ~ rs(X0,X1)
    | rinvS(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_71]) ).

cnf(c_123,plain,
    ( ~ cUnsatisfiable(X0)
    | rs(X0,sK3(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_58]) ).

cnf(c_125,plain,
    ( ~ cUnsatisfiable(X0)
    | ca_Vx2(sK4(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_59]) ).

cnf(c_127,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK4(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_60]) ).

cnf(c_129,plain,
    ( ~ cp(X0)
    | ~ ra_Px1(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_65]) ).

cnf(c_130,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ cp(X0) ),
    inference(renaming,[status(thm)],[c_129]) ).

cnf(c_210,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ cUnsatisfiable(X0)
    | X1 = X2 ),
    inference(bin_hyper_res,[status(thm)],[c_61,c_105]) ).

cnf(c_502,plain,
    ( sK6(X1) != X2
    | X0 != X1
    | ~ cpxcomp(X1)
    | ~ cp(X0) ),
    inference(resolution_lifted,[status(thm)],[c_130,c_107]) ).

cnf(c_503,plain,
    ( ~ cpxcomp(X0)
    | ~ cp(X0) ),
    inference(unflattening,[status(thm)],[c_502]) ).

cnf(c_528,plain,
    ( X0 != X1
    | X2 != X3
    | ~ rs(X3,X1)
    | ~ ca_Vx2(X0)
    | cp(X2) ),
    inference(resolution_lifted,[status(thm)],[c_70,c_115]) ).

cnf(c_529,plain,
    ( ~ rs(X0,X1)
    | ~ ca_Vx2(X1)
    | cp(X0) ),
    inference(unflattening,[status(thm)],[c_528]) ).

cnf(c_616,plain,
    ( X0 != X1
    | ~ cp(X1)
    | ~ cUnsatisfiable(X0) ),
    inference(resolution_lifted,[status(thm)],[c_110,c_503]) ).

cnf(c_617,plain,
    ( ~ cp(X0)
    | ~ cUnsatisfiable(X0) ),
    inference(unflattening,[status(thm)],[c_616]) ).

cnf(c_660,plain,
    ( sK3(X1) != X2
    | X0 != X1
    | ~ ca_Vx2(X2)
    | ~ cUnsatisfiable(X1)
    | cp(X0) ),
    inference(resolution_lifted,[status(thm)],[c_529,c_123]) ).

cnf(c_661,plain,
    ( ~ ca_Vx2(sK3(X0))
    | ~ cUnsatisfiable(X0)
    | cp(X0) ),
    inference(unflattening,[status(thm)],[c_660]) ).

cnf(c_663,plain,
    ( ~ cUnsatisfiable(X0)
    | ~ ca_Vx2(sK3(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_661,c_617,c_661]) ).

cnf(c_664,plain,
    ( ~ ca_Vx2(sK3(X0))
    | ~ cUnsatisfiable(X0) ),
    inference(renaming,[status(thm)],[c_663]) ).

cnf(c_672,plain,
    ( sK3(X1) != X2
    | X0 != X1
    | ~ cUnsatisfiable(X1)
    | rr(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_113,c_123]) ).

cnf(c_673,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK3(X0)) ),
    inference(unflattening,[status(thm)],[c_672]) ).

cnf(c_1002,plain,
    ( sK3(X0) != sK4(X1)
    | ~ cUnsatisfiable(X0)
    | ~ cUnsatisfiable(X1) ),
    inference(resolution_lifted,[status(thm)],[c_125,c_664]) ).

cnf(c_1003,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_1002]) ).

cnf(c_1808,plain,
    ( ~ rr(X0,X1)
    | ~ cUnsatisfiable(X0)
    | sK4(X0) = X1 ),
    inference(superposition,[status(thm)],[c_127,c_210]) ).

cnf(c_1830,plain,
    ( ~ cUnsatisfiable(X0)
    | sK3(X0) = sK4(X0) ),
    inference(superposition,[status(thm)],[c_673,c_1808]) ).

cnf(c_1837,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_1830]) ).

cnf(c_1838,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1837,c_1003,c_73]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : KRS113+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n007.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31  % CPULimit : 300
% 0.16/0.31  % WCLimit  : 300
% 0.16/0.31  % DateTime : Thu May  2 22:31:05 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.42/1.11  % SZS status Started for theBenchmark.p
% 0.42/1.11  % SZS status Unsatisfiable for theBenchmark.p
% 0.42/1.11  
% 0.42/1.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.42/1.11  
% 0.42/1.11  ------  iProver source info
% 0.42/1.11  
% 0.42/1.11  git: date: 2024-05-02 19:28:25 +0000
% 0.42/1.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.42/1.11  git: non_committed_changes: false
% 0.42/1.11  
% 0.42/1.11  ------ Parsing...
% 0.42/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.42/1.11  
% 0.42/1.11  ------ 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 
% 0.42/1.11  
% 0.42/1.11  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.42/1.11  
% 0.42/1.11  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.42/1.11  ------ Proving...
% 0.42/1.11  ------ Problem Properties 
% 0.42/1.11  
% 0.42/1.11  
% 0.42/1.11  clauses                                 12
% 0.42/1.11  conjectures                             0
% 0.42/1.11  EPR                                     2
% 0.42/1.11  Horn                                    9
% 0.42/1.11  unary                                   1
% 0.42/1.11  binary                                  6
% 0.42/1.11  lits                                    35
% 0.42/1.11  lits eq                                 3
% 0.42/1.11  fd_pure                                 0
% 0.42/1.11  fd_pseudo                               0
% 0.42/1.11  fd_cond                                 0
% 0.42/1.11  fd_pseudo_cond                          1
% 0.42/1.11  AC symbols                              0
% 0.42/1.11  
% 0.42/1.11  ------ Schedule dynamic 5 is on 
% 0.42/1.11  
% 0.42/1.11  ------ no conjectures: strip conj schedule 
% 0.42/1.11  
% 0.42/1.11  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.42/1.11  
% 0.42/1.11  
% 0.42/1.11  ------ 
% 0.42/1.11  Current options:
% 0.42/1.11  ------ 
% 0.42/1.11  
% 0.42/1.11  
% 0.42/1.11  
% 0.42/1.11  
% 0.42/1.11  ------ Proving...
% 0.42/1.11  
% 0.42/1.11  
% 0.42/1.11  % SZS status Unsatisfiable for theBenchmark.p
% 0.42/1.11  
% 0.42/1.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/1.11  
% 0.42/1.11  
%------------------------------------------------------------------------------