TSTP Solution File: KRS098+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS098+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 02:33:36 EDT 2024

% Result   : Unsatisfiable 1.84s 1.19s
% Output   : CNFRefutation 1.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  134 (  16 unt;   0 def)
%            Number of atoms       :  539 (  84 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  639 ( 234   ~; 211   |; 164   &)
%                                         (   9 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   1 con; 0-1 aty)
%            Number of variables   :  316 (   0 sgn 156   !;  72   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f28,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ? [X4] :
            ( ? [X5] :
                ( cc(X5)
                & rt1(X4,X5) )
            & ! [X6,X7] :
                ( ( rtt(X4,X7)
                  & rtt(X4,X6) )
               => X6 = X7 )
            & rr1(X3,X4) )
        & ~ ? [X8,X9] :
              ( X8 != X9
              & rr(X3,X9)
              & rr(X3,X8) )
        & ? [X4] :
            ( ? [X5] :
                ( cd(X5)
                & rt2(X4,X5) )
            & ! [X6,X7] :
                ( ( rtt(X4,X7)
                  & rtt(X4,X6) )
               => X6 = X7 )
            & rr2(X3,X4) )
        & ? [X4] :
            ( ! [X6,X7] :
                ( ( rtt(X4,X7)
                  & rtt(X4,X6) )
               => X6 = X7 )
            & ? [X5] :
                ( ce(X5)
                & rt3(X4,X5) )
            & rr3(X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f30,axiom,
    cUnsatisfiable(i2003_11_14_17_20_25524),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f31,axiom,
    ! [X3] :
      ~ ( cd(X3)
        & cc(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f34,axiom,
    ! [X3,X4] :
      ( rr1(X3,X4)
     => rr(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(f35,axiom,
    ! [X3,X4] :
      ( rr2(X3,X4)
     => rr(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

fof(f36,axiom,
    ! [X3,X4] :
      ( rt1(X3,X4)
     => rtt(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

fof(f37,axiom,
    ! [X3,X4] :
      ( rt2(X3,X4)
     => rtt(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

fof(f42,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2] :
                ( cc(X2)
                & rt1(X1,X2) )
            & ! [X3,X4] :
                ( ( rtt(X1,X4)
                  & rtt(X1,X3) )
               => X3 = X4 )
            & rr1(X0,X1) )
        & ~ ? [X5,X6] :
              ( X5 != X6
              & rr(X0,X6)
              & rr(X0,X5) )
        & ? [X7] :
            ( ? [X8] :
                ( cd(X8)
                & rt2(X7,X8) )
            & ! [X9,X10] :
                ( ( rtt(X7,X10)
                  & rtt(X7,X9) )
               => X9 = X10 )
            & rr2(X0,X7) )
        & ? [X11] :
            ( ! [X12,X13] :
                ( ( rtt(X11,X13)
                  & rtt(X11,X12) )
               => X12 = X13 )
            & ? [X14] :
                ( ce(X14)
                & rt3(X11,X14) )
            & rr3(X0,X11) ) ) ),
    inference(rectify,[],[f28]) ).

fof(f44,plain,
    ! [X0] :
      ~ ( cd(X0)
        & cc(X0) ),
    inference(rectify,[],[f31]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( rr1(X0,X1)
     => rr(X0,X1) ),
    inference(rectify,[],[f34]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( rr2(X0,X1)
     => rr(X0,X1) ),
    inference(rectify,[],[f35]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( rt1(X0,X1)
     => rtt(X0,X1) ),
    inference(rectify,[],[f36]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( rt2(X0,X1)
     => rtt(X0,X1) ),
    inference(rectify,[],[f37]) ).

fof(f103,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2] :
                ( cc(X2)
                & rt1(X1,X2) )
            & ! [X3,X4] :
                ( X3 = X4
                | ~ rtt(X1,X4)
                | ~ rtt(X1,X3) )
            & rr1(X0,X1) )
        & ! [X5,X6] :
            ( X5 = X6
            | ~ rr(X0,X6)
            | ~ rr(X0,X5) )
        & ? [X7] :
            ( ? [X8] :
                ( cd(X8)
                & rt2(X7,X8) )
            & ! [X9,X10] :
                ( X9 = X10
                | ~ rtt(X7,X10)
                | ~ rtt(X7,X9) )
            & rr2(X0,X7) )
        & ? [X11] :
            ( ! [X12,X13] :
                ( X12 = X13
                | ~ rtt(X11,X13)
                | ~ rtt(X11,X12) )
            & ? [X14] :
                ( ce(X14)
                & rt3(X11,X14) )
            & rr3(X0,X11) ) ) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f104,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2] :
                ( cc(X2)
                & rt1(X1,X2) )
            & ! [X3,X4] :
                ( X3 = X4
                | ~ rtt(X1,X4)
                | ~ rtt(X1,X3) )
            & rr1(X0,X1) )
        & ! [X5,X6] :
            ( X5 = X6
            | ~ rr(X0,X6)
            | ~ rr(X0,X5) )
        & ? [X7] :
            ( ? [X8] :
                ( cd(X8)
                & rt2(X7,X8) )
            & ! [X9,X10] :
                ( X9 = X10
                | ~ rtt(X7,X10)
                | ~ rtt(X7,X9) )
            & rr2(X0,X7) )
        & ? [X11] :
            ( ! [X12,X13] :
                ( X12 = X13
                | ~ rtt(X11,X13)
                | ~ rtt(X11,X12) )
            & ? [X14] :
                ( ce(X14)
                & rt3(X11,X14) )
            & rr3(X0,X11) ) ) ),
    inference(flattening,[],[f103]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rr1(X0,X1) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rr2(X0,X1) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( rtt(X0,X1)
      | ~ rt1(X0,X1) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( rtt(X0,X1)
      | ~ rt2(X0,X1) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f114,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ? [X11] :
          ( ! [X12,X13] :
              ( X12 = X13
              | ~ rtt(X11,X13)
              | ~ rtt(X11,X12) )
          & ? [X14] :
              ( ce(X14)
              & rt3(X11,X14) )
          & rr3(X0,X11) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f115,plain,
    ! [X0] :
      ( sP1(X0)
    <=> ? [X7] :
          ( ? [X8] :
              ( cd(X8)
              & rt2(X7,X8) )
          & ! [X9,X10] :
              ( X9 = X10
              | ~ rtt(X7,X10)
              | ~ rtt(X7,X9) )
          & rr2(X0,X7) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f116,plain,
    ! [X0] :
      ( sP2(X0)
    <=> ! [X5,X6] :
          ( X5 = X6
          | ~ rr(X0,X6)
          | ~ rr(X0,X5) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f117,plain,
    ! [X0] :
      ( sP3(X0)
    <=> ( ? [X1] :
            ( ? [X2] :
                ( cc(X2)
                & rt1(X1,X2) )
            & ! [X3,X4] :
                ( X3 = X4
                | ~ rtt(X1,X4)
                | ~ rtt(X1,X3) )
            & rr1(X0,X1) )
        & sP2(X0)
        & sP1(X0)
        & sP0(X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f118,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP3(X0) ),
    inference(definition_folding,[],[f104,f117,f116,f115,f114]) ).

fof(f120,plain,
    ! [X0] :
      ( ( sP3(X0)
        | ! [X1] :
            ( ! [X2] :
                ( ~ cc(X2)
                | ~ rt1(X1,X2) )
            | ? [X3,X4] :
                ( X3 != X4
                & rtt(X1,X4)
                & rtt(X1,X3) )
            | ~ rr1(X0,X1) )
        | ~ sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0) )
      & ( ( ? [X1] :
              ( ? [X2] :
                  ( cc(X2)
                  & rt1(X1,X2) )
              & ! [X3,X4] :
                  ( X3 = X4
                  | ~ rtt(X1,X4)
                  | ~ rtt(X1,X3) )
              & rr1(X0,X1) )
          & sP2(X0)
          & sP1(X0)
          & sP0(X0) )
        | ~ sP3(X0) ) ),
    inference(nnf_transformation,[],[f117]) ).

fof(f121,plain,
    ! [X0] :
      ( ( sP3(X0)
        | ! [X1] :
            ( ! [X2] :
                ( ~ cc(X2)
                | ~ rt1(X1,X2) )
            | ? [X3,X4] :
                ( X3 != X4
                & rtt(X1,X4)
                & rtt(X1,X3) )
            | ~ rr1(X0,X1) )
        | ~ sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0) )
      & ( ( ? [X1] :
              ( ? [X2] :
                  ( cc(X2)
                  & rt1(X1,X2) )
              & ! [X3,X4] :
                  ( X3 = X4
                  | ~ rtt(X1,X4)
                  | ~ rtt(X1,X3) )
              & rr1(X0,X1) )
          & sP2(X0)
          & sP1(X0)
          & sP0(X0) )
        | ~ sP3(X0) ) ),
    inference(flattening,[],[f120]) ).

fof(f122,plain,
    ! [X0] :
      ( ( sP3(X0)
        | ! [X1] :
            ( ! [X2] :
                ( ~ cc(X2)
                | ~ rt1(X1,X2) )
            | ? [X3,X4] :
                ( X3 != X4
                & rtt(X1,X4)
                & rtt(X1,X3) )
            | ~ rr1(X0,X1) )
        | ~ sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0) )
      & ( ( ? [X5] :
              ( ? [X6] :
                  ( cc(X6)
                  & rt1(X5,X6) )
              & ! [X7,X8] :
                  ( X7 = X8
                  | ~ rtt(X5,X8)
                  | ~ rtt(X5,X7) )
              & rr1(X0,X5) )
          & sP2(X0)
          & sP1(X0)
          & sP0(X0) )
        | ~ sP3(X0) ) ),
    inference(rectify,[],[f121]) ).

fof(f123,plain,
    ! [X1] :
      ( ? [X3,X4] :
          ( X3 != X4
          & rtt(X1,X4)
          & rtt(X1,X3) )
     => ( sK4(X1) != sK5(X1)
        & rtt(X1,sK5(X1))
        & rtt(X1,sK4(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0] :
      ( ? [X5] :
          ( ? [X6] :
              ( cc(X6)
              & rt1(X5,X6) )
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rtt(X5,X8)
              | ~ rtt(X5,X7) )
          & rr1(X0,X5) )
     => ( ? [X6] :
            ( cc(X6)
            & rt1(sK6(X0),X6) )
        & ! [X8,X7] :
            ( X7 = X8
            | ~ rtt(sK6(X0),X8)
            | ~ rtt(sK6(X0),X7) )
        & rr1(X0,sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0] :
      ( ? [X6] :
          ( cc(X6)
          & rt1(sK6(X0),X6) )
     => ( cc(sK7(X0))
        & rt1(sK6(X0),sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ! [X0] :
      ( ( sP3(X0)
        | ! [X1] :
            ( ! [X2] :
                ( ~ cc(X2)
                | ~ rt1(X1,X2) )
            | ( sK4(X1) != sK5(X1)
              & rtt(X1,sK5(X1))
              & rtt(X1,sK4(X1)) )
            | ~ rr1(X0,X1) )
        | ~ sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0) )
      & ( ( cc(sK7(X0))
          & rt1(sK6(X0),sK7(X0))
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rtt(sK6(X0),X8)
              | ~ rtt(sK6(X0),X7) )
          & rr1(X0,sK6(X0))
          & sP2(X0)
          & sP1(X0)
          & sP0(X0) )
        | ~ sP3(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f122,f125,f124,f123]) ).

fof(f127,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ? [X5,X6] :
            ( X5 != X6
            & rr(X0,X6)
            & rr(X0,X5) ) )
      & ( ! [X5,X6] :
            ( X5 = X6
            | ~ rr(X0,X6)
            | ~ rr(X0,X5) )
        | ~ sP2(X0) ) ),
    inference(nnf_transformation,[],[f116]) ).

fof(f128,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rr(X0,X2)
            & rr(X0,X1) ) )
      & ( ! [X3,X4] :
            ( X3 = X4
            | ~ rr(X0,X4)
            | ~ rr(X0,X3) )
        | ~ sP2(X0) ) ),
    inference(rectify,[],[f127]) ).

fof(f129,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & rr(X0,X2)
          & rr(X0,X1) )
     => ( sK8(X0) != sK9(X0)
        & rr(X0,sK9(X0))
        & rr(X0,sK8(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ( sK8(X0) != sK9(X0)
          & rr(X0,sK9(X0))
          & rr(X0,sK8(X0)) ) )
      & ( ! [X3,X4] :
            ( X3 = X4
            | ~ rr(X0,X4)
            | ~ rr(X0,X3) )
        | ~ sP2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f128,f129]) ).

fof(f131,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X7] :
            ( ! [X8] :
                ( ~ cd(X8)
                | ~ rt2(X7,X8) )
            | ? [X9,X10] :
                ( X9 != X10
                & rtt(X7,X10)
                & rtt(X7,X9) )
            | ~ rr2(X0,X7) ) )
      & ( ? [X7] :
            ( ? [X8] :
                ( cd(X8)
                & rt2(X7,X8) )
            & ! [X9,X10] :
                ( X9 = X10
                | ~ rtt(X7,X10)
                | ~ rtt(X7,X9) )
            & rr2(X0,X7) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f115]) ).

fof(f132,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1] :
            ( ! [X2] :
                ( ~ cd(X2)
                | ~ rt2(X1,X2) )
            | ? [X3,X4] :
                ( X3 != X4
                & rtt(X1,X4)
                & rtt(X1,X3) )
            | ~ rr2(X0,X1) ) )
      & ( ? [X5] :
            ( ? [X6] :
                ( cd(X6)
                & rt2(X5,X6) )
            & ! [X7,X8] :
                ( X7 = X8
                | ~ rtt(X5,X8)
                | ~ rtt(X5,X7) )
            & rr2(X0,X5) )
        | ~ sP1(X0) ) ),
    inference(rectify,[],[f131]) ).

fof(f133,plain,
    ! [X1] :
      ( ? [X3,X4] :
          ( X3 != X4
          & rtt(X1,X4)
          & rtt(X1,X3) )
     => ( sK10(X1) != sK11(X1)
        & rtt(X1,sK11(X1))
        & rtt(X1,sK10(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ! [X0] :
      ( ? [X5] :
          ( ? [X6] :
              ( cd(X6)
              & rt2(X5,X6) )
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rtt(X5,X8)
              | ~ rtt(X5,X7) )
          & rr2(X0,X5) )
     => ( ? [X6] :
            ( cd(X6)
            & rt2(sK12(X0),X6) )
        & ! [X8,X7] :
            ( X7 = X8
            | ~ rtt(sK12(X0),X8)
            | ~ rtt(sK12(X0),X7) )
        & rr2(X0,sK12(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ! [X0] :
      ( ? [X6] :
          ( cd(X6)
          & rt2(sK12(X0),X6) )
     => ( cd(sK13(X0))
        & rt2(sK12(X0),sK13(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1] :
            ( ! [X2] :
                ( ~ cd(X2)
                | ~ rt2(X1,X2) )
            | ( sK10(X1) != sK11(X1)
              & rtt(X1,sK11(X1))
              & rtt(X1,sK10(X1)) )
            | ~ rr2(X0,X1) ) )
      & ( ( cd(sK13(X0))
          & rt2(sK12(X0),sK13(X0))
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rtt(sK12(X0),X8)
              | ~ rtt(sK12(X0),X7) )
          & rr2(X0,sK12(X0)) )
        | ~ sP1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f132,f135,f134,f133]) ).

fof(f143,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ sP3(X0) )
      & ( sP3(X0)
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f176,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f177,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f178,plain,
    ! [X0] :
      ( rr1(X0,sK6(X0))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f179,plain,
    ! [X0,X8,X7] :
      ( X7 = X8
      | ~ rtt(sK6(X0),X8)
      | ~ rtt(sK6(X0),X7)
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f180,plain,
    ! [X0] :
      ( rt1(sK6(X0),sK7(X0))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f181,plain,
    ! [X0] :
      ( cc(sK7(X0))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f185,plain,
    ! [X3,X0,X4] :
      ( X3 = X4
      | ~ rr(X0,X4)
      | ~ rr(X0,X3)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f189,plain,
    ! [X0] :
      ( rr2(X0,sK12(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f191,plain,
    ! [X0] :
      ( rt2(sK12(X0),sK13(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f192,plain,
    ! [X0] :
      ( cd(sK13(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f203,plain,
    ! [X0] :
      ( sP3(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f208,plain,
    cUnsatisfiable(i2003_11_14_17_20_25524),
    inference(cnf_transformation,[],[f30]) ).

fof(f209,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f212,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rr1(X0,X1) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rr2(X0,X1) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( rtt(X0,X1)
      | ~ rt1(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( rtt(X0,X1)
      | ~ rt2(X0,X1) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_56,plain,
    ( ~ sP3(X0)
    | cc(sK7(X0)) ),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_57,plain,
    ( ~ sP3(X0)
    | rt1(sK6(X0),sK7(X0)) ),
    inference(cnf_transformation,[],[f180]) ).

cnf(c_58,plain,
    ( ~ rtt(sK6(X0),X1)
    | ~ rtt(sK6(X0),X2)
    | ~ sP3(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_59,plain,
    ( ~ sP3(X0)
    | rr1(X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_60,plain,
    ( ~ sP3(X0)
    | sP2(X0) ),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_61,plain,
    ( ~ sP3(X0)
    | sP1(X0) ),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_66,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ sP2(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f185]) ).

cnf(c_70,plain,
    ( ~ sP1(X0)
    | cd(sK13(X0)) ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_71,plain,
    ( ~ sP1(X0)
    | rt2(sK12(X0),sK13(X0)) ),
    inference(cnf_transformation,[],[f191]) ).

cnf(c_73,plain,
    ( ~ sP1(X0)
    | rr2(X0,sK12(X0)) ),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_82,plain,
    ( ~ cUnsatisfiable(X0)
    | sP3(X0) ),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_86,plain,
    cUnsatisfiable(i2003_11_14_17_20_25524),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_87,plain,
    ( ~ cc(X0)
    | ~ cd(X0) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_90,plain,
    ( ~ rr1(X0,X1)
    | rr(X0,X1) ),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_91,plain,
    ( ~ rr2(X0,X1)
    | rr(X0,X1) ),
    inference(cnf_transformation,[],[f213]) ).

cnf(c_92,plain,
    ( ~ rt1(X0,X1)
    | rtt(X0,X1) ),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_93,plain,
    ( ~ rt2(X0,X1)
    | rtt(X0,X1) ),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_147,plain,
    ( ~ cUnsatisfiable(X0)
    | sP3(X0) ),
    inference(prop_impl_just,[status(thm)],[c_82]) ).

cnf(c_155,plain,
    ( sP2(X0)
    | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_82,c_60]) ).

cnf(c_156,plain,
    ( ~ cUnsatisfiable(X0)
    | sP2(X0) ),
    inference(renaming,[status(thm)],[c_155]) ).

cnf(c_157,plain,
    ( ~ sP1(X0)
    | cd(sK13(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_70]) ).

cnf(c_159,plain,
    ( ~ sP1(X0)
    | rt2(sK12(X0),sK13(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_71]) ).

cnf(c_161,plain,
    ( ~ sP1(X0)
    | rr2(X0,sK12(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_73]) ).

cnf(c_163,plain,
    ( sP1(X0)
    | ~ cUnsatisfiable(X0) ),
    inference(prop_impl_just,[status(thm)],[c_82,c_61]) ).

cnf(c_164,plain,
    ( ~ cUnsatisfiable(X0)
    | sP1(X0) ),
    inference(renaming,[status(thm)],[c_163]) ).

cnf(c_173,plain,
    ( ~ rt1(X0,X1)
    | rtt(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_92]) ).

cnf(c_177,plain,
    ( rr(X0,X1)
    | ~ rr1(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_90]) ).

cnf(c_178,plain,
    ( ~ rr1(X0,X1)
    | rr(X0,X1) ),
    inference(renaming,[status(thm)],[c_177]) ).

cnf(c_179,plain,
    ( rr(X0,X1)
    | ~ rr2(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_91]) ).

cnf(c_180,plain,
    ( ~ rr2(X0,X1)
    | rr(X0,X1) ),
    inference(renaming,[status(thm)],[c_179]) ).

cnf(c_183,plain,
    ( ~ rt2(X0,X1)
    | rtt(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_93]) ).

cnf(c_193,plain,
    ( ~ cUnsatisfiable(X0)
    | cc(sK7(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_82,c_56]) ).

cnf(c_195,plain,
    ( ~ cUnsatisfiable(X0)
    | rt1(sK6(X0),sK7(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_82,c_57]) ).

cnf(c_197,plain,
    ( ~ cUnsatisfiable(X0)
    | rr1(X0,sK6(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_82,c_59]) ).

cnf(c_201,plain,
    ( ~ cd(X0)
    | ~ cc(X0) ),
    inference(prop_impl_just,[status(thm)],[c_87]) ).

cnf(c_202,plain,
    ( ~ cc(X0)
    | ~ cd(X0) ),
    inference(renaming,[status(thm)],[c_201]) ).

cnf(c_331,plain,
    ( ~ rtt(sK6(X0),X1)
    | ~ rtt(sK6(X0),X2)
    | ~ cUnsatisfiable(X0)
    | X1 = X2 ),
    inference(bin_hyper_res,[status(thm)],[c_58,c_147]) ).

cnf(c_894,plain,
    ( sK13(X0) != X2
    | sK12(X0) != X1
    | ~ sP1(X0)
    | rtt(X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_183,c_159]) ).

cnf(c_895,plain,
    ( ~ sP1(X0)
    | rtt(sK12(X0),sK13(X0)) ),
    inference(unflattening,[status(thm)],[c_894]) ).

cnf(c_976,plain,
    ( sK13(X0) != X1
    | ~ cc(X1)
    | ~ sP1(X0) ),
    inference(resolution_lifted,[status(thm)],[c_157,c_202]) ).

cnf(c_977,plain,
    ( ~ cc(sK13(X0))
    | ~ sP1(X0) ),
    inference(unflattening,[status(thm)],[c_976]) ).

cnf(c_989,plain,
    ( sK12(X0) != X1
    | X0 != X2
    | ~ sP1(X0)
    | rr(X2,X1) ),
    inference(resolution_lifted,[status(thm)],[c_161,c_180]) ).

cnf(c_990,plain,
    ( ~ sP1(X0)
    | rr(X0,sK12(X0)) ),
    inference(unflattening,[status(thm)],[c_989]) ).

cnf(c_1302,plain,
    ( sK7(X0) != X2
    | sK6(X0) != X1
    | ~ cUnsatisfiable(X0)
    | rtt(X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_173,c_195]) ).

cnf(c_1303,plain,
    ( ~ cUnsatisfiable(X0)
    | rtt(sK6(X0),sK7(X0)) ),
    inference(unflattening,[status(thm)],[c_1302]) ).

cnf(c_1359,plain,
    ( sK6(X0) != X1
    | X0 != X2
    | ~ cUnsatisfiable(X0)
    | rr(X2,X1) ),
    inference(resolution_lifted,[status(thm)],[c_197,c_178]) ).

cnf(c_1360,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK6(X0)) ),
    inference(unflattening,[status(thm)],[c_1359]) ).

cnf(c_1376,plain,
    ( X0 != i2003_11_14_17_20_25524
    | rr(X0,sK6(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_1360,c_86]) ).

cnf(c_1377,plain,
    rr(i2003_11_14_17_20_25524,sK6(i2003_11_14_17_20_25524)),
    inference(unflattening,[status(thm)],[c_1376]) ).

cnf(c_1381,plain,
    ( X0 != i2003_11_14_17_20_25524
    | rtt(sK6(X0),sK7(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_1303,c_86]) ).

cnf(c_1382,plain,
    rtt(sK6(i2003_11_14_17_20_25524),sK7(i2003_11_14_17_20_25524)),
    inference(unflattening,[status(thm)],[c_1381]) ).

cnf(c_1386,plain,
    ( X0 != i2003_11_14_17_20_25524
    | ~ rtt(sK6(X0),X1)
    | ~ rtt(sK6(X0),X2)
    | X1 = X2 ),
    inference(resolution_lifted,[status(thm)],[c_331,c_86]) ).

cnf(c_1387,plain,
    ( ~ rtt(sK6(i2003_11_14_17_20_25524),X0)
    | ~ rtt(sK6(i2003_11_14_17_20_25524),X1)
    | X0 = X1 ),
    inference(unflattening,[status(thm)],[c_1386]) ).

cnf(c_1398,plain,
    ( X0 != i2003_11_14_17_20_25524
    | cc(sK7(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_193,c_86]) ).

cnf(c_1399,plain,
    cc(sK7(i2003_11_14_17_20_25524)),
    inference(unflattening,[status(thm)],[c_1398]) ).

cnf(c_1408,plain,
    ( X0 != i2003_11_14_17_20_25524
    | sP1(X0) ),
    inference(resolution_lifted,[status(thm)],[c_164,c_86]) ).

cnf(c_1409,plain,
    sP1(i2003_11_14_17_20_25524),
    inference(unflattening,[status(thm)],[c_1408]) ).

cnf(c_1413,plain,
    ( X0 != i2003_11_14_17_20_25524
    | sP2(X0) ),
    inference(resolution_lifted,[status(thm)],[c_156,c_86]) ).

cnf(c_1414,plain,
    sP2(i2003_11_14_17_20_25524),
    inference(unflattening,[status(thm)],[c_1413]) ).

cnf(c_1432,plain,
    ( sK13(X0) != sK7(i2003_11_14_17_20_25524)
    | ~ sP1(X0) ),
    inference(resolution_lifted,[status(thm)],[c_1399,c_977]) ).

cnf(c_1514,plain,
    ( sK13(X0) != sK7(i2003_11_14_17_20_25524)
    | X0 != i2003_11_14_17_20_25524 ),
    inference(resolution_lifted,[status(thm)],[c_1432,c_1409]) ).

cnf(c_1515,plain,
    sK13(i2003_11_14_17_20_25524) != sK7(i2003_11_14_17_20_25524),
    inference(unflattening,[status(thm)],[c_1514]) ).

cnf(c_1519,plain,
    ( X0 != i2003_11_14_17_20_25524
    | rr(X0,sK12(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_990,c_1409]) ).

cnf(c_1520,plain,
    rr(i2003_11_14_17_20_25524,sK12(i2003_11_14_17_20_25524)),
    inference(unflattening,[status(thm)],[c_1519]) ).

cnf(c_1529,plain,
    ( X0 != i2003_11_14_17_20_25524
    | rtt(sK12(X0),sK13(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_895,c_1409]) ).

cnf(c_1530,plain,
    rtt(sK12(i2003_11_14_17_20_25524),sK13(i2003_11_14_17_20_25524)),
    inference(unflattening,[status(thm)],[c_1529]) ).

cnf(c_2107,plain,
    ( ~ rr(i2003_11_14_17_20_25524,X0)
    | ~ sP2(i2003_11_14_17_20_25524)
    | sK6(i2003_11_14_17_20_25524) = X0 ),
    inference(superposition,[status(thm)],[c_1377,c_66]) ).

cnf(c_2108,plain,
    ( ~ rr(i2003_11_14_17_20_25524,X0)
    | sK6(i2003_11_14_17_20_25524) = X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2107,c_1414]) ).

cnf(c_2126,plain,
    sK6(i2003_11_14_17_20_25524) = sK12(i2003_11_14_17_20_25524),
    inference(superposition,[status(thm)],[c_1520,c_2108]) ).

cnf(c_2129,plain,
    rtt(sK6(i2003_11_14_17_20_25524),sK13(i2003_11_14_17_20_25524)),
    inference(demodulation,[status(thm)],[c_1530,c_2126]) ).

cnf(c_2141,plain,
    ( ~ rtt(sK6(i2003_11_14_17_20_25524),X0)
    | sK7(i2003_11_14_17_20_25524) = X0 ),
    inference(superposition,[status(thm)],[c_1382,c_1387]) ).

cnf(c_2158,plain,
    sK7(i2003_11_14_17_20_25524) = sK13(i2003_11_14_17_20_25524),
    inference(superposition,[status(thm)],[c_2129,c_2141]) ).

cnf(c_2161,plain,
    sK7(i2003_11_14_17_20_25524) != sK7(i2003_11_14_17_20_25524),
    inference(demodulation,[status(thm)],[c_1515,c_2158]) ).

cnf(c_2163,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_2161]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KRS098+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n031.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 23:16:31 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.84/1.19  % SZS status Started for theBenchmark.p
% 1.84/1.19  % SZS status Unsatisfiable for theBenchmark.p
% 1.84/1.19  
% 1.84/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.84/1.19  
% 1.84/1.19  ------  iProver source info
% 1.84/1.19  
% 1.84/1.19  git: date: 2024-05-02 19:28:25 +0000
% 1.84/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.84/1.19  git: non_committed_changes: false
% 1.84/1.19  
% 1.84/1.19  ------ Parsing...
% 1.84/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.84/1.19  
% 1.84/1.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 10 0s  sf_e  pe_s  pe_e 
% 1.84/1.19  
% 1.84/1.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.84/1.19  
% 1.84/1.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.84/1.19  ------ Proving...
% 1.84/1.19  ------ Problem Properties 
% 1.84/1.19  
% 1.84/1.19  
% 1.84/1.19  clauses                                 18
% 1.84/1.19  conjectures                             0
% 1.84/1.19  EPR                                     2
% 1.84/1.19  Horn                                    16
% 1.84/1.19  unary                                   11
% 1.84/1.19  binary                                  3
% 1.84/1.19  lits                                    30
% 1.84/1.19  lits eq                                 6
% 1.84/1.19  fd_pure                                 0
% 1.84/1.19  fd_pseudo                               0
% 1.84/1.19  fd_cond                                 0
% 1.84/1.19  fd_pseudo_cond                          4
% 1.84/1.19  AC symbols                              0
% 1.84/1.19  
% 1.84/1.19  ------ Schedule dynamic 5 is on 
% 1.84/1.19  
% 1.84/1.19  ------ no conjectures: strip conj schedule 
% 1.84/1.19  
% 1.84/1.19  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.84/1.19  
% 1.84/1.19  
% 1.84/1.19  ------ 
% 1.84/1.19  Current options:
% 1.84/1.19  ------ 
% 1.84/1.19  
% 1.84/1.19  
% 1.84/1.19  
% 1.84/1.19  
% 1.84/1.19  ------ Proving...
% 1.84/1.19  
% 1.84/1.19  
% 1.84/1.19  % SZS status Unsatisfiable for theBenchmark.p
% 1.84/1.19  
% 1.84/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/1.19  
% 1.84/1.19  
%------------------------------------------------------------------------------