TSTP Solution File: NUN057+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN057+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n013.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 : Wed Aug 31 18:08:01 EDT 2022

% Result   : Theorem 0.19s 0.56s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  101 (  26 unt;   0 def)
%            Number of atoms       :  327 (  59 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  375 ( 149   ~; 110   |;  99   &)
%                                         (   8 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   3 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  243 ( 176   !;  67   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f404,plain,
    $false,
    inference(avatar_sat_refutation,[],[f394,f399,f403]) ).

fof(f403,plain,
    spl26_7,
    inference(avatar_contradiction_clause,[],[f402]) ).

fof(f402,plain,
    ( $false
    | spl26_7 ),
    inference(subsumption_resolution,[],[f401,f111]) ).

fof(f111,plain,
    r1(sK17),
    inference(equality_resolution,[],[f93]) ).

fof(f93,plain,
    ! [X1] :
      ( sK17 != X1
      | r1(X1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X1] :
      ( ( sK17 != X1
        & ~ r1(X1) )
      | ( sK17 = X1
        & r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f1,f54]) ).

fof(f54,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 != X1
          & ~ r1(X1) )
        | ( X0 = X1
          & r1(X1) ) )
   => ! [X1] :
        ( ( sK17 != X1
          & ~ r1(X1) )
        | ( sK17 = X1
          & r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( X0 != X1
        & ~ r1(X1) )
      | ( X0 = X1
        & r1(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f401,plain,
    ( ~ r1(sK17)
    | spl26_7 ),
    inference(resolution,[],[f400,f140]) ).

fof(f140,plain,
    ! [X0] :
      ( sP20(sK8(X0))
      | ~ r1(X0) ),
    inference(resolution,[],[f114,f108]) ).

fof(f108,plain,
    ! [X0] : r2(X0,sK8(X0)),
    inference(equality_resolution,[],[f77]) ).

fof(f77,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK8(X0) != X2 ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X2] :
      ( ( sK8(X0) = X2
        & r2(X0,X2) )
      | ( sK8(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK8(X0) = X2
            & r2(X0,X2) )
          | ( sK8(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 = X2
        & r2(X0,X2) )
      | ( X1 != X2
        & ~ r2(X0,X2) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( r2(X2,X4)
        & X3 = X4 )
      | ( ~ r2(X2,X4)
        & X3 != X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f114,plain,
    ! [X8,X7] :
      ( ~ r2(X8,X7)
      | sP20(X7)
      | ~ r1(X8) ),
    inference(cnf_transformation,[],[f114_D]) ).

fof(f114_D,plain,
    ! [X7] :
      ( ! [X8] :
          ( ~ r2(X8,X7)
          | ~ r1(X8) )
    <=> ~ sP20(X7) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP20])]) ).

fof(f400,plain,
    ( ~ sP20(sK8(sK17))
    | spl26_7 ),
    inference(resolution,[],[f393,f143]) ).

fof(f143,plain,
    ! [X0] :
      ( sP21(sK8(X0))
      | ~ sP20(X0) ),
    inference(resolution,[],[f116,f108]) ).

fof(f116,plain,
    ! [X6,X7] :
      ( ~ r2(X7,X6)
      | sP21(X6)
      | ~ sP20(X7) ),
    inference(cnf_transformation,[],[f116_D]) ).

fof(f116_D,plain,
    ! [X6] :
      ( ! [X7] :
          ( ~ r2(X7,X6)
          | ~ sP20(X7) )
    <=> ~ sP21(X6) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).

fof(f393,plain,
    ( ~ sP21(sK8(sK8(sK17)))
    | spl26_7 ),
    inference(avatar_component_clause,[],[f391]) ).

fof(f391,plain,
    ( spl26_7
  <=> sP21(sK8(sK8(sK17))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).

fof(f399,plain,
    ~ spl26_6,
    inference(avatar_contradiction_clause,[],[f398]) ).

fof(f398,plain,
    ( $false
    | ~ spl26_6 ),
    inference(subsumption_resolution,[],[f397,f111]) ).

fof(f397,plain,
    ( ~ r1(sK17)
    | ~ spl26_6 ),
    inference(resolution,[],[f396,f155]) ).

fof(f155,plain,
    ! [X0] :
      ( ~ sP25(sK8(X0))
      | ~ r1(X0) ),
    inference(resolution,[],[f125,f108]) ).

fof(f125,plain,
    ! [X4,X5] :
      ( ~ r2(X5,X4)
      | ~ r1(X5)
      | ~ sP25(X4) ),
    inference(general_splitting,[],[f123,f124_D]) ).

fof(f124,plain,
    ! [X3,X4] :
      ( ~ r2(X4,X3)
      | ~ sP24(X3)
      | sP25(X4) ),
    inference(cnf_transformation,[],[f124_D]) ).

fof(f124_D,plain,
    ! [X4] :
      ( ! [X3] :
          ( ~ r2(X4,X3)
          | ~ sP24(X3) )
    <=> ~ sP25(X4) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP25])]) ).

fof(f123,plain,
    ! [X3,X4,X5] :
      ( ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ sP24(X3) ),
    inference(general_splitting,[],[f121,f122_D]) ).

fof(f122,plain,
    ! [X2,X3] :
      ( ~ r2(X3,X2)
      | sP24(X3)
      | ~ sP23(X2) ),
    inference(cnf_transformation,[],[f122_D]) ).

fof(f122_D,plain,
    ! [X3] :
      ( ! [X2] :
          ( ~ r2(X3,X2)
          | ~ sP23(X2) )
    <=> ~ sP24(X3) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP24])]) ).

fof(f121,plain,
    ! [X2,X3,X4,X5] :
      ( ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ sP23(X2) ),
    inference(general_splitting,[],[f119,f120_D]) ).

fof(f120,plain,
    ! [X2,X1] :
      ( ~ r2(X2,X1)
      | sP23(X2)
      | ~ sP22(X1) ),
    inference(cnf_transformation,[],[f120_D]) ).

fof(f120_D,plain,
    ! [X2] :
      ( ! [X1] :
          ( ~ r2(X2,X1)
          | ~ sP22(X1) )
    <=> ~ sP23(X2) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP23])]) ).

fof(f119,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ r2(X2,X1)
      | ~ sP22(X1) ),
    inference(general_splitting,[],[f117,f118_D]) ).

fof(f118,plain,
    ! [X1,X6] :
      ( ~ r3(X6,X6,X1)
      | ~ sP21(X6)
      | sP22(X1) ),
    inference(cnf_transformation,[],[f118_D]) ).

fof(f118_D,plain,
    ! [X1] :
      ( ! [X6] :
          ( ~ r3(X6,X6,X1)
          | ~ sP21(X6) )
    <=> ~ sP22(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP22])]) ).

fof(f117,plain,
    ! [X2,X3,X1,X6,X4,X5] :
      ( ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ r2(X2,X1)
      | ~ r3(X6,X6,X1)
      | ~ sP21(X6) ),
    inference(general_splitting,[],[f115,f116_D]) ).

fof(f115,plain,
    ! [X2,X3,X1,X6,X7,X4,X5] :
      ( ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ r2(X2,X1)
      | ~ r2(X7,X6)
      | ~ r3(X6,X6,X1)
      | ~ sP20(X7) ),
    inference(general_splitting,[],[f113,f114_D]) ).

fof(f113,plain,
    ! [X2,X3,X1,X8,X6,X7,X4,X5] :
      ( ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ r2(X2,X1)
      | ~ r2(X8,X7)
      | ~ r1(X8)
      | ~ r2(X7,X6)
      | ~ r3(X6,X6,X1) ),
    inference(equality_resolution,[],[f99]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( X0 != X1
      | ~ r2(X3,X2)
      | ~ r2(X4,X3)
      | ~ r1(X5)
      | ~ r2(X5,X4)
      | ~ r2(X2,X1)
      | ~ r2(X8,X7)
      | ~ r1(X8)
      | ~ r2(X7,X6)
      | ~ r3(X6,X6,X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 != X1
          | ! [X2] :
              ( ! [X3] :
                  ( ~ r2(X3,X2)
                  | ! [X4] :
                      ( ~ r2(X4,X3)
                      | ! [X5] :
                          ( ~ r1(X5)
                          | ~ r2(X5,X4) ) ) )
              | ~ r2(X2,X1) ) )
      | ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ~ r2(X8,X7)
                  | ~ r1(X8) )
              | ~ r2(X7,X6) )
          | ~ r3(X6,X6,X0) ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( r1(X5)
                            & r2(X5,X4) )
                        & r2(X4,X3) )
                    & r2(X3,X2) )
                & r2(X2,X1) )
            & X0 = X1 )
        & ? [X6] :
            ( ? [X7] :
                ( r2(X7,X6)
                & ? [X8] :
                    ( r1(X8)
                    & r2(X8,X7) ) )
            & r3(X6,X6,X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X38] :
        ( ? [X21] :
            ( ? [X22] :
                ( ? [X15] :
                    ( ? [X24] :
                        ( r2(X24,X15)
                        & ? [X33] :
                            ( r1(X33)
                            & r2(X33,X24) ) )
                    & r2(X15,X22) )
                & r2(X22,X21) )
            & X21 = X38 )
        & ? [X16] :
            ( ? [X18] :
                ( ? [X30] :
                    ( r1(X30)
                    & r2(X30,X18) )
                & r2(X18,X16) )
            & r3(X16,X16,X38) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X38] :
      ( ? [X21] :
          ( ? [X22] :
              ( ? [X15] :
                  ( ? [X24] :
                      ( r2(X24,X15)
                      & ? [X33] :
                          ( r1(X33)
                          & r2(X33,X24) ) )
                  & r2(X15,X22) )
              & r2(X22,X21) )
          & X21 = X38 )
      & ? [X16] :
          ( ? [X18] :
              ( ? [X30] :
                  ( r1(X30)
                  & r2(X30,X18) )
              & r2(X18,X16) )
          & r3(X16,X16,X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',twoplustwoeqfour) ).

fof(f396,plain,
    ( sP25(sK8(sK17))
    | ~ spl26_6 ),
    inference(resolution,[],[f395,f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ~ sP24(sK8(X0))
      | sP25(X0) ),
    inference(resolution,[],[f124,f108]) ).

fof(f395,plain,
    ( sP24(sK8(sK8(sK17)))
    | ~ spl26_6 ),
    inference(resolution,[],[f389,f149]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ sP23(sK8(X0))
      | sP24(X0) ),
    inference(resolution,[],[f122,f108]) ).

fof(f389,plain,
    ( sP23(sK8(sK8(sK8(sK17))))
    | ~ spl26_6 ),
    inference(avatar_component_clause,[],[f387]) ).

fof(f387,plain,
    ( spl26_6
  <=> sP23(sK8(sK8(sK8(sK17)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).

fof(f394,plain,
    ( spl26_6
    | ~ spl26_7 ),
    inference(avatar_split_clause,[],[f385,f391,f387]) ).

fof(f385,plain,
    ( ~ sP21(sK8(sK8(sK17)))
    | sP23(sK8(sK8(sK8(sK17)))) ),
    inference(resolution,[],[f339,f220]) ).

fof(f220,plain,
    ! [X0] :
      ( sP22(sK14(sK8(X0),X0))
      | ~ sP21(sK8(X0)) ),
    inference(resolution,[],[f219,f118]) ).

fof(f219,plain,
    ! [X0,X1] : r3(X0,sK8(X1),sK14(X0,X1)),
    inference(forward_demodulation,[],[f90,f161]) ).

fof(f161,plain,
    ! [X3,X4] : sK8(X3) = sK15(X4,X3),
    inference(resolution,[],[f78,f89]) ).

fof(f89,plain,
    ! [X0,X1] : r2(X1,sK15(X0,X1)),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( r3(X0,sK15(X0,X1),sK14(X0,X1))
      & r2(X1,sK15(X0,X1))
      & sK13(X0,X1) = sK14(X0,X1)
      & r2(sK16(X0,X1),sK13(X0,X1))
      & r3(X0,X1,sK16(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f48,f52,f51,f50,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( r3(X0,X4,X3)
                  & r2(X1,X4) )
              & X2 = X3 )
          & ? [X5] :
              ( r2(X5,X2)
              & r3(X0,X1,X5) ) )
     => ( ? [X3] :
            ( ? [X4] :
                ( r3(X0,X4,X3)
                & r2(X1,X4) )
            & sK13(X0,X1) = X3 )
        & ? [X5] :
            ( r2(X5,sK13(X0,X1))
            & r3(X0,X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) )
          & sK13(X0,X1) = X3 )
     => ( ? [X4] :
            ( r3(X0,X4,sK14(X0,X1))
            & r2(X1,X4) )
        & sK13(X0,X1) = sK14(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r3(X0,X4,sK14(X0,X1))
          & r2(X1,X4) )
     => ( r3(X0,sK15(X0,X1),sK14(X0,X1))
        & r2(X1,sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r2(X5,sK13(X0,X1))
          & r3(X0,X1,X5) )
     => ( r2(sK16(X0,X1),sK13(X0,X1))
        & r3(X0,X1,sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) )
          & X2 = X3 )
      & ? [X5] :
          ( r2(X5,X2)
          & r3(X0,X1,X5) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & X2 = X4 )
      & ? [X3] :
          ( r2(X3,X2)
          & r3(X0,X1,X3) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13,X14] :
    ? [X15] :
      ( ? [X18] :
          ( r2(X18,X15)
          & r3(X13,X14,X18) )
      & ? [X16] :
          ( X15 = X16
          & ? [X17] :
              ( r2(X14,X17)
              & r3(X13,X17,X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).

fof(f78,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK8(X0) = X2 ),
    inference(cnf_transformation,[],[f40]) ).

fof(f90,plain,
    ! [X0,X1] : r3(X0,sK15(X0,X1),sK14(X0,X1)),
    inference(cnf_transformation,[],[f53]) ).

fof(f339,plain,
    ! [X1] :
      ( ~ sP22(sK14(X1,sK8(sK17)))
      | sP23(sK8(X1)) ),
    inference(superposition,[],[f269,f322]) ).

fof(f322,plain,
    ! [X0] : sK3(X0,sK8(sK17)) = sK8(X0),
    inference(resolution,[],[f311,f64]) ).

fof(f64,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X0,X1,X3)
      | sK3(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X3] :
      ( ( sK3(X0,X1) != X3
        & ~ r3(X0,X1,X3) )
      | ( r3(X0,X1,X3)
        & sK3(X0,X1) = X3 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f21,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 != X3
            & ~ r3(X0,X1,X3) )
          | ( r3(X0,X1,X3)
            & X2 = X3 ) )
     => ! [X3] :
          ( ( sK3(X0,X1) != X3
            & ~ r3(X0,X1,X3) )
          | ( r3(X0,X1,X3)
            & sK3(X0,X1) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 != X3
        & ~ r3(X0,X1,X3) )
      | ( r3(X0,X1,X3)
        & X2 = X3 ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X5,X6] :
    ? [X7] :
    ! [X8] :
      ( ( ~ r3(X5,X6,X8)
        & X7 != X8 )
      | ( X7 = X8
        & r3(X5,X6,X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f311,plain,
    ! [X2] : r3(X2,sK8(sK17),sK8(X2)),
    inference(superposition,[],[f219,f283]) ).

fof(f283,plain,
    ! [X0] : sK14(X0,sK17) = sK8(X0),
    inference(resolution,[],[f282,f78]) ).

fof(f282,plain,
    ! [X0] : r2(X0,sK14(X0,sK17)),
    inference(superposition,[],[f265,f259]) ).

fof(f259,plain,
    ! [X4] : sK3(X4,sK17) = X4,
    inference(resolution,[],[f64,f139]) ).

fof(f139,plain,
    ! [X0] : r3(X0,sK17,X0),
    inference(forward_demodulation,[],[f138,f129]) ).

fof(f129,plain,
    ! [X2] : sK19(X2) = sK17,
    inference(resolution,[],[f92,f96]) ).

fof(f96,plain,
    ! [X0] : r1(sK19(X0)),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( sK18(X0) = X0
      & r3(X0,sK19(X0),sK18(X0))
      & r1(sK19(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f24,f58,f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) ) )
     => ( sK18(X0) = X0
        & ? [X2] :
            ( r3(X0,X2,sK18(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK18(X0))
          & r1(X2) )
     => ( r3(X0,sK19(X0),sK18(X0))
        & r1(sK19(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0] :
    ? [X1] :
      ( X0 = X1
      & ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X29] :
    ? [X30] :
      ( X29 = X30
      & ? [X31] :
          ( r1(X31)
          & r3(X29,X31,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).

fof(f92,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK17 = X1 ),
    inference(cnf_transformation,[],[f55]) ).

fof(f138,plain,
    ! [X0] : r3(X0,sK19(X0),X0),
    inference(forward_demodulation,[],[f97,f98]) ).

fof(f98,plain,
    ! [X0] : sK18(X0) = X0,
    inference(cnf_transformation,[],[f59]) ).

fof(f97,plain,
    ! [X0] : r3(X0,sK19(X0),sK18(X0)),
    inference(cnf_transformation,[],[f59]) ).

fof(f265,plain,
    ! [X0,X1] : r2(sK3(X0,X1),sK14(X0,X1)),
    inference(backward_demodulation,[],[f102,f257]) ).

fof(f257,plain,
    ! [X0,X1] : sK16(X0,X1) = sK3(X0,X1),
    inference(resolution,[],[f64,f86]) ).

fof(f86,plain,
    ! [X0,X1] : r3(X0,X1,sK16(X0,X1)),
    inference(cnf_transformation,[],[f53]) ).

fof(f102,plain,
    ! [X0,X1] : r2(sK16(X0,X1),sK14(X0,X1)),
    inference(definition_unfolding,[],[f87,f88]) ).

fof(f88,plain,
    ! [X0,X1] : sK13(X0,X1) = sK14(X0,X1),
    inference(cnf_transformation,[],[f53]) ).

fof(f87,plain,
    ! [X0,X1] : r2(sK16(X0,X1),sK13(X0,X1)),
    inference(cnf_transformation,[],[f53]) ).

fof(f269,plain,
    ! [X8,X9] :
      ( sP23(sK3(X8,X9))
      | ~ sP22(sK14(X8,X9)) ),
    inference(backward_demodulation,[],[f182,f257]) ).

fof(f182,plain,
    ! [X8,X9] :
      ( sP23(sK16(X8,X9))
      | ~ sP22(sK14(X8,X9)) ),
    inference(resolution,[],[f102,f120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUN057+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 09:38:47 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.51  % (8021)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  % (8009)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (8015)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (8030)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.51  % (8009)Refutation not found, incomplete strategy% (8009)------------------------------
% 0.19/0.51  % (8009)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (8016)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52  % (8009)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (8009)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (8009)Memory used [KB]: 5500
% 0.19/0.52  % (8009)Time elapsed: 0.110 s
% 0.19/0.52  % (8009)Instructions burned: 4 (million)
% 0.19/0.52  % (8009)------------------------------
% 0.19/0.52  % (8009)------------------------------
% 0.19/0.52  % (8016)Instruction limit reached!
% 0.19/0.52  % (8016)------------------------------
% 0.19/0.52  % (8016)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (8016)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (8016)Termination reason: Unknown
% 0.19/0.52  % (8016)Termination phase: Preprocessing 3
% 0.19/0.52  
% 0.19/0.52  % (8016)Memory used [KB]: 895
% 0.19/0.52  % (8016)Time elapsed: 0.003 s
% 0.19/0.52  % (8016)Instructions burned: 2 (million)
% 0.19/0.52  % (8016)------------------------------
% 0.19/0.52  % (8016)------------------------------
% 0.19/0.52  % (8015)Instruction limit reached!
% 0.19/0.52  % (8015)------------------------------
% 0.19/0.52  % (8015)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (8015)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (8015)Termination reason: Unknown
% 0.19/0.52  % (8015)Termination phase: Saturation
% 0.19/0.52  
% 0.19/0.52  % (8015)Memory used [KB]: 5500
% 0.19/0.52  % (8015)Time elapsed: 0.118 s
% 0.19/0.52  % (8015)Instructions burned: 7 (million)
% 0.19/0.52  % (8015)------------------------------
% 0.19/0.52  % (8015)------------------------------
% 0.19/0.52  % (8032)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.52  % (8022)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.52  % (8013)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52  % (8033)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.53  % (8012)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (8010)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53  % (8011)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (8025)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.53  % (8019)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53  % (8020)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.53  % (8014)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (8017)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  TRYING [1]
% 0.19/0.53  TRYING [2]
% 0.19/0.54  TRYING [1]
% 0.19/0.54  TRYING [3]
% 0.19/0.54  % (8037)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.19/0.54  TRYING [2]
% 0.19/0.54  TRYING [3]
% 0.19/0.54  % (8035)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.54  % (8036)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.54  % (8031)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.54  % (8008)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.55  % (8029)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.55  TRYING [1]
% 0.19/0.55  TRYING [2]
% 0.19/0.55  TRYING [3]
% 0.19/0.55  TRYING [4]
% 0.19/0.55  % (8028)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.55  % (8027)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.55  % (8013)First to succeed.
% 0.19/0.55  % (8034)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.55  % (8023)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.56  % (8010)Also succeeded, but the first one will report.
% 0.19/0.56  % (8026)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.56  % (8013)Refutation found. Thanks to Tanya!
% 0.19/0.56  % SZS status Theorem for theBenchmark
% 0.19/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.56  % (8013)------------------------------
% 0.19/0.56  % (8013)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  % (8013)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56  % (8013)Termination reason: Refutation
% 0.19/0.56  
% 0.19/0.56  % (8013)Memory used [KB]: 5628
% 0.19/0.56  % (8013)Time elapsed: 0.152 s
% 0.19/0.56  % (8013)Instructions burned: 13 (million)
% 0.19/0.56  % (8013)------------------------------
% 0.19/0.56  % (8013)------------------------------
% 0.19/0.56  % (8007)Success in time 0.207 s
%------------------------------------------------------------------------------