TSTP Solution File: NUN071+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN071+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 : n026.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 18:08:05 EDT 2022

% Result   : Theorem 1.35s 0.52s
% Output   : Refutation 1.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  111 (  47 unt;   0 def)
%            Number of atoms       :  339 ( 100 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  320 (  92   ~;  60   |; 150   &)
%                                         (   1 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   1 con; 0-2 aty)
%            Number of variables   :  284 ( 188   !;  96   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f289,plain,
    $false,
    inference(avatar_sat_refutation,[],[f274,f279]) ).

fof(f279,plain,
    ~ spl20_2,
    inference(avatar_contradiction_clause,[],[f278]) ).

fof(f278,plain,
    ( $false
    | ~ spl20_2 ),
    inference(subsumption_resolution,[],[f276,f108]) ).

fof(f108,plain,
    r1(sK2),
    inference(equality_resolution,[],[f68]) ).

fof(f68,plain,
    ! [X1] :
      ( sK2 != X1
      | r1(X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X1] :
      ( ( ~ r1(X1)
        & sK2 != X1 )
      | ( sK2 = X1
        & r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f1,f32]) ).

fof(f32,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ~ r1(X1)
          & X0 != X1 )
        | ( X0 = X1
          & r1(X1) ) )
   => ! [X1] :
        ( ( ~ r1(X1)
          & sK2 != X1 )
        | ( sK2 = X1
          & r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f276,plain,
    ( ~ r1(sK2)
    | ~ spl20_2 ),
    inference(resolution,[],[f273,f109]) ).

fof(f109,plain,
    ! [X0] : r2(X0,sK12(X0)),
    inference(equality_resolution,[],[f87]) ).

fof(f87,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK12(X0) != X2 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X2] :
      ( ( r2(X0,X2)
        & sK12(X0) = X2 )
      | ( sK12(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f23,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( r2(X0,X2)
            & X1 = X2 )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( r2(X0,X2)
            & sK12(X0) = X2 )
          | ( sK12(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( r2(X0,X2)
        & X1 = X2 )
      | ( X1 != X2
        & ~ r2(X0,X2) ) ),
    inference(rectify,[],[f2]) ).

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

fof(f273,plain,
    ( ! [X1] :
        ( ~ r2(X1,sK12(sK2))
        | ~ r1(X1) )
    | ~ spl20_2 ),
    inference(avatar_component_clause,[],[f272]) ).

fof(f272,plain,
    ( spl20_2
  <=> ! [X1] :
        ( ~ r1(X1)
        | ~ r2(X1,sK12(sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).

fof(f274,plain,
    ( spl20_2
    | spl20_2 ),
    inference(avatar_split_clause,[],[f270,f272,f272]) ).

fof(f270,plain,
    ! [X2,X1] :
      ( ~ r2(X2,sK12(sK2))
      | ~ r1(X1)
      | ~ r1(X2)
      | ~ r2(X1,sK12(sK2)) ),
    inference(forward_demodulation,[],[f269,f241]) ).

fof(f241,plain,
    ! [X2] : sK12(X2) = sK13(X2,sK2),
    inference(resolution,[],[f239,f84]) ).

fof(f84,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK12(X0) = X2 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f239,plain,
    ! [X0] : r2(X0,sK13(X0,sK2)),
    inference(superposition,[],[f218,f190]) ).

fof(f190,plain,
    ! [X0] : sK1(sK2,X0) = X0,
    inference(forward_demodulation,[],[f180,f115]) ).

fof(f115,plain,
    ! [X0] : sK2 = sK11(X0),
    inference(resolution,[],[f71,f82]) ).

fof(f82,plain,
    ! [X0] : r1(sK11(X0)),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( r3(X0,sK11(X0),sK10(X0))
      & r1(sK11(X0))
      & sK10(X0) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f15,f44,f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & X0 = X1 )
     => ( ? [X2] :
            ( r3(X0,X2,sK10(X0))
            & r1(X2) )
        & sK10(X0) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK10(X0))
          & r1(X2) )
     => ( r3(X0,sK11(X0),sK10(X0))
        & r1(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) )
      & X0 = X1 ),
    inference(rectify,[],[f8]) ).

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

fof(f71,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK2 = X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f180,plain,
    ! [X0] : sK1(sK11(X0),X0) = X0,
    inference(resolution,[],[f67,f113]) ).

fof(f113,plain,
    ! [X0] : r3(X0,sK11(X0),X0),
    inference(forward_demodulation,[],[f83,f81]) ).

fof(f81,plain,
    ! [X0] : sK10(X0) = X0,
    inference(cnf_transformation,[],[f45]) ).

fof(f83,plain,
    ! [X0] : r3(X0,sK11(X0),sK10(X0)),
    inference(cnf_transformation,[],[f45]) ).

fof(f67,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X1,X0,X3)
      | sK1(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X3] :
      ( ( ~ r3(X1,X0,X3)
        & sK1(X0,X1) != X3 )
      | ( sK1(X0,X1) = X3
        & r3(X1,X0,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( ~ r3(X1,X0,X3)
            & X2 != X3 )
          | ( X2 = X3
            & r3(X1,X0,X3) ) )
     => ! [X3] :
          ( ( ~ r3(X1,X0,X3)
            & sK1(X0,X1) != X3 )
          | ( sK1(X0,X1) = X3
            & r3(X1,X0,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ r3(X1,X0,X3)
        & X2 != X3 )
      | ( X2 = X3
        & r3(X1,X0,X3) ) ),
    inference(rectify,[],[f3]) ).

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

fof(f218,plain,
    ! [X2,X3] : r2(sK1(X3,X2),sK13(X2,X3)),
    inference(superposition,[],[f90,f185]) ).

fof(f185,plain,
    ! [X8,X9] : sK1(X8,X9) = sK16(X9,X8),
    inference(resolution,[],[f67,f91]) ).

fof(f91,plain,
    ! [X0,X1] : r3(X0,X1,sK16(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( sK14(X0,X1) = sK13(X0,X1)
      & r2(X1,sK15(X0,X1))
      & r3(X0,sK15(X0,X1),sK14(X0,X1))
      & r3(X0,X1,sK16(X0,X1))
      & r2(sK16(X0,X1),sK13(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f49,f53,f52,f51,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( X2 = X3
              & ? [X4] :
                  ( r2(X1,X4)
                  & r3(X0,X4,X3) ) )
          & ? [X5] :
              ( r3(X0,X1,X5)
              & r2(X5,X2) ) )
     => ( ? [X3] :
            ( sK13(X0,X1) = X3
            & ? [X4] :
                ( r2(X1,X4)
                & r3(X0,X4,X3) ) )
        & ? [X5] :
            ( r3(X0,X1,X5)
            & r2(X5,sK13(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sK13(X0,X1) = X3
          & ? [X4] :
              ( r2(X1,X4)
              & r3(X0,X4,X3) ) )
     => ( sK14(X0,X1) = sK13(X0,X1)
        & ? [X4] :
            ( r2(X1,X4)
            & r3(X0,X4,sK14(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r2(X1,X4)
          & r3(X0,X4,sK14(X0,X1)) )
     => ( r2(X1,sK15(X0,X1))
        & r3(X0,sK15(X0,X1),sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,sK13(X0,X1)) )
     => ( r3(X0,X1,sK16(X0,X1))
        & r2(sK16(X0,X1),sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r2(X1,X4)
              & r3(X0,X4,X3) ) )
      & ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,X2) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r2(X0,X4)
              & r3(X1,X4,X3) ) )
      & ? [X5] :
          ( r3(X1,X0,X5)
          & r2(X5,X2) ) ),
    inference(rectify,[],[f5]) ).

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

fof(f90,plain,
    ! [X0,X1] : r2(sK16(X0,X1),sK13(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f269,plain,
    ! [X2,X1] :
      ( ~ r2(X1,sK13(sK2,sK2))
      | ~ r1(X1)
      | ~ r2(X2,sK12(sK2))
      | ~ r1(X2) ),
    inference(forward_demodulation,[],[f267,f191]) ).

fof(f191,plain,
    ! [X4,X5] : sK1(sK12(X5),X4) = sK13(X4,X5),
    inference(forward_demodulation,[],[f183,f132]) ).

fof(f132,plain,
    ! [X3,X4] : sK12(X3) = sK15(X4,X3),
    inference(resolution,[],[f84,f93]) ).

fof(f93,plain,
    ! [X0,X1] : r2(X1,sK15(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f183,plain,
    ! [X4,X5] : sK1(sK15(X4,X5),X4) = sK13(X4,X5),
    inference(resolution,[],[f67,f100]) ).

fof(f100,plain,
    ! [X0,X1] : r3(X0,sK15(X0,X1),sK13(X0,X1)),
    inference(definition_unfolding,[],[f92,f94]) ).

fof(f94,plain,
    ! [X0,X1] : sK14(X0,X1) = sK13(X0,X1),
    inference(cnf_transformation,[],[f54]) ).

fof(f92,plain,
    ! [X0,X1] : r3(X0,sK15(X0,X1),sK14(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f267,plain,
    ! [X2,X1] :
      ( ~ r1(X2)
      | ~ r2(X1,sK1(sK12(sK2),sK2))
      | ~ r2(X2,sK12(sK2))
      | ~ r1(X1) ),
    inference(resolution,[],[f265,f112]) ).

fof(f112,plain,
    ! [X2,X3,X1,X4] :
      ( ~ r4(X3,X3,X1)
      | ~ r1(X2)
      | ~ r2(X2,X1)
      | ~ r1(X4)
      | ~ r2(X4,X3) ),
    inference(equality_resolution,[],[f89]) ).

fof(f89,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ r1(X2)
      | ~ r2(X2,X1)
      | X0 != X1
      | ~ r1(X4)
      | ~ r2(X4,X3)
      | ~ r4(X3,X3,X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ~ r1(X2)
              | ~ r2(X2,X1) )
          | X0 != X1 )
      | ! [X3] :
          ( ! [X4] :
              ( ~ r1(X4)
              | ~ r2(X4,X3) )
          | ~ r4(X3,X3,X0) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( ! [X3] :
          ( ! [X4] :
              ( ~ r1(X4)
              | ~ r2(X4,X3) )
          | X0 != X3 )
      | ! [X1] :
          ( ! [X2] :
              ( ~ r1(X2)
              | ~ r2(X2,X1) )
          | ~ r4(X1,X1,X0) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( r4(X1,X1,X0)
            & ? [X2] :
                ( r1(X2)
                & r2(X2,X1) ) )
        & ? [X3] :
            ( X0 = X3
            & ? [X4] :
                ( r2(X4,X3)
                & r1(X4) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X38] :
        ( ? [X21] :
            ( r4(X21,X21,X38)
            & ? [X15] :
                ( r2(X15,X21)
                & r1(X15) ) )
        & ? [X22] :
            ( ? [X16] :
                ( r1(X16)
                & r2(X16,X22) )
            & X22 = X38 ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X38] :
      ( ? [X21] :
          ( r4(X21,X21,X38)
          & ? [X15] :
              ( r2(X15,X21)
              & r1(X15) ) )
      & ? [X22] :
          ( ? [X16] :
              ( r1(X16)
              & r2(X16,X22) )
          & X22 = X38 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onetimesoneeqone) ).

fof(f265,plain,
    ! [X4] : r4(X4,sK12(sK2),sK1(X4,sK2)),
    inference(forward_demodulation,[],[f261,f131]) ).

fof(f131,plain,
    ! [X2,X1] : sK12(X1) = sK6(X2,X1),
    inference(resolution,[],[f84,f73]) ).

fof(f73,plain,
    ! [X0,X1] : r2(X1,sK6(X0,X1)),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( r3(sK4(X0,X1),X0,sK3(X0,X1))
      & r4(X0,X1,sK4(X0,X1))
      & r4(X0,sK6(X0,X1),sK5(X0,X1))
      & r2(X1,sK6(X0,X1))
      & sK3(X0,X1) = sK5(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f34,f38,f37,f36,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X3,X0,X2)
              & r4(X0,X1,X3) )
          & ? [X4] :
              ( ? [X5] :
                  ( r4(X0,X5,X4)
                  & r2(X1,X5) )
              & X2 = X4 ) )
     => ( ? [X3] :
            ( r3(X3,X0,sK3(X0,X1))
            & r4(X0,X1,X3) )
        & ? [X4] :
            ( ? [X5] :
                ( r4(X0,X5,X4)
                & r2(X1,X5) )
            & sK3(X0,X1) = X4 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X3,X0,sK3(X0,X1))
          & r4(X0,X1,X3) )
     => ( r3(sK4(X0,X1),X0,sK3(X0,X1))
        & r4(X0,X1,sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) )
          & sK3(X0,X1) = X4 )
     => ( ? [X5] :
            ( r4(X0,X5,sK5(X0,X1))
            & r2(X1,X5) )
        & sK3(X0,X1) = sK5(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X0,X5,sK5(X0,X1))
          & r2(X1,X5) )
     => ( r4(X0,sK6(X0,X1),sK5(X0,X1))
        & r2(X1,sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X3,X0,X2)
          & r4(X0,X1,X3) )
      & ? [X4] :
          ( ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) )
          & X2 = X4 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X3,X1,X2)
          & r4(X1,X0,X3) )
      & ? [X4] :
          ( ? [X5] :
              ( r4(X1,X5,X4)
              & r2(X0,X5) )
          & X2 = X4 ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X20,X19] :
    ? [X21] :
      ( ? [X24] :
          ( r4(X19,X20,X24)
          & r3(X24,X19,X21) )
      & ? [X22] :
          ( X21 = X22
          & ? [X23] :
              ( r2(X20,X23)
              & r4(X19,X23,X22) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).

fof(f261,plain,
    ! [X4] : r4(X4,sK6(X4,sK2),sK1(X4,sK2)),
    inference(superposition,[],[f74,f187]) ).

fof(f187,plain,
    ! [X12] : sK5(X12,sK2) = sK1(X12,sK2),
    inference(resolution,[],[f67,f178]) ).

fof(f178,plain,
    ! [X0] : r3(sK2,X0,sK5(X0,sK2)),
    inference(superposition,[],[f174,f172]) ).

fof(f172,plain,
    ! [X9] : sK2 = sK0(X9,sK2),
    inference(forward_demodulation,[],[f171,f116]) ).

fof(f116,plain,
    ! [X1] : sK2 = sK18(X1),
    inference(resolution,[],[f71,f98]) ).

fof(f98,plain,
    ! [X0] : r1(sK18(X0)),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( r1(sK18(X0))
      & r4(X0,sK18(X0),sK17(X0))
      & r1(sK19(X0))
      & sK17(X0) = sK19(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f17,f57,f56,f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r1(X2)
              & r4(X0,X2,X1) )
          & ? [X3] :
              ( r1(X3)
              & X1 = X3 ) )
     => ( ? [X2] :
            ( r1(X2)
            & r4(X0,X2,sK17(X0)) )
        & ? [X3] :
            ( r1(X3)
            & sK17(X0) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0] :
      ( ? [X2] :
          ( r1(X2)
          & r4(X0,X2,sK17(X0)) )
     => ( r1(sK18(X0))
        & r4(X0,sK18(X0),sK17(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0] :
      ( ? [X3] :
          ( r1(X3)
          & sK17(X0) = X3 )
     => ( r1(sK19(X0))
        & sK17(X0) = sK19(X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r1(X2)
          & r4(X0,X2,X1) )
      & ? [X3] :
          ( r1(X3)
          & X1 = X3 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X32] :
    ? [X33] :
      ( ? [X34] :
          ( r1(X34)
          & r4(X32,X34,X33) )
      & ? [X35] :
          ( r1(X35)
          & X33 = X35 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).

fof(f171,plain,
    ! [X9] : sK2 = sK0(X9,sK18(X9)),
    inference(forward_demodulation,[],[f169,f117]) ).

fof(f117,plain,
    ! [X2] : sK19(X2) = sK2,
    inference(resolution,[],[f71,f96]) ).

fof(f96,plain,
    ! [X0] : r1(sK19(X0)),
    inference(cnf_transformation,[],[f58]) ).

fof(f169,plain,
    ! [X9] : sK0(X9,sK18(X9)) = sK19(X9),
    inference(resolution,[],[f62,f101]) ).

fof(f101,plain,
    ! [X0] : r4(X0,sK18(X0),sK19(X0)),
    inference(definition_unfolding,[],[f97,f95]) ).

fof(f95,plain,
    ! [X0] : sK17(X0) = sK19(X0),
    inference(cnf_transformation,[],[f58]) ).

fof(f97,plain,
    ! [X0] : r4(X0,sK18(X0),sK17(X0)),
    inference(cnf_transformation,[],[f58]) ).

fof(f62,plain,
    ! [X3,X0,X1] :
      ( ~ r4(X0,X1,X3)
      | sK0(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X3] :
      ( ( sK0(X0,X1) = X3
        & r4(X0,X1,X3) )
      | ( sK0(X0,X1) != X3
        & ~ r4(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r4(X0,X1,X3) )
          | ( X2 != X3
            & ~ r4(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK0(X0,X1) = X3
            & r4(X0,X1,X3) )
          | ( sK0(X0,X1) != X3
            & ~ r4(X0,X1,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r4(X0,X1,X3) )
      | ( X2 != X3
        & ~ r4(X0,X1,X3) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r4(X1,X0,X3) )
      | ( X2 != X3
        & ~ r4(X1,X0,X3) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X10,X9] :
    ? [X11] :
    ! [X12] :
      ( ( r4(X9,X10,X12)
        & X11 = X12 )
      | ( X11 != X12
        & ~ r4(X9,X10,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f174,plain,
    ! [X0,X1] : r3(sK0(X0,X1),X0,sK5(X0,X1)),
    inference(superposition,[],[f99,f164]) ).

fof(f164,plain,
    ! [X0,X1] : sK0(X0,X1) = sK4(X0,X1),
    inference(resolution,[],[f62,f75]) ).

fof(f75,plain,
    ! [X0,X1] : r4(X0,X1,sK4(X0,X1)),
    inference(cnf_transformation,[],[f39]) ).

fof(f99,plain,
    ! [X0,X1] : r3(sK4(X0,X1),X0,sK5(X0,X1)),
    inference(definition_unfolding,[],[f76,f72]) ).

fof(f72,plain,
    ! [X0,X1] : sK3(X0,X1) = sK5(X0,X1),
    inference(cnf_transformation,[],[f39]) ).

fof(f76,plain,
    ! [X0,X1] : r3(sK4(X0,X1),X0,sK3(X0,X1)),
    inference(cnf_transformation,[],[f39]) ).

fof(f74,plain,
    ! [X0,X1] : r4(X0,sK6(X0,X1),sK5(X0,X1)),
    inference(cnf_transformation,[],[f39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem    : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 10:02:36 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.48  % (21270)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)
% 0.18/0.48  % (21256)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)
% 0.18/0.49  % (21271)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)
% 0.18/0.49  % (21258)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)
% 0.18/0.49  % (21261)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)
% 0.18/0.49  % (21279)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)
% 0.18/0.49  % (21269)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.50  % (21260)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)
% 0.18/0.50  TRYING [1]
% 0.18/0.50  % (21262)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.50  % (21273)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.18/0.50  % (21277)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.18/0.50  TRYING [2]
% 0.18/0.50  % (21264)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)
% 0.18/0.50  TRYING [3]
% 0.18/0.50  % (21286)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)
% 0.18/0.51  % (21256)Refutation not found, incomplete strategy% (21256)------------------------------
% 0.18/0.51  % (21256)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (21256)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (21256)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.51  
% 0.18/0.51  % (21256)Memory used [KB]: 5500
% 0.18/0.51  % (21256)Time elapsed: 0.122 s
% 0.18/0.51  % (21256)Instructions burned: 3 (million)
% 0.18/0.51  % (21256)------------------------------
% 0.18/0.51  % (21256)------------------------------
% 0.18/0.51  % (21269)First to succeed.
% 0.18/0.51  % (21281)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.18/0.51  TRYING [4]
% 0.18/0.51  % (21257)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)
% 1.35/0.52  % (21268)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.35/0.52  TRYING [1]
% 1.35/0.52  TRYING [2]
% 1.35/0.52  % (21269)Refutation found. Thanks to Tanya!
% 1.35/0.52  % SZS status Theorem for theBenchmark
% 1.35/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.35/0.52  % (21269)------------------------------
% 1.35/0.52  % (21269)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.52  % (21269)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.52  % (21269)Termination reason: Refutation
% 1.35/0.52  
% 1.35/0.52  % (21269)Memory used [KB]: 5628
% 1.35/0.52  % (21269)Time elapsed: 0.116 s
% 1.35/0.52  % (21269)Instructions burned: 8 (million)
% 1.35/0.52  % (21269)------------------------------
% 1.35/0.52  % (21269)------------------------------
% 1.35/0.52  % (21253)Success in time 0.174 s
%------------------------------------------------------------------------------