TSTP Solution File: NUN084+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUN084+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_uns --cores 0 -t %d %s

% Computer : n012.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 18:07:49 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  111 (  50 unt;   0 def)
%            Number of atoms       :  323 ( 100 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  292 (  80   ~;  48   |; 147   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   1 con; 0-2 aty)
%            Number of variables   :  297 ( 198   !;  99   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f348,plain,
    $false,
    inference(subsumption_resolution,[],[f341,f103]) ).

fof(f103,plain,
    r1(sK4),
    inference(equality_resolution,[],[f68]) ).

fof(f68,plain,
    ! [X1] :
      ( sK4 != X1
      | r1(X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X1] :
      ( ( sK4 != X1
        & ~ r1(X1) )
      | ( r1(X1)
        & sK4 = X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f1,f32]) ).

fof(f32,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 != X1
          & ~ r1(X1) )
        | ( r1(X1)
          & X0 = X1 ) )
   => ! [X1] :
        ( ( sK4 != X1
          & ~ r1(X1) )
        | ( r1(X1)
          & sK4 = X1 ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f341,plain,
    ~ r1(sK4),
    inference(resolution,[],[f339,f109]) ).

fof(f109,plain,
    ! [X0] : r2(X0,sK6(X0)),
    inference(equality_resolution,[],[f76]) ).

fof(f76,plain,
    ! [X2,X0] :
      ( sK6(X0) != X2
      | r2(X0,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X2] :
      ( ( ~ r2(X0,X2)
        & sK6(X0) != X2 )
      | ( r2(X0,X2)
        & sK6(X0) = X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f20,f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( ~ r2(X0,X2)
            & X1 != X2 )
          | ( r2(X0,X2)
            & X1 = X2 ) )
     => ! [X2] :
          ( ( ~ r2(X0,X2)
            & sK6(X0) != X2 )
          | ( r2(X0,X2)
            & sK6(X0) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( ~ r2(X0,X2)
        & X1 != X2 )
      | ( r2(X0,X2)
        & X1 = 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(f339,plain,
    ! [X1] :
      ( ~ r2(X1,sK6(sK4))
      | ~ r1(X1) ),
    inference(superposition,[],[f336,f252]) ).

fof(f252,plain,
    sK0(sK4,sK6(sK4)) = sK6(sK4),
    inference(superposition,[],[f239,f214]) ).

fof(f214,plain,
    ! [X9] : sK9(X9,sK4) = sK0(sK4,X9),
    inference(resolution,[],[f82,f197]) ).

fof(f197,plain,
    ! [X3] : r3(sK4,X3,sK0(sK4,X3)),
    inference(superposition,[],[f64,f194]) ).

fof(f194,plain,
    ! [X0] : sK1(sK4,X0) = sK4,
    inference(superposition,[],[f181,f182]) ).

fof(f182,plain,
    ! [X2,X1] : sK1(X2,X1) = sK5(X1,X2),
    inference(resolution,[],[f74,f63]) ).

fof(f63,plain,
    ! [X0,X1] : r4(X1,X0,sK1(X0,X1)),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( r3(sK1(X0,X1),X1,sK0(X0,X1))
      & r4(X1,X0,sK1(X0,X1))
      & r4(X1,sK3(X0,X1),sK2(X0,X1))
      & r2(X0,sK3(X0,X1))
      & sK2(X0,X1) = sK0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f26,f30,f29,f28,f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X3,X1,X2)
              & r4(X1,X0,X3) )
          & ? [X4] :
              ( ? [X5] :
                  ( r4(X1,X5,X4)
                  & r2(X0,X5) )
              & X2 = X4 ) )
     => ( ? [X3] :
            ( r3(X3,X1,sK0(X0,X1))
            & r4(X1,X0,X3) )
        & ? [X4] :
            ( ? [X5] :
                ( r4(X1,X5,X4)
                & r2(X0,X5) )
            & sK0(X0,X1) = X4 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X3,X1,sK0(X0,X1))
          & r4(X1,X0,X3) )
     => ( r3(sK1(X0,X1),X1,sK0(X0,X1))
        & r4(X1,X0,sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r4(X1,X5,X4)
              & r2(X0,X5) )
          & sK0(X0,X1) = X4 )
     => ( ? [X5] :
            ( r4(X1,X5,sK2(X0,X1))
            & r2(X0,X5) )
        & sK2(X0,X1) = sK0(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X1,X5,sK2(X0,X1))
          & r2(X0,X5) )
     => ( r4(X1,sK3(X0,X1),sK2(X0,X1))
        & r2(X0,sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X3,X1,X2)
          & r4(X1,X0,X3) )
      & ? [X4] :
          ( ? [X5] :
              ( r4(X1,X5,X4)
              & r2(X0,X5) )
          & X2 = X4 ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X5] :
          ( r3(X5,X0,X2)
          & r4(X0,X1,X5) )
      & ? [X3] :
          ( ? [X4] :
              ( r4(X0,X4,X3)
              & r2(X1,X4) )
          & X2 = X3 ) ),
    inference(rectify,[],[f6]) ).

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

fof(f74,plain,
    ! [X3,X0,X1] :
      ( ~ r4(X0,X1,X3)
      | sK5(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X3] :
      ( ( sK5(X0,X1) = X3
        & r4(X0,X1,X3) )
      | ( ~ r4(X0,X1,X3)
        & sK5(X0,X1) != X3 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f15,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r4(X0,X1,X3) )
          | ( ~ r4(X0,X1,X3)
            & X2 != X3 ) )
     => ! [X3] :
          ( ( sK5(X0,X1) = X3
            & r4(X0,X1,X3) )
          | ( ~ r4(X0,X1,X3)
            & sK5(X0,X1) != X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r4(X0,X1,X3) )
      | ( ~ r4(X0,X1,X3)
        & X2 != X3 ) ),
    inference(rectify,[],[f4]) ).

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

fof(f181,plain,
    ! [X0] : sK5(X0,sK4) = sK4,
    inference(resolution,[],[f74,f123]) ).

fof(f123,plain,
    ! [X0] : r4(X0,sK4,sK4),
    inference(backward_demodulation,[],[f122,f118]) ).

fof(f118,plain,
    ! [X2] : sK12(X2) = sK4,
    inference(resolution,[],[f65,f87]) ).

fof(f87,plain,
    ! [X0] : r1(sK12(X0)),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( sK11(X0) = sK10(X0)
      & r1(sK11(X0))
      & r1(sK12(X0))
      & r4(X0,sK12(X0),sK10(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f17,f47,f46,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( X1 = X2
              & r1(X2) )
          & ? [X3] :
              ( r1(X3)
              & r4(X0,X3,X1) ) )
     => ( ? [X2] :
            ( sK10(X0) = X2
            & r1(X2) )
        & ? [X3] :
            ( r1(X3)
            & r4(X0,X3,sK10(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X2] :
          ( sK10(X0) = X2
          & r1(X2) )
     => ( sK11(X0) = sK10(X0)
        & r1(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0] :
      ( ? [X3] :
          ( r1(X3)
          & r4(X0,X3,sK10(X0)) )
     => ( r1(sK12(X0))
        & r4(X0,sK12(X0),sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f65,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK4 = X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f122,plain,
    ! [X0] : r4(X0,sK12(X0),sK4),
    inference(backward_demodulation,[],[f86,f117]) ).

fof(f117,plain,
    ! [X1] : sK4 = sK10(X1),
    inference(resolution,[],[f65,f101]) ).

fof(f101,plain,
    ! [X0] : r1(sK10(X0)),
    inference(definition_unfolding,[],[f88,f89]) ).

fof(f89,plain,
    ! [X0] : sK11(X0) = sK10(X0),
    inference(cnf_transformation,[],[f48]) ).

fof(f88,plain,
    ! [X0] : r1(sK11(X0)),
    inference(cnf_transformation,[],[f48]) ).

fof(f86,plain,
    ! [X0] : r4(X0,sK12(X0),sK10(X0)),
    inference(cnf_transformation,[],[f48]) ).

fof(f64,plain,
    ! [X0,X1] : r3(sK1(X0,X1),X1,sK0(X0,X1)),
    inference(cnf_transformation,[],[f31]) ).

fof(f82,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X1,X0,X3)
      | sK9(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X3] :
      ( ( r3(X1,X0,X3)
        & sK9(X0,X1) = X3 )
      | ( sK9(X0,X1) != X3
        & ~ r3(X1,X0,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f42,f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( r3(X1,X0,X3)
            & X2 = X3 )
          | ( X2 != X3
            & ~ r3(X1,X0,X3) ) )
     => ! [X3] :
          ( ( r3(X1,X0,X3)
            & sK9(X0,X1) = X3 )
          | ( sK9(X0,X1) != X3
            & ~ r3(X1,X0,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( r3(X1,X0,X3)
        & X2 = X3 )
      | ( X2 != X3
        & ~ r3(X1,X0,X3) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0] :
    ? [X2] :
    ! [X3] :
      ( ( r3(X0,X1,X3)
        & X2 = X3 )
      | ( X2 != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(rectify,[],[f3]) ).

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

fof(f239,plain,
    ! [X0] : sK9(sK6(sK4),X0) = sK6(X0),
    inference(resolution,[],[f235,f82]) ).

fof(f235,plain,
    ! [X2] : r3(X2,sK6(sK4),sK6(X2)),
    inference(superposition,[],[f140,f228]) ).

fof(f228,plain,
    ! [X0] : sK13(X0,sK4) = sK6(X0),
    inference(resolution,[],[f227,f77]) ).

fof(f77,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK6(X0) = X2 ),
    inference(cnf_transformation,[],[f38]) ).

fof(f227,plain,
    ! [X0] : r2(X0,sK13(X0,sK4)),
    inference(superposition,[],[f215,f209]) ).

fof(f209,plain,
    ! [X0] : sK9(sK4,X0) = X0,
    inference(resolution,[],[f82,f120]) ).

fof(f120,plain,
    ! [X0] : r3(X0,sK4,X0),
    inference(backward_demodulation,[],[f114,f116]) ).

fof(f116,plain,
    ! [X0] : sK4 = sK8(X0),
    inference(resolution,[],[f65,f80]) ).

fof(f80,plain,
    ! [X0] : r1(sK8(X0)),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( r3(X0,sK8(X0),sK7(X0))
      & r1(sK8(X0))
      & sK7(X0) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f24,f40,f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & X0 = X1 )
     => ( ? [X2] :
            ( r3(X0,X2,sK7(X0))
            & r1(X2) )
        & sK7(X0) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK7(X0))
          & r1(X2) )
     => ( r3(X0,sK8(X0),sK7(X0))
        & r1(sK8(X0)) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f114,plain,
    ! [X0] : r3(X0,sK8(X0),X0),
    inference(forward_demodulation,[],[f81,f79]) ).

fof(f79,plain,
    ! [X0] : sK7(X0) = X0,
    inference(cnf_transformation,[],[f41]) ).

fof(f81,plain,
    ! [X0] : r3(X0,sK8(X0),sK7(X0)),
    inference(cnf_transformation,[],[f41]) ).

fof(f215,plain,
    ! [X0,X1] : r2(sK9(X1,X0),sK13(X0,X1)),
    inference(backward_demodulation,[],[f93,f210]) ).

fof(f210,plain,
    ! [X2,X1] : sK9(X1,X2) = sK14(X2,X1),
    inference(resolution,[],[f82,f94]) ).

fof(f94,plain,
    ! [X0,X1] : r3(X0,X1,sK14(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK14(X0,X1))
      & r2(sK14(X0,X1),sK13(X0,X1))
      & sK15(X0,X1) = sK13(X0,X1)
      & r2(X1,sK16(X0,X1))
      & r3(X0,sK16(X0,X1),sK15(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] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r2(X1,X5)
                  & r3(X0,X5,X4) ) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK13(X0,X1)) )
        & ? [X4] :
            ( sK13(X0,X1) = X4
            & ? [X5] :
                ( r2(X1,X5)
                & r3(X0,X5,X4) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK13(X0,X1) = X4
          & ? [X5] :
              ( r2(X1,X5)
              & r3(X0,X5,X4) ) )
     => ( sK15(X0,X1) = sK13(X0,X1)
        & ? [X5] :
            ( r2(X1,X5)
            & r3(X0,X5,sK15(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r2(X1,X5)
          & r3(X0,X5,sK15(X0,X1)) )
     => ( r2(X1,sK16(X0,X1))
        & r3(X0,sK16(X0,X1),sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) )
      & ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r2(X1,X5)
              & r3(X0,X5,X4) ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,X2) )
      & ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r2(X1,X4)
              & r3(X0,X4,X3) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13,X14] :
    ? [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(f93,plain,
    ! [X0,X1] : r2(sK14(X0,X1),sK13(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f140,plain,
    ! [X0,X1] : r3(X0,sK6(X1),sK13(X0,X1)),
    inference(backward_demodulation,[],[f102,f136]) ).

fof(f136,plain,
    ! [X3,X4] : sK16(X4,X3) = sK6(X3),
    inference(resolution,[],[f77,f91]) ).

fof(f91,plain,
    ! [X0,X1] : r2(X1,sK16(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f102,plain,
    ! [X0,X1] : r3(X0,sK16(X0,X1),sK13(X0,X1)),
    inference(definition_unfolding,[],[f90,f92]) ).

fof(f92,plain,
    ! [X0,X1] : sK15(X0,X1) = sK13(X0,X1),
    inference(cnf_transformation,[],[f54]) ).

fof(f90,plain,
    ! [X0,X1] : r3(X0,sK16(X0,X1),sK15(X0,X1)),
    inference(cnf_transformation,[],[f54]) ).

fof(f336,plain,
    ! [X2,X3] :
      ( ~ r2(X2,sK0(sK4,X3))
      | ~ r1(X2) ),
    inference(forward_demodulation,[],[f333,f214]) ).

fof(f333,plain,
    ! [X2,X3] :
      ( ~ r2(X2,sK9(X3,sK4))
      | ~ r1(X2) ),
    inference(resolution,[],[f328,f215]) ).

fof(f328,plain,
    ! [X8,X6,X7] :
      ( ~ r2(X7,sK13(sK4,X6))
      | ~ r1(X8)
      | ~ r2(X8,X7) ),
    inference(superposition,[],[f149,f304]) ).

fof(f304,plain,
    ! [X5] : sK0(sK4,sK6(X5)) = sK13(sK4,X5),
    inference(superposition,[],[f214,f212]) ).

fof(f212,plain,
    ! [X6,X5] : sK9(sK6(X5),X6) = sK13(X6,X5),
    inference(resolution,[],[f82,f140]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1] :
      ( ~ r2(X0,sK0(X1,X2))
      | ~ r2(X3,X0)
      | ~ r1(X3) ),
    inference(resolution,[],[f143,f105]) ).

fof(f105,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ r4(X2,X1,X3)
      | ~ r2(X4,X3)
      | ~ r2(X5,X4)
      | ~ r1(X5) ),
    inference(equality_resolution,[],[f69]) ).

fof(f69,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ r2(X4,X3)
      | ~ r2(X5,X4)
      | ~ r1(X5)
      | X0 != X3
      | ~ r4(X2,X1,X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ! [X4] :
              ( ~ r2(X4,X3)
              | ! [X5] :
                  ( ~ r2(X5,X4)
                  | ~ r1(X5) ) )
          | X0 != X3 )
      | ~ r4(X2,X1,X0) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( ! [X4] :
              ( ~ r2(X4,X3)
              | ! [X5] :
                  ( ~ r2(X5,X4)
                  | ~ r1(X5) ) )
          | X2 != X3 )
      | ~ r4(X1,X0,X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ? [X1,X0,X2] :
        ( r4(X1,X0,X2)
        & ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( r2(X5,X4)
                    & r1(X5) )
                & r2(X4,X3) )
            & X2 = X3 ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X21,X38,X22] :
        ( r4(X38,X21,X22)
        & ? [X15] :
            ( X15 = X22
            & ? [X16] :
                ( ? [X24] :
                    ( r1(X24)
                    & r2(X24,X16) )
                & r2(X16,X15) ) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X21,X38,X22] :
      ( r4(X38,X21,X22)
      & ? [X15] :
          ( X15 = X22
          & ? [X16] :
              ( ? [X24] :
                  ( r1(X24)
                  & r2(X24,X16) )
              & r2(X16,X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xtimesyeqtwo) ).

fof(f143,plain,
    ! [X0,X1] : r4(X1,sK6(X0),sK0(X0,X1)),
    inference(backward_demodulation,[],[f100,f135]) ).

fof(f135,plain,
    ! [X2,X1] : sK3(X1,X2) = sK6(X1),
    inference(resolution,[],[f77,f61]) ).

fof(f61,plain,
    ! [X0,X1] : r2(X0,sK3(X0,X1)),
    inference(cnf_transformation,[],[f31]) ).

fof(f100,plain,
    ! [X0,X1] : r4(X1,sK3(X0,X1),sK0(X0,X1)),
    inference(definition_unfolding,[],[f62,f60]) ).

fof(f60,plain,
    ! [X0,X1] : sK2(X0,X1) = sK0(X0,X1),
    inference(cnf_transformation,[],[f31]) ).

fof(f62,plain,
    ! [X0,X1] : r4(X1,sK3(X0,X1),sK2(X0,X1)),
    inference(cnf_transformation,[],[f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n012.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 09:49:20 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.49  % (29986)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.49  % (29993)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (29984)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (29984)Refutation not found, incomplete strategy% (29984)------------------------------
% 0.19/0.50  % (29984)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (29984)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (29984)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50  
% 0.19/0.50  % (29984)Memory used [KB]: 6012
% 0.19/0.50  % (29984)Time elapsed: 0.101 s
% 0.19/0.50  % (29984)Instructions burned: 2 (million)
% 0.19/0.50  % (29984)------------------------------
% 0.19/0.50  % (29984)------------------------------
% 0.19/0.50  % (29985)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (29987)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.50  % (29995)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (30003)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.50  % (30007)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.50  % (29993)Instruction limit reached!
% 0.19/0.50  % (29993)------------------------------
% 0.19/0.50  % (29993)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (29993)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (29993)Termination reason: Unknown
% 0.19/0.50  % (29993)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (29993)Memory used [KB]: 6140
% 0.19/0.50  % (29993)Time elapsed: 0.113 s
% 0.19/0.50  % (29993)Instructions burned: 7 (million)
% 0.19/0.50  % (29993)------------------------------
% 0.19/0.50  % (29993)------------------------------
% 0.19/0.50  % (29982)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (30007)Refutation not found, incomplete strategy% (30007)------------------------------
% 0.19/0.50  % (30007)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (30007)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (30007)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50  
% 0.19/0.50  % (30007)Memory used [KB]: 1535
% 0.19/0.50  % (30007)Time elapsed: 0.074 s
% 0.19/0.50  % (30007)Instructions burned: 3 (million)
% 0.19/0.50  % (30007)------------------------------
% 0.19/0.50  % (30007)------------------------------
% 0.19/0.51  % (29992)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.51  % (30011)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.51  % (30010)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  % (30000)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51  % (30010)Refutation not found, incomplete strategy% (30010)------------------------------
% 0.19/0.51  % (30010)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (30010)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (30010)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (30010)Memory used [KB]: 6012
% 0.19/0.51  % (30010)Time elapsed: 0.095 s
% 0.19/0.51  % (30010)Instructions burned: 3 (million)
% 0.19/0.51  % (30010)------------------------------
% 0.19/0.51  % (30010)------------------------------
% 0.19/0.51  % (29985)Refutation not found, incomplete strategy% (29985)------------------------------
% 0.19/0.51  % (29985)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (29985)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (29985)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (29985)Memory used [KB]: 6140
% 0.19/0.51  % (29985)Time elapsed: 0.114 s
% 0.19/0.51  % (29985)Instructions burned: 7 (million)
% 0.19/0.51  % (29985)------------------------------
% 0.19/0.51  % (29985)------------------------------
% 0.19/0.51  % (29986)First to succeed.
% 0.19/0.51  % (30003)Refutation not found, incomplete strategy% (30003)------------------------------
% 0.19/0.51  % (30003)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (29992)Refutation not found, incomplete strategy% (29992)------------------------------
% 0.19/0.51  % (29992)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (29992)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (29992)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (29992)Memory used [KB]: 6012
% 0.19/0.51  % (29992)Time elapsed: 0.118 s
% 0.19/0.51  % (29992)Instructions burned: 3 (million)
% 0.19/0.51  % (29992)------------------------------
% 0.19/0.51  % (29992)------------------------------
% 0.19/0.51  % (30003)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (30003)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (30003)Memory used [KB]: 6012
% 0.19/0.51  % (30003)Time elapsed: 0.130 s
% 0.19/0.51  % (30003)Instructions burned: 7 (million)
% 0.19/0.51  % (30003)------------------------------
% 0.19/0.51  % (30003)------------------------------
% 0.19/0.51  % (30000)Instruction limit reached!
% 0.19/0.51  % (30000)------------------------------
% 0.19/0.51  % (30000)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (30000)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (30000)Termination reason: Unknown
% 0.19/0.51  % (30000)Termination phase: Preprocessing 3
% 0.19/0.51  
% 0.19/0.51  % (30000)Memory used [KB]: 1407
% 0.19/0.51  % (30000)Time elapsed: 0.003 s
% 0.19/0.51  % (30000)Instructions burned: 2 (million)
% 0.19/0.51  % (30000)------------------------------
% 0.19/0.51  % (30000)------------------------------
% 0.19/0.51  % (29988)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (29983)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (29989)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (29994)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.52  % (29996)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.52  % (29994)Refutation not found, incomplete strategy% (29994)------------------------------
% 0.19/0.52  % (29994)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (29994)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (29994)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (29994)Memory used [KB]: 1535
% 0.19/0.52  % (29994)Time elapsed: 0.122 s
% 0.19/0.52  % (29994)Instructions burned: 3 (million)
% 0.19/0.52  % (29994)------------------------------
% 0.19/0.52  % (29994)------------------------------
% 0.19/0.52  % (30006)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.52  % (29986)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (29986)------------------------------
% 0.19/0.52  % (29986)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (29986)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (29986)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (29986)Memory used [KB]: 6140
% 0.19/0.52  % (29986)Time elapsed: 0.122 s
% 0.19/0.52  % (29986)Instructions burned: 12 (million)
% 0.19/0.52  % (29986)------------------------------
% 0.19/0.52  % (29986)------------------------------
% 0.19/0.52  % (29981)Success in time 0.171 s
%------------------------------------------------------------------------------