TSTP Solution File: NUN059+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% 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 : Tue Apr 30 14:40:17 EDT 2024

% Result   : Theorem 3.94s 0.92s
% Output   : Refutation 3.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  117 (  29 unt;   0 def)
%            Number of atoms       :  327 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  366 ( 156   ~; 119   |;  79   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-2 aty)
%            Number of variables   :  264 ( 214   !;  50   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f28712,plain,
    $false,
    inference(avatar_sat_refutation,[],[f14661,f19364,f28567,f28576,f28711]) ).

fof(f28711,plain,
    ~ spl20_294,
    inference(avatar_contradiction_clause,[],[f28710]) ).

fof(f28710,plain,
    ( $false
    | ~ spl20_294 ),
    inference(subsumption_resolution,[],[f28683,f77]) ).

fof(f77,plain,
    ! [X0] : r1(sK7(X0)),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( r1(sK6(X0))
      & id(sK5(X0),sK6(X0))
      & r4(X0,sK7(X0),sK5(X0))
      & r1(sK7(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f48,f47,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r1(X2)
              & id(X1,X2) )
          & ? [X3] :
              ( r4(X0,X3,X1)
              & r1(X3) ) )
     => ( ? [X2] :
            ( r1(X2)
            & id(sK5(X0),X2) )
        & ? [X3] :
            ( r4(X0,X3,sK5(X0))
            & r1(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0] :
      ( ? [X2] :
          ( r1(X2)
          & id(sK5(X0),X2) )
     => ( r1(sK6(X0))
        & id(sK5(X0),sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X3] :
          ( r4(X0,X3,sK5(X0))
          & r1(X3) )
     => ( r4(X0,sK7(X0),sK5(X0))
        & r1(sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r1(X2)
          & id(X1,X2) )
      & ? [X3] :
          ( r4(X0,X3,X1)
          & r1(X3) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X56] :
    ? [X57] :
      ( ? [X59] :
          ( r1(X59)
          & id(X57,X59) )
      & ? [X58] :
          ( r4(X56,X58,X57)
          & r1(X58) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).

fof(f28683,plain,
    ( ~ r1(sK7(sK19))
    | ~ spl20_294 ),
    inference(resolution,[],[f28590,f133]) ).

fof(f133,plain,
    ! [X0] :
      ( id(sK19,X0)
      | ~ r1(X0) ),
    inference(resolution,[],[f85,f123]) ).

fof(f123,plain,
    ! [X1] :
      ( id(X1,sK19)
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X1] :
      ( ( ~ id(X1,sK19)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,sK19) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1,f66]) ).

fof(f66,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ~ id(X1,X0)
          & ~ r1(X1) )
        | ( r1(X1)
          & id(X1,X0) ) )
   => ! [X1] :
        ( ( ~ id(X1,sK19)
          & ~ r1(X1) )
        | ( r1(X1)
          & id(X1,sK19) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f85,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X1,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( id(X1,X0)
      | ~ id(X0,X1) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X14,X15] :
      ( id(X15,X14)
      | ~ id(X14,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

fof(f28590,plain,
    ( ! [X0] : ~ id(X0,sK7(X0))
    | ~ spl20_294 ),
    inference(subsumption_resolution,[],[f28585,f1145]) ).

fof(f1145,plain,
    ! [X0,X1] : id(sK5(X0),sK4(X1)),
    inference(resolution,[],[f1124,f85]) ).

fof(f1124,plain,
    ! [X0,X1] : id(sK4(X0),sK5(X1)),
    inference(resolution,[],[f505,f75]) ).

fof(f75,plain,
    ! [X0] : r1(sK4(X0)),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( r3(X0,sK4(X0),sK3(X0))
      & r1(sK4(X0))
      & id(sK3(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f24,f44,f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & id(X1,X0) )
     => ( ? [X2] :
            ( r3(X0,X2,sK3(X0))
            & r1(X2) )
        & id(sK3(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK3(X0))
          & r1(X2) )
     => ( r3(X0,sK4(X0),sK3(X0))
        & r1(sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) )
      & id(X1,X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X53] :
    ? [X54] :
      ( ? [X55] :
          ( r3(X53,X55,X54)
          & r1(X55) )
      & id(X54,X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).

fof(f505,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | id(X0,sK5(X1)) ),
    inference(resolution,[],[f485,f268]) ).

fof(f268,plain,
    ! [X0,X1] :
      ( ~ id(sK19,X1)
      | id(X0,X1)
      | ~ r1(X0) ),
    inference(resolution,[],[f110,f123]) ).

fof(f110,plain,
    ! [X2,X0,X1] :
      ( ~ id(X0,X1)
      | id(X0,X2)
      | ~ id(X1,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ~ id(X1,X2)
      | id(X0,X2)
      | ~ id(X0,X1) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X16,X17,X18] :
      ( ~ id(X17,X18)
      | id(X16,X18)
      | ~ id(X16,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

fof(f485,plain,
    ! [X0] : id(sK19,sK5(X0)),
    inference(resolution,[],[f481,f85]) ).

fof(f481,plain,
    ! [X0] : id(sK5(X0),sK19),
    inference(subsumption_resolution,[],[f480,f80]) ).

fof(f80,plain,
    ! [X0] : r1(sK6(X0)),
    inference(cnf_transformation,[],[f49]) ).

fof(f480,plain,
    ! [X0] :
      ( id(sK5(X0),sK19)
      | ~ r1(sK6(X0)) ),
    inference(resolution,[],[f264,f123]) ).

fof(f264,plain,
    ! [X0,X1] :
      ( ~ id(sK6(X0),X1)
      | id(sK5(X0),X1) ),
    inference(resolution,[],[f110,f79]) ).

fof(f79,plain,
    ! [X0] : id(sK5(X0),sK6(X0)),
    inference(cnf_transformation,[],[f49]) ).

fof(f28585,plain,
    ( ! [X0] :
        ( ~ id(sK5(X0),sK4(sK19))
        | ~ id(X0,sK7(X0)) )
    | ~ spl20_294 ),
    inference(resolution,[],[f28555,f918]) ).

fof(f918,plain,
    ! [X2,X0,X1] :
      ( r4(X2,sK7(X0),X1)
      | ~ id(sK5(X0),X1)
      | ~ id(X0,X2) ),
    inference(resolution,[],[f307,f69]) ).

fof(f69,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f307,plain,
    ! [X2,X3,X0,X1] :
      ( ~ id(sK7(X3),X1)
      | ~ id(sK5(X3),X2)
      | r4(X0,X1,X2)
      | ~ id(X3,X0) ),
    inference(resolution,[],[f117,f78]) ).

fof(f78,plain,
    ! [X0] : r4(X0,sK7(X0),sK5(X0)),
    inference(cnf_transformation,[],[f49]) ).

fof(f117,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ r4(X0,X1,X2)
      | r4(X3,X4,X5)
      | ~ id(X2,X5)
      | ~ id(X1,X4)
      | ~ id(X0,X3) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( r4(X3,X4,X5)
        & r4(X0,X1,X2) )
      | ( ~ r4(X3,X4,X5)
        & ~ r4(X0,X1,X2) )
      | ~ id(X2,X5)
      | ~ id(X1,X4)
      | ~ id(X0,X3) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X31,X32,X33,X34,X35,X36] :
      ( ( r4(X34,X35,X36)
        & r4(X31,X32,X33) )
      | ( ~ r4(X34,X35,X36)
        & ~ r4(X31,X32,X33) )
      | ~ id(X33,X36)
      | ~ id(X32,X35)
      | ~ id(X31,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).

fof(f28555,plain,
    ( ! [X1] : ~ r4(X1,X1,sK4(sK19))
    | ~ spl20_294 ),
    inference(avatar_component_clause,[],[f28554]) ).

fof(f28554,plain,
    ( spl20_294
  <=> ! [X1] : ~ r4(X1,X1,sK4(sK19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_294])]) ).

fof(f28576,plain,
    ~ spl20_295,
    inference(avatar_contradiction_clause,[],[f28575]) ).

fof(f28575,plain,
    ( $false
    | ~ spl20_295 ),
    inference(resolution,[],[f28558,f12418]) ).

fof(f12418,plain,
    ! [X0] : r4(X0,sK19,sK19),
    inference(resolution,[],[f3732,f69]) ).

fof(f3732,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | r4(X0,sK19,sK19) ),
    inference(subsumption_resolution,[],[f3728,f180]) ).

fof(f180,plain,
    ! [X0] : r1(sK5(X0)),
    inference(resolution,[],[f146,f79]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ id(X0,sK6(X1))
      | r1(X0) ),
    inference(resolution,[],[f87,f80]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ r1(X1)
      | r1(X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( r1(X1)
        & r1(X0) )
      | ( ~ r1(X1)
        & ~ r1(X0) )
      | ~ id(X0,X1) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X19,X20] :
      ( ( r1(X20)
        & r1(X19) )
      | ( ~ r1(X20)
        & ~ r1(X19) )
      | ~ id(X19,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

fof(f3728,plain,
    ! [X0,X1] :
      ( r4(X0,sK19,sK19)
      | ~ id(X0,X1)
      | ~ r1(sK5(X1)) ),
    inference(resolution,[],[f886,f133]) ).

fof(f886,plain,
    ! [X2,X0,X1] :
      ( ~ id(X0,sK5(X1))
      | r4(X2,sK19,X0)
      | ~ id(X2,X1) ),
    inference(subsumption_resolution,[],[f884,f77]) ).

fof(f884,plain,
    ! [X2,X0,X1] :
      ( ~ id(X0,sK5(X1))
      | r4(X2,sK19,X0)
      | ~ id(X2,X1)
      | ~ r1(sK7(X1)) ),
    inference(resolution,[],[f296,f133]) ).

fof(f296,plain,
    ! [X2,X3,X0,X1] :
      ( ~ id(X1,sK7(X3))
      | ~ id(X2,sK5(X3))
      | r4(X0,X1,X2)
      | ~ id(X0,X3) ),
    inference(resolution,[],[f116,f78]) ).

fof(f116,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ r4(X3,X4,X5)
      | r4(X0,X1,X2)
      | ~ id(X2,X5)
      | ~ id(X1,X4)
      | ~ id(X0,X3) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f28558,plain,
    ( ! [X0] : ~ r4(X0,X0,sK19)
    | ~ spl20_295 ),
    inference(avatar_component_clause,[],[f28557]) ).

fof(f28557,plain,
    ( spl20_295
  <=> ! [X0] : ~ r4(X0,X0,sK19) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_295])]) ).

fof(f28567,plain,
    ( spl20_294
    | spl20_295
    | ~ spl20_97 ),
    inference(avatar_split_clause,[],[f28544,f6747,f28557,f28554]) ).

fof(f6747,plain,
    ( spl20_97
  <=> ! [X0,X3,X2,X1] :
        ( ~ r4(X0,X0,X1)
        | ~ r4(X3,X3,X2)
        | ~ r3(X2,X1,sK19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_97])]) ).

fof(f28544,plain,
    ( ! [X0,X1] :
        ( ~ r4(X0,X0,sK19)
        | ~ r4(X1,X1,sK4(sK19)) )
    | ~ spl20_97 ),
    inference(resolution,[],[f6748,f1487]) ).

fof(f1487,plain,
    r3(sK19,sK4(sK19),sK19),
    inference(resolution,[],[f254,f401]) ).

fof(f401,plain,
    r1(sK18(sK19,sK4(sK19))),
    inference(resolution,[],[f232,f149]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ id(sK3(sK19),X0)
      | r1(X0) ),
    inference(resolution,[],[f88,f129]) ).

fof(f129,plain,
    r1(sK3(sK19)),
    inference(resolution,[],[f126,f74]) ).

fof(f74,plain,
    ! [X0] : id(sK3(X0),X0),
    inference(cnf_transformation,[],[f45]) ).

fof(f126,plain,
    ! [X1] :
      ( ~ id(X1,sK19)
      | r1(X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ~ r1(X0)
      | r1(X1)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f232,plain,
    ! [X0] : id(sK3(X0),sK18(X0,sK4(X0))),
    inference(resolution,[],[f106,f76]) ).

fof(f76,plain,
    ! [X0] : r3(X0,sK4(X0),sK3(X0)),
    inference(cnf_transformation,[],[f45]) ).

fof(f106,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X0,X1,X3)
      | id(X3,sK18(X0,X1)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X3] :
      ( ( ~ id(X3,sK18(X0,X1))
        & ~ r3(X0,X1,X3) )
      | ( r3(X0,X1,X3)
        & id(X3,sK18(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f34,f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( ~ id(X3,X2)
            & ~ r3(X0,X1,X3) )
          | ( r3(X0,X1,X3)
            & id(X3,X2) ) )
     => ! [X3] :
          ( ( ~ id(X3,sK18(X0,X1))
            & ~ r3(X0,X1,X3) )
          | ( r3(X0,X1,X3)
            & id(X3,sK18(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ id(X3,X2)
        & ~ r3(X0,X1,X3) )
      | ( r3(X0,X1,X3)
        & id(X3,X2) ) ),
    inference(rectify,[],[f3]) ).

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

fof(f254,plain,
    ! [X0,X1] :
      ( ~ r1(sK18(X0,X1))
      | r3(X0,X1,sK19) ),
    inference(resolution,[],[f109,f133]) ).

fof(f109,plain,
    ! [X3,X0,X1] :
      ( ~ id(X3,sK18(X0,X1))
      | r3(X0,X1,X3) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f6748,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ r3(X2,X1,sK19)
        | ~ r4(X3,X3,X2)
        | ~ r4(X0,X0,X1) )
    | ~ spl20_97 ),
    inference(avatar_component_clause,[],[f6747]) ).

fof(f19364,plain,
    ( spl20_97
    | spl20_96 ),
    inference(avatar_split_clause,[],[f19348,f6744,f6747]) ).

fof(f6744,plain,
    ( spl20_96
  <=> ! [X4] : ~ r1(sK17(X4,X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_96])]) ).

fof(f19348,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ r1(sK17(X0,X0))
      | ~ r4(X1,X1,X2)
      | ~ r3(X3,X2,sK19)
      | ~ r4(X4,X4,X3) ),
    inference(resolution,[],[f13501,f396]) ).

fof(f396,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ id(X4,sK3(sK17(X5,X5)))
      | ~ r4(X2,X2,X3)
      | ~ r3(X1,X3,X4)
      | ~ r4(X0,X0,X1) ),
    inference(resolution,[],[f227,f68]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ r4(X2,X2,X6)
      | ~ r4(X0,X0,X5)
      | ~ r4(X1,X1,X4)
      | ~ r3(X5,X4,X3)
      | ~ id(X3,X6) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2,X3] :
      ( ! [X4] :
          ( ! [X5] :
              ( ~ r3(X5,X4,X3)
              | ~ r4(X0,X0,X5) )
          | ~ r4(X1,X1,X4) )
      | ! [X6] :
          ( ~ r4(X2,X2,X6)
          | ~ id(X3,X6) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ? [X0,X1,X2,X3] :
        ( ? [X4] :
            ( ? [X5] :
                ( r3(X5,X4,X3)
                & r4(X0,X0,X5) )
            & r4(X1,X1,X4) )
        & ? [X6] :
            ( r4(X2,X2,X6)
            & id(X3,X6) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ? [X62,X46,X45,X39] :
        ( ? [X48] :
            ( ? [X42] :
                ( r3(X42,X48,X39)
                & r4(X62,X62,X42) )
            & r4(X46,X46,X48) )
        & ? [X40] :
            ( r4(X45,X45,X40)
            & id(X39,X40) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ? [X62,X46,X45,X39] :
      ( ? [X48] :
          ( ? [X42] :
              ( r3(X42,X48,X39)
              & r4(X62,X62,X42) )
          & r4(X46,X46,X48) )
      & ? [X40] :
          ( r4(X45,X45,X40)
          & id(X39,X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fermattothepoweroftwoid) ).

fof(f227,plain,
    ! [X0,X1] : r4(X0,X1,sK3(sK17(X0,X1))),
    inference(resolution,[],[f105,f74]) ).

fof(f105,plain,
    ! [X3,X0,X1] :
      ( ~ id(X3,sK17(X0,X1))
      | r4(X0,X1,X3) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X3] :
      ( ( ~ id(X3,sK17(X0,X1))
        & ~ r4(X0,X1,X3) )
      | ( r4(X0,X1,X3)
        & id(X3,sK17(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f33,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( ~ id(X3,X2)
            & ~ r4(X0,X1,X3) )
          | ( r4(X0,X1,X3)
            & id(X3,X2) ) )
     => ! [X3] :
          ( ( ~ id(X3,sK17(X0,X1))
            & ~ r4(X0,X1,X3) )
          | ( r4(X0,X1,X3)
            & id(X3,sK17(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ id(X3,X2)
        & ~ r4(X0,X1,X3) )
      | ( r4(X0,X1,X3)
        & id(X3,X2) ) ),
    inference(rectify,[],[f4]) ).

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

fof(f13501,plain,
    ! [X0] :
      ( id(sK19,sK3(X0))
      | ~ r1(X0) ),
    inference(resolution,[],[f1247,f490]) ).

fof(f490,plain,
    ! [X0] :
      ( id(X0,sK3(sK19))
      | ~ r1(X0) ),
    inference(resolution,[],[f268,f131]) ).

fof(f131,plain,
    ! [X0] : id(X0,sK3(X0)),
    inference(resolution,[],[f85,f74]) ).

fof(f1247,plain,
    ! [X0,X1] :
      ( ~ id(X0,sK3(X1))
      | id(X1,sK3(X0)) ),
    inference(resolution,[],[f436,f262]) ).

fof(f262,plain,
    ! [X0,X1] :
      ( ~ id(sK3(X0),X1)
      | id(X0,X1) ),
    inference(resolution,[],[f110,f131]) ).

fof(f436,plain,
    ! [X0,X1] :
      ( id(X1,sK3(X0))
      | ~ id(X0,X1) ),
    inference(resolution,[],[f258,f85]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( id(sK3(X0),X1)
      | ~ id(X0,X1) ),
    inference(resolution,[],[f110,f74]) ).

fof(f14661,plain,
    ~ spl20_96,
    inference(avatar_contradiction_clause,[],[f14639]) ).

fof(f14639,plain,
    ( $false
    | ~ spl20_96 ),
    inference(resolution,[],[f14586,f6745]) ).

fof(f6745,plain,
    ( ! [X4] : ~ r1(sK17(X4,X4))
    | ~ spl20_96 ),
    inference(avatar_component_clause,[],[f6744]) ).

fof(f14586,plain,
    ! [X0] : r1(sK17(X0,sK19)),
    inference(resolution,[],[f12817,f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ~ id(sK19,X0)
      | r1(X0) ),
    inference(resolution,[],[f88,f128]) ).

fof(f128,plain,
    r1(sK19),
    inference(resolution,[],[f126,f69]) ).

fof(f12817,plain,
    ! [X0] : id(sK19,sK17(X0,sK19)),
    inference(resolution,[],[f12418,f102]) ).

fof(f102,plain,
    ! [X3,X0,X1] :
      ( ~ r4(X0,X1,X3)
      | id(X3,sK17(X0,X1)) ),
    inference(cnf_transformation,[],[f63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n031.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 03:02:13 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (6172)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (6178)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (6173)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (6176)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37  % (6174)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (6175)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.37  % (6177)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (6179)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.14/0.38  TRYING [3]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.14/0.40  TRYING [4]
% 0.22/0.41  TRYING [5]
% 0.22/0.41  TRYING [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.22/0.42  TRYING [4]
% 0.22/0.45  TRYING [6]
% 0.22/0.46  TRYING [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.22/0.49  TRYING [5]
% 0.22/0.52  TRYING [7]
% 0.22/0.55  TRYING [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.22/0.58  TRYING [5]
% 2.05/0.70  TRYING [6]
% 3.72/0.89  TRYING [8]
% 3.94/0.92  % (6178)First to succeed.
% 3.94/0.92  % (6178)Refutation found. Thanks to Tanya!
% 3.94/0.92  % SZS status Theorem for theBenchmark
% 3.94/0.92  % SZS output start Proof for theBenchmark
% See solution above
% 3.94/0.92  % (6178)------------------------------
% 3.94/0.92  % (6178)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.94/0.92  % (6178)Termination reason: Refutation
% 3.94/0.92  
% 3.94/0.92  % (6178)Memory used [KB]: 7722
% 3.94/0.92  % (6178)Time elapsed: 0.545 s
% 3.94/0.92  % (6178)Instructions burned: 1647 (million)
% 3.94/0.92  % (6178)------------------------------
% 3.94/0.92  % (6178)------------------------------
% 3.94/0.92  % (6172)Success in time 0.548 s
%------------------------------------------------------------------------------