TSTP Solution File: NUN065+2 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : NUN065+2 : TPTP v8.2.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n006.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 : Mon Jun 24 13:32:46 EDT 2024

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  120 (  26 unt;   0 def)
%            Number of atoms       :  356 ( 128 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  342 ( 106   ~; 100   |; 120   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   1 con; 0-2 aty)
%            Number of variables   :  262 ( 188   !;  74   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1613,plain,
    $false,
    inference(subsumption_resolution,[],[f1523,f116]) ).

fof(f116,plain,
    r1(sK23),
    inference(equality_resolution,[],[f104]) ).

fof(f104,plain,
    ! [X1] :
      ( r1(X1)
      | sK23 != X1 ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X1] :
      ( ( sK23 = X1
        & r1(X1) )
      | ( sK23 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1,f61]) ).

fof(f61,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 = X1
          & r1(X1) )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( sK23 = X1
          & r1(X1) )
        | ( sK23 != 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',unknown) ).

fof(f1523,plain,
    ~ r1(sK23),
    inference(backward_demodulation,[],[f613,f1230]) ).

fof(f1230,plain,
    ! [X0] : sK23 = X0,
    inference(resolution,[],[f1110,f614]) ).

fof(f614,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK12(X0))
      | X0 = X1 ),
    inference(forward_demodulation,[],[f606,f604]) ).

fof(f604,plain,
    ! [X0] : sK12(X0) = sK17(X0,sK23),
    inference(resolution,[],[f602,f81]) ).

fof(f81,plain,
    ! [X2,X0] :
      ( sK12(X0) = X2
      | ~ r2(X0,X2) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X2] :
      ( ( sK12(X0) = X2
        & r2(X0,X2) )
      | ( sK12(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f18,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK12(X0) = X2
            & r2(X0,X2) )
          | ( sK12(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 = X2
        & r2(X0,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',unknown) ).

fof(f602,plain,
    ! [X0] : r2(X0,sK17(X0,sK23)),
    inference(superposition,[],[f93,f597]) ).

fof(f597,plain,
    ! [X0] : sK18(X0,sK23) = X0,
    inference(resolution,[],[f537,f94]) ).

fof(f94,plain,
    ! [X0,X1] : r3(X0,X1,sK18(X0,X1)),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK18(X0,X1))
      & r2(sK18(X0,X1),sK17(X0,X1))
      & sK17(X0,X1) = sK19(X0,X1)
      & r3(X0,sK20(X0,X1),sK19(X0,X1))
      & r2(X1,sK20(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20])],[f22,f55,f54,f53,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) ) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK17(X0,X1)) )
        & ? [X4] :
            ( sK17(X0,X1) = X4
            & ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,sK17(X0,X1)) )
     => ( r3(X0,X1,sK18(X0,X1))
        & r2(sK18(X0,X1),sK17(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK17(X0,X1) = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK17(X0,X1) = sK19(X0,X1)
        & ? [X5] :
            ( r3(X0,X5,sK19(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK19(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK20(X0,X1),sK19(X0,X1))
        & r2(X1,sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f537,plain,
    ! [X0,X1] :
      ( ~ r3(X0,sK23,X1)
      | X0 = X1 ),
    inference(superposition,[],[f530,f101]) ).

fof(f101,plain,
    ! [X3,X0,X1] :
      ( sK22(X0,X1) = X3
      | ~ r3(X0,X1,X3) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1,X3] :
      ( ( sK22(X0,X1) = X3
        & r3(X0,X1,X3) )
      | ( sK22(X0,X1) != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f24,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r3(X0,X1,X3) )
          | ( X2 != X3
            & ~ r3(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK22(X0,X1) = X3
            & r3(X0,X1,X3) )
          | ( sK22(X0,X1) != X3
            & ~ r3(X0,X1,X3) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f530,plain,
    ! [X0] : sK22(X0,sK23) = X0,
    inference(resolution,[],[f527,f101]) ).

fof(f527,plain,
    ! [X0] : r3(X0,sK23,X0),
    inference(forward_demodulation,[],[f525,f78]) ).

fof(f78,plain,
    ! [X0] : sK10(X0) = X0,
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( sK10(X0) = X0
      & r3(X0,sK11(X0),sK10(X0))
      & r1(sK11(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f17,f43,f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) ) )
     => ( sK10(X0) = X0
        & ? [X2] :
            ( r3(X0,X2,sK10(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK10(X0))
          & r1(X2) )
     => ( r3(X0,sK11(X0),sK10(X0))
        & r1(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0] :
    ? [X1] :
      ( X0 = X1
      & ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) ) ),
    inference(rectify,[],[f8]) ).

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

fof(f525,plain,
    ! [X0] : r3(X0,sK23,sK10(X0)),
    inference(backward_demodulation,[],[f77,f521]) ).

fof(f521,plain,
    ! [X0] : sK11(X0) = sK23,
    inference(backward_demodulation,[],[f338,f493]) ).

fof(f493,plain,
    ! [X0] : sK23 = sK3(sK11(X0)),
    inference(resolution,[],[f479,f76]) ).

fof(f76,plain,
    ! [X0] : r1(sK11(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f479,plain,
    ! [X0] :
      ( ~ r1(X0)
      | sK3(X0) = sK23 ),
    inference(subsumption_resolution,[],[f474,f117]) ).

fof(f117,plain,
    ! [X0] :
      ( sP0(X0)
      | sK3(X0) = sK23 ),
    inference(resolution,[],[f66,f105]) ).

fof(f105,plain,
    ! [X1] :
      ( sK23 = X1
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f66,plain,
    ! [X0] :
      ( r1(sK3(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ( sK3(X0) = X0
        & r1(sK3(X0)) )
      | sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & r1(X1) )
     => ( sK3(X0) = X0
        & r1(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & r1(X1) )
      | sP0(X0) ),
    inference(definition_folding,[],[f25,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ? [X2] :
          ( X0 = X2
          & ? [X3] :
              ( r2(X3,X2)
              & r1(X3) ) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f25,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & r1(X1) )
      | ? [X2] :
          ( X0 = X2
          & ? [X3] :
              ( r2(X3,X2)
              & r1(X3) ) ) ),
    inference(ennf_transformation,[],[f14]) ).

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

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

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

fof(f474,plain,
    ! [X0] :
      ( ~ r1(X0)
      | sK3(X0) = sK23
      | ~ sP0(X0) ),
    inference(superposition,[],[f443,f65]) ).

fof(f65,plain,
    ! [X0] :
      ( sK1(X0) = X0
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ( sK1(X0) = X0
        & r2(sK2(X0),sK1(X0))
        & r1(sK2(X0)) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f29,f31,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r2(X2,X1)
              & r1(X2) ) )
     => ( sK1(X0) = X0
        & ? [X2] :
            ( r2(X2,sK1(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0] :
      ( ? [X2] :
          ( r2(X2,sK1(X0))
          & r1(X2) )
     => ( r2(sK2(X0),sK1(X0))
        & r1(sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r2(X2,X1)
              & r1(X2) ) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ? [X2] :
          ( X0 = X2
          & ? [X3] :
              ( r2(X3,X2)
              & r1(X3) ) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f443,plain,
    ! [X0] :
      ( ~ r1(sK1(X0))
      | sK3(X0) = sK23 ),
    inference(resolution,[],[f123,f109]) ).

fof(f109,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | ~ r1(X2) ),
    inference(equality_resolution,[],[f83]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( X1 != X2
          | ~ r1(X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X40,X41] :
      ( ~ r2(X40,X41)
      | ! [X42] :
          ( X41 != X42
          | ~ r1(X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f123,plain,
    ! [X0] :
      ( r2(sK2(X0),sK1(X0))
      | sK3(X0) = sK23 ),
    inference(resolution,[],[f117,f64]) ).

fof(f64,plain,
    ! [X0] :
      ( r2(sK2(X0),sK1(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f338,plain,
    ! [X0] : sK11(X0) = sK3(sK11(X0)),
    inference(resolution,[],[f325,f76]) ).

fof(f325,plain,
    ! [X0] :
      ( ~ r1(X0)
      | sK3(X0) = X0 ),
    inference(subsumption_resolution,[],[f320,f67]) ).

fof(f67,plain,
    ! [X0] :
      ( sP0(X0)
      | sK3(X0) = X0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f320,plain,
    ! [X0] :
      ( ~ r1(X0)
      | sK3(X0) = X0
      | ~ sP0(X0) ),
    inference(superposition,[],[f291,f65]) ).

fof(f291,plain,
    ! [X0] :
      ( ~ r1(sK1(X0))
      | sK3(X0) = X0 ),
    inference(resolution,[],[f120,f109]) ).

fof(f120,plain,
    ! [X0] :
      ( r2(sK2(X0),sK1(X0))
      | sK3(X0) = X0 ),
    inference(resolution,[],[f67,f64]) ).

fof(f77,plain,
    ! [X0] : r3(X0,sK11(X0),sK10(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f93,plain,
    ! [X0,X1] : r2(sK18(X0,X1),sK17(X0,X1)),
    inference(cnf_transformation,[],[f56]) ).

fof(f606,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ r2(X1,sK17(X0,sK23)) ),
    inference(resolution,[],[f602,f110]) ).

fof(f110,plain,
    ! [X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X3)
      | ~ r2(X0,X3) ),
    inference(equality_resolution,[],[f84]) ).

fof(f84,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X2)
      | X2 != X3
      | ~ r2(X0,X3) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ! [X2] :
          ( ~ r2(X1,X2)
          | ! [X3] :
              ( X2 != X3
              | ~ r2(X0,X3) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X25,X26] :
      ( X25 = X26
      | ! [X27] :
          ( ~ r2(X26,X27)
          | ! [X28] :
              ( X27 != X28
              | ~ r2(X25,X28) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f1110,plain,
    ! [X1] : r2(X1,sK12(sK23)),
    inference(backward_demodulation,[],[f85,f1095]) ).

fof(f1095,plain,
    ! [X0,X1] : sK16(X0,X1) = sK12(sK23),
    inference(resolution,[],[f1093,f85]) ).

fof(f1093,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK12(sK23) = X0 ),
    inference(subsumption_resolution,[],[f1085,f241]) ).

fof(f241,plain,
    ! [X0,X1] :
      ( ~ sP0(X1)
      | sK12(sK23) = X1
      | ~ r2(X0,X1) ),
    inference(superposition,[],[f228,f81]) ).

fof(f228,plain,
    ! [X0] :
      ( ~ sP0(sK12(X0))
      | sK12(X0) = sK12(sK23) ),
    inference(resolution,[],[f190,f81]) ).

fof(f190,plain,
    ! [X0] :
      ( r2(sK23,sK12(X0))
      | ~ sP0(sK12(X0)) ),
    inference(backward_demodulation,[],[f143,f183]) ).

fof(f183,plain,
    ! [X0] : sK23 = sK2(sK12(X0)),
    inference(resolution,[],[f182,f108]) ).

fof(f108,plain,
    ! [X0] : r2(X0,sK12(X0)),
    inference(equality_resolution,[],[f80]) ).

fof(f80,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK12(X0) != X2 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK2(X0) = sK23 ),
    inference(resolution,[],[f180,f109]) ).

fof(f180,plain,
    ! [X0] :
      ( r1(X0)
      | sK2(X0) = sK23 ),
    inference(subsumption_resolution,[],[f177,f105]) ).

fof(f177,plain,
    ! [X0] :
      ( r1(X0)
      | sK2(X0) = sK23
      | r1(sK2(X0)) ),
    inference(resolution,[],[f156,f63]) ).

fof(f63,plain,
    ! [X0] :
      ( r1(sK2(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f156,plain,
    ! [X0] :
      ( sP0(X0)
      | r1(X0)
      | sK2(X0) = sK23 ),
    inference(superposition,[],[f66,f125]) ).

fof(f125,plain,
    ! [X0] :
      ( sK3(X0) = X0
      | sK2(X0) = sK23 ),
    inference(resolution,[],[f119,f105]) ).

fof(f119,plain,
    ! [X0] :
      ( r1(sK2(X0))
      | sK3(X0) = X0 ),
    inference(resolution,[],[f67,f63]) ).

fof(f143,plain,
    ! [X0] :
      ( r2(sK2(sK12(X0)),sK12(X0))
      | ~ sP0(sK12(X0)) ),
    inference(superposition,[],[f64,f135]) ).

fof(f135,plain,
    ! [X0] : sK12(X0) = sK1(sK12(X0)),
    inference(resolution,[],[f131,f108]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK1(X0) = X0 ),
    inference(subsumption_resolution,[],[f129,f65]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sP0(X0)
      | sK1(X0) = X0 ),
    inference(superposition,[],[f118,f121]) ).

fof(f121,plain,
    ! [X0] :
      ( sK3(X0) = X0
      | sK1(X0) = X0 ),
    inference(resolution,[],[f67,f65]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK3(X0))
      | sP0(X0) ),
    inference(resolution,[],[f66,f109]) ).

fof(f1085,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sP0(X0)
      | sK12(sK23) = X0 ),
    inference(superposition,[],[f118,f1062]) ).

fof(f1062,plain,
    ! [X0] :
      ( sK3(X0) = X0
      | sK12(sK23) = X0 ),
    inference(subsumption_resolution,[],[f1053,f67]) ).

fof(f1053,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK12(sK23) = X0
      | sK3(X0) = X0 ),
    inference(superposition,[],[f228,f392]) ).

fof(f392,plain,
    ! [X0] :
      ( sK12(sK2(X0)) = X0
      | sK3(X0) = X0 ),
    inference(resolution,[],[f315,f81]) ).

fof(f315,plain,
    ! [X0] :
      ( r2(sK2(X0),X0)
      | sK3(X0) = X0 ),
    inference(subsumption_resolution,[],[f306,f67]) ).

fof(f306,plain,
    ! [X0] :
      ( r2(sK2(X0),X0)
      | sK3(X0) = X0
      | ~ sP0(X0) ),
    inference(superposition,[],[f120,f65]) ).

fof(f85,plain,
    ! [X0,X1] : r2(X1,sK16(X0,X1)),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( r4(X0,X1,sK14(X0,X1))
      & r3(sK14(X0,X1),X0,sK13(X0,X1))
      & sK13(X0,X1) = sK15(X0,X1)
      & r4(X0,sK16(X0,X1),sK15(X0,X1))
      & r2(X1,sK16(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f21,f50,f49,f48,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r4(X0,X1,X3)
              & r3(X3,X0,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r4(X0,X5,X4)
                  & r2(X1,X5) ) ) )
     => ( ? [X3] :
            ( r4(X0,X1,X3)
            & r3(X3,X0,sK13(X0,X1)) )
        & ? [X4] :
            ( sK13(X0,X1) = X4
            & ? [X5] :
                ( r4(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,sK13(X0,X1)) )
     => ( r4(X0,X1,sK14(X0,X1))
        & r3(sK14(X0,X1),X0,sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK13(X0,X1) = X4
          & ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK13(X0,X1) = sK15(X0,X1)
        & ? [X5] :
            ( r4(X0,X5,sK15(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X0,X5,sK15(X0,X1))
          & r2(X1,X5) )
     => ( r4(X0,sK16(X0,X1),sK15(X0,X1))
        & r2(X1,sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f613,plain,
    ! [X0] : ~ r1(sK12(X0)),
    inference(forward_demodulation,[],[f605,f604]) ).

fof(f605,plain,
    ! [X0] : ~ r1(sK17(X0,sK23)),
    inference(resolution,[],[f602,f109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUN065+2 : TPTP v8.2.0. Released v7.3.0.
% 0.07/0.13  % Command    : run_vampire %s %d THM
% 0.11/0.34  % Computer : n006.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit   : 300
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Tue Jun 18 21:18:24 EDT 2024
% 0.11/0.34  % CPUTime    : 
% 0.11/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.11/0.36  Running first-order theorem proving
% 0.11/0.36  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42  % (26223)lrs-1011_37821:262144_bsr=unit_only:sil=2000:fde=none:plsq=on:plsqr=43543,131072:bce=on:rnwc=on:plsql=on:rp=on:nwc=10.0:newcnf=on:i=109:awrs=decay:awrsf=10:ep=R:mep=off:amm=sco_0 on theBenchmark for (2999ds/109Mi)
% 0.19/0.42  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42  % (26222)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=109:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on theBenchmark for (2999ds/109Mi)
% 0.19/0.42  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42  % (26225)lrs+1010_1:1_to=lpo:sil=2000:sos=on:fd=off:i=117:bd=off_0 on theBenchmark for (2999ds/117Mi)
% 0.19/0.42  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42  % (26224)ott-1011_16:1_sil=2000:sp=const_max:urr=on:lsd=20:st=3.0:i=117:ss=axioms:gsp=on:rp=on:sos=on:fd=off:aac=none_0 on theBenchmark for (2999ds/117Mi)
% 0.19/0.42  % (26223)Refutation not found, incomplete strategy% (26223)------------------------------
% 0.19/0.42  % (26223)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.42  % (26223)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.42  % (26223)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.42  
% 0.19/0.42  % (26223)Memory used [KB]: 1149
% 0.19/0.42  % (26223)Time elapsed: 0.003 s
% 0.19/0.42  % (26223)Instructions burned: 3 (million)
% 0.19/0.42  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42  % (26220)lrs+1011_8:1_sil=128000:tgt=ground:fde=unused:sp=frequency:nwc=5.0:lwlo=on:i=105338:awrs=converge:awrsf=1385:av=off_0 on theBenchmark for (2999ds/105338Mi)
% 0.19/0.42  % (26223)------------------------------
% 0.19/0.42  % (26223)------------------------------
% 0.19/0.43  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43  % (26219)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency:i=69040_0 on theBenchmark for (2999ds/69040Mi)
% 0.19/0.43  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43  % (26221)dis+1011_1:99_anc=none:fde=unused:plsqc=2:bsd=on:plsq=on:plsqr=109,504:sp=reverse_frequency:spb=intro:rp=on:alpa=random:s2a=on:i=257151:s2at=-1.0:aac=none:nm=16:rawr=on:sil=256000:acc=model_0 on theBenchmark for (2999ds/257151Mi)
% 0.19/0.47  % (26222)Instruction limit reached!
% 0.19/0.47  % (26222)------------------------------
% 0.19/0.47  % (26222)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47  % (26222)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47  % (26222)Termination reason: Time limit
% 0.19/0.47  % (26222)Termination phase: Saturation
% 0.19/0.47  
% 0.19/0.47  % (26222)Memory used [KB]: 1751
% 0.19/0.47  % (26222)Time elapsed: 0.047 s
% 0.19/0.47  % (26222)Instructions burned: 109 (million)
% 0.19/0.47  % (26219)First to succeed.
% 0.19/0.47  % (26219)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26218"
% 0.19/0.47  % (26225)Refutation not found, incomplete strategy% (26225)------------------------------
% 0.19/0.47  % (26225)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47  % (26225)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47  % (26225)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47  
% 0.19/0.47  % (26225)Memory used [KB]: 1300
% 0.19/0.47  % (26225)Time elapsed: 0.050 s
% 0.19/0.47  % (26225)Instructions burned: 102 (million)
% 0.19/0.47  % (26225)------------------------------
% 0.19/0.47  % (26225)------------------------------
% 0.19/0.47  % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.47  % (26219)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (26219)------------------------------
% 0.19/0.47  % (26219)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47  % (26219)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47  % (26219)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (26219)Memory used [KB]: 1520
% 0.19/0.47  % (26219)Time elapsed: 0.044 s
% 0.19/0.47  % (26219)Instructions burned: 72 (million)
% 0.19/0.47  % (26219)------------------------------
% 0.19/0.47  % (26219)------------------------------
% 0.19/0.47  % (26218)Success in time 0.102 s
%------------------------------------------------------------------------------