TSTP Solution File: NUN086+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 May  1 03:36:30 EDT 2024

% Result   : Theorem 0.60s 0.79s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   93 (  35 unt;   0 def)
%            Number of atoms       :  298 (  90 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  282 (  77   ~;  48   |; 140   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   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   :  245 ( 158   !;  87   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f245,plain,
    $false,
    inference(subsumption_resolution,[],[f244,f100]) ).

fof(f100,plain,
    r1(sK8),
    inference(equality_resolution,[],[f68]) ).

fof(f68,plain,
    ! [X1] :
      ( r1(X1)
      | sK8 != X1 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X1] :
      ( ( sK8 = X1
        & r1(X1) )
      | ( sK8 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f1,f36]) ).

fof(f36,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 = X1
          & r1(X1) )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( sK8 = X1
          & r1(X1) )
        | ( sK8 != X1
          & ~ r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( X0 = X1
        & r1(X1) )
      | ( X0 != X1
        & ~ r1(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_1) ).

fof(f244,plain,
    ~ r1(sK8),
    inference(duplicate_literal_removal,[],[f241]) ).

fof(f241,plain,
    ( ~ r1(sK8)
    | ~ r1(sK8) ),
    inference(superposition,[],[f156,f230]) ).

fof(f230,plain,
    sK8 = sK11(sK8,sK8),
    inference(superposition,[],[f212,f196]) ).

fof(f196,plain,
    ! [X0] : sK14(X0,sK8) = X0,
    inference(resolution,[],[f184,f132]) ).

fof(f132,plain,
    ! [X0] : r3(X0,sK8,X0),
    inference(backward_demodulation,[],[f108,f119]) ).

fof(f119,plain,
    ! [X0] : sK7(X0) = sK8,
    inference(resolution,[],[f69,f64]) ).

fof(f64,plain,
    ! [X0] : r1(sK7(X0)),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( sK6(X0) = X0
      & r3(X0,sK7(X0),sK6(X0))
      & r1(sK7(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f18,f34,f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) ) )
     => ( sK6(X0) = X0
        & ? [X2] :
            ( r3(X0,X2,sK6(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK6(X0))
          & r1(X2) )
     => ( r3(X0,sK7(X0),sK6(X0))
        & r1(sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,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/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_4a) ).

fof(f69,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK8 = X1 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f108,plain,
    ! [X0] : r3(X0,sK7(X0),X0),
    inference(forward_demodulation,[],[f65,f66]) ).

fof(f66,plain,
    ! [X0] : sK6(X0) = X0,
    inference(cnf_transformation,[],[f35]) ).

fof(f65,plain,
    ! [X0] : r3(X0,sK7(X0),sK6(X0)),
    inference(cnf_transformation,[],[f35]) ).

fof(f184,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X0,X1,X3)
      | sK14(X0,X1) = X3 ),
    inference(backward_demodulation,[],[f92,f179]) ).

fof(f179,plain,
    ! [X0,X1] : sK14(X0,X1) = sK19(X0,X1),
    inference(resolution,[],[f92,f81]) ).

fof(f81,plain,
    ! [X0,X1] : r3(X0,X1,sK14(X0,X1)),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK14(X0,X1))
      & r2(sK14(X0,X1),sK13(X0,X1))
      & sK13(X0,X1) = sK15(X0,X1)
      & r3(X0,sK16(X0,X1),sK15(X0,X1))
      & r2(X1,sK16(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f21,f46,f45,f44,f43]) ).

fof(f43,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,sK13(X0,X1)) )
        & ? [X4] :
            ( sK13(X0,X1) = X4
            & ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,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(f45,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK13(X0,X1) = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK13(X0,X1) = sK15(X0,X1)
        & ? [X5] :
            ( r3(X0,X5,sK15(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK15(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK16(X0,X1),sK15(X0,X1))
        & r2(X1,sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,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/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_1a) ).

fof(f92,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X0,X1,X3)
      | sK19(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X3] :
      ( ( sK19(X0,X1) = X3
        & r3(X0,X1,X3) )
      | ( sK19(X0,X1) != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f24,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r3(X0,X1,X3) )
          | ( X2 != X3
            & ~ r3(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK19(X0,X1) = X3
            & r3(X0,X1,X3) )
          | ( sK19(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/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_3) ).

fof(f212,plain,
    ! [X0] : sK11(X0,sK8) = sK14(sK8,X0),
    inference(resolution,[],[f194,f184]) ).

fof(f194,plain,
    ! [X0] : r3(sK8,X0,sK11(X0,sK8)),
    inference(superposition,[],[f95,f190]) ).

fof(f190,plain,
    ! [X0] : sK8 = sK10(X0,sK8),
    inference(resolution,[],[f176,f125]) ).

fof(f125,plain,
    ! [X0] : r4(X0,sK8,sK8),
    inference(backward_demodulation,[],[f123,f118]) ).

fof(f118,plain,
    ! [X0] : sK5(X0) = sK8,
    inference(resolution,[],[f69,f60]) ).

fof(f60,plain,
    ! [X0] : r1(sK5(X0)),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( sK3(X0) = sK4(X0)
      & r1(sK4(X0))
      & r4(X0,sK5(X0),sK3(X0))
      & r1(sK5(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f31,f30,f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( X1 = X2
              & r1(X2) )
          & ? [X3] :
              ( r4(X0,X3,X1)
              & r1(X3) ) )
     => ( ? [X2] :
            ( sK3(X0) = X2
            & r1(X2) )
        & ? [X3] :
            ( r4(X0,X3,sK3(X0))
            & r1(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0] :
      ( ? [X2] :
          ( sK3(X0) = X2
          & r1(X2) )
     => ( sK3(X0) = sK4(X0)
        & r1(sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0] :
      ( ? [X3] :
          ( r4(X0,X3,sK3(X0))
          & r1(X3) )
     => ( r4(X0,sK5(X0),sK3(X0))
        & r1(sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f9,axiom,
    ! [X32] :
    ? [X33] :
      ( ? [X35] :
          ( X33 = X35
          & r1(X35) )
      & ? [X34] :
          ( r4(X32,X34,X33)
          & r1(X34) ) ),
    file('/export/starexec/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_5a) ).

fof(f123,plain,
    ! [X0] : r4(X0,sK5(X0),sK8),
    inference(backward_demodulation,[],[f94,f117]) ).

fof(f117,plain,
    ! [X0] : sK4(X0) = sK8,
    inference(resolution,[],[f69,f62]) ).

fof(f62,plain,
    ! [X0] : r1(sK4(X0)),
    inference(cnf_transformation,[],[f32]) ).

fof(f94,plain,
    ! [X0] : r4(X0,sK5(X0),sK4(X0)),
    inference(definition_unfolding,[],[f61,f63]) ).

fof(f63,plain,
    ! [X0] : sK3(X0) = sK4(X0),
    inference(cnf_transformation,[],[f32]) ).

fof(f61,plain,
    ! [X0] : r4(X0,sK5(X0),sK3(X0)),
    inference(cnf_transformation,[],[f32]) ).

fof(f176,plain,
    ! [X3,X0,X1] :
      ( ~ r4(X0,X1,X3)
      | sK10(X0,X1) = X3 ),
    inference(backward_demodulation,[],[f88,f172]) ).

fof(f172,plain,
    ! [X0,X1] : sK10(X0,X1) = sK18(X0,X1),
    inference(resolution,[],[f88,f76]) ).

fof(f76,plain,
    ! [X0,X1] : r4(X0,X1,sK10(X0,X1)),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( r4(X0,X1,sK10(X0,X1))
      & r3(sK10(X0,X1),X0,sK9(X0,X1))
      & sK9(X0,X1) = sK11(X0,X1)
      & r4(X0,sK12(X0,X1),sK11(X0,X1))
      & r2(X1,sK12(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f20,f41,f40,f39,f38]) ).

fof(f38,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,sK9(X0,X1)) )
        & ? [X4] :
            ( sK9(X0,X1) = X4
            & ? [X5] :
                ( r4(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,sK9(X0,X1)) )
     => ( r4(X0,X1,sK10(X0,X1))
        & r3(sK10(X0,X1),X0,sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK9(X0,X1) = X4
          & ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK9(X0,X1) = sK11(X0,X1)
        & ? [X5] :
            ( r4(X0,X5,sK11(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X0,X5,sK11(X0,X1))
          & r2(X1,X5) )
     => ( r4(X0,sK12(X0,X1),sK11(X0,X1))
        & r2(X1,sK12(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,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/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_2a) ).

fof(f88,plain,
    ! [X3,X0,X1] :
      ( ~ r4(X0,X1,X3)
      | sK18(X0,X1) = X3 ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X3] :
      ( ( sK18(X0,X1) = X3
        & r4(X0,X1,X3) )
      | ( sK18(X0,X1) != X3
        & ~ r4(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f23,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r4(X0,X1,X3) )
          | ( X2 != X3
            & ~ r4(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK18(X0,X1) = X3
            & r4(X0,X1,X3) )
          | ( sK18(X0,X1) != X3
            & ~ r4(X0,X1,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r4(X0,X1,X3) )
      | ( X2 != X3
        & ~ r4(X0,X1,X3) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X9,X10] :
    ? [X11] :
    ! [X12] :
      ( ( X11 = X12
        & r4(X9,X10,X12) )
      | ( X11 != X12
        & ~ r4(X9,X10,X12) ) ),
    file('/export/starexec/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_4) ).

fof(f95,plain,
    ! [X0,X1] : r3(sK10(X0,X1),X0,sK11(X0,X1)),
    inference(definition_unfolding,[],[f75,f74]) ).

fof(f74,plain,
    ! [X0,X1] : sK9(X0,X1) = sK11(X0,X1),
    inference(cnf_transformation,[],[f42]) ).

fof(f75,plain,
    ! [X0,X1] : r3(sK10(X0,X1),X0,sK9(X0,X1)),
    inference(cnf_transformation,[],[f42]) ).

fof(f156,plain,
    ! [X0] :
      ( ~ r1(sK11(X0,sK8))
      | ~ r1(X0) ),
    inference(resolution,[],[f146,f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ~ r4(X0,sK17(sK8),X1)
      | ~ r1(X0)
      | ~ r1(X1) ),
    inference(resolution,[],[f103,f109]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( ~ r2(sK8,X1)
      | ~ r1(X0)
      | ~ r4(X0,X1,X2)
      | ~ r1(X2) ),
    inference(resolution,[],[f100,f97]) ).

fof(f97,plain,
    ! [X2,X3,X1,X4] :
      ( ~ r1(X4)
      | ~ r4(X3,X2,X1)
      | ~ r1(X3)
      | ~ r2(X4,X2)
      | ~ r1(X1) ),
    inference(equality_resolution,[],[f54]) ).

fof(f54,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X0 != X1
      | ~ r1(X1)
      | ~ r4(X3,X2,X0)
      | ~ r1(X3)
      | ~ r2(X4,X2)
      | ~ r1(X4) ),
    inference(cnf_transformation,[],[f25]) ).

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

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

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

fof(f12,conjecture,
    ? [X38] :
      ( ? [X16] :
          ( X16 = X38
          & r1(X16) )
      & ? [X21] :
          ( ? [X15] :
              ( r4(X15,X21,X38)
              & r1(X15) )
          & ? [X22] :
              ( r2(X22,X21)
              & r1(X22) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',zerotimesoneeqzero) ).

fof(f103,plain,
    ! [X0] : r2(X0,sK17(X0)),
    inference(equality_resolution,[],[f83]) ).

fof(f83,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK17(X0) != X2 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X2] :
      ( ( sK17(X0) = X2
        & r2(X0,X2) )
      | ( sK17(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f22,f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK17(X0) = X2
            & r2(X0,X2) )
          | ( sK17(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,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/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391',axiom_2) ).

fof(f146,plain,
    ! [X0,X1] : r4(X0,sK17(X1),sK11(X0,X1)),
    inference(backward_demodulation,[],[f73,f143]) ).

fof(f143,plain,
    ! [X0,X1] : sK17(X0) = sK12(X1,X0),
    inference(resolution,[],[f84,f72]) ).

fof(f72,plain,
    ! [X0,X1] : r2(X1,sK12(X0,X1)),
    inference(cnf_transformation,[],[f42]) ).

fof(f84,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK17(X0) = X2 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f73,plain,
    ! [X0,X1] : r4(X0,sK12(X0,X1),sK11(X0,X1)),
    inference(cnf_transformation,[],[f42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem    : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.09/0.30  % Computer : n005.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Tue Apr 30 17:37:41 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.09/0.30  This is a FOF_THM_RFO_SEQ problem
% 0.09/0.31  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.4K2QBvckzo/Vampire---4.8_30391
% 0.60/0.78  % (30508)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.60/0.78  % (30510)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.60/0.78  % (30507)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.60/0.78  % (30505)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.60/0.78  % (30509)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.60/0.79  % (30511)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.60/0.79  % (30506)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.60/0.79  % (30512)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.60/0.79  % (30509)Refutation not found, incomplete strategy% (30509)------------------------------
% 0.60/0.79  % (30509)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.79  % (30509)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79  
% 0.60/0.79  % (30509)Memory used [KB]: 1059
% 0.60/0.79  % (30510)Refutation not found, incomplete strategy% (30510)------------------------------
% 0.60/0.79  % (30510)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.79  % (30509)Time elapsed: 0.003 s
% 0.60/0.79  % (30509)Instructions burned: 4 (million)
% 0.60/0.79  % (30509)------------------------------
% 0.60/0.79  % (30509)------------------------------
% 0.60/0.79  % (30510)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79  
% 0.60/0.79  % (30510)Memory used [KB]: 1056
% 0.60/0.79  % (30510)Time elapsed: 0.003 s
% 0.60/0.79  % (30510)Instructions burned: 4 (million)
% 0.60/0.79  % (30510)------------------------------
% 0.60/0.79  % (30510)------------------------------
% 0.60/0.79  % (30505)Refutation not found, incomplete strategy% (30505)------------------------------
% 0.60/0.79  % (30505)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.79  % (30505)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79  
% 0.60/0.79  % (30505)Memory used [KB]: 1059
% 0.60/0.79  % (30505)Time elapsed: 0.004 s
% 0.60/0.79  % (30505)Instructions burned: 5 (million)
% 0.60/0.79  % (30505)------------------------------
% 0.60/0.79  % (30505)------------------------------
% 0.60/0.79  % (30508)Refutation not found, incomplete strategy% (30508)------------------------------
% 0.60/0.79  % (30508)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.79  % (30508)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79  
% 0.60/0.79  % (30508)Memory used [KB]: 1063
% 0.60/0.79  % (30508)Time elapsed: 0.004 s
% 0.60/0.79  % (30508)Instructions burned: 4 (million)
% 0.60/0.79  % (30508)------------------------------
% 0.60/0.79  % (30508)------------------------------
% 0.60/0.79  % (30512)Refutation not found, incomplete strategy% (30512)------------------------------
% 0.60/0.79  % (30512)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.79  % (30512)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79  
% 0.60/0.79  % (30512)Memory used [KB]: 1059
% 0.60/0.79  % (30512)Time elapsed: 0.003 s
% 0.60/0.79  % (30512)Instructions burned: 4 (million)
% 0.60/0.79  % (30512)------------------------------
% 0.60/0.79  % (30512)------------------------------
% 0.60/0.79  % (30513)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.60/0.79  % (30507)First to succeed.
% 0.60/0.79  % (30514)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.60/0.79  % (30515)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.60/0.79  % (30516)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.60/0.79  % (30517)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.60/0.79  % (30507)Refutation found. Thanks to Tanya!
% 0.60/0.79  % SZS status Theorem for Vampire---4
% 0.60/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.79  % (30507)------------------------------
% 0.60/0.79  % (30507)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.79  % (30507)Termination reason: Refutation
% 0.60/0.79  
% 0.60/0.79  % (30507)Memory used [KB]: 1154
% 0.60/0.79  % (30507)Time elapsed: 0.009 s
% 0.60/0.79  % (30507)Instructions burned: 13 (million)
% 0.60/0.79  % (30507)------------------------------
% 0.60/0.79  % (30507)------------------------------
% 0.60/0.79  % (30500)Success in time 0.483 s
% 0.60/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------