TSTP Solution File: NUN068+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.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 : Sun May  5 08:45:02 EDT 2024

% Result   : Theorem 0.16s 0.36s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   64 (   8 unt;   0 def)
%            Number of atoms       :  185 (  76 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  197 (  76   ~;  74   |;  42   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :  117 (  94   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f950,plain,
    $false,
    inference(subsumption_resolution,[],[f852,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',axiom_1) ).

fof(f852,plain,
    ~ r1(sK23),
    inference(superposition,[],[f131,f766]) ).

fof(f766,plain,
    ! [X0] : sK23 = X0,
    inference(subsumption_resolution,[],[f765,f729]) ).

fof(f729,plain,
    ! [X0] :
      ( ~ sP0(sK12(X0))
      | sK23 = X0 ),
    inference(resolution,[],[f697,f177]) ).

fof(f177,plain,
    ! [X0] :
      ( r2(sK23,sK12(X0))
      | ~ sP0(sK12(X0)) ),
    inference(forward_demodulation,[],[f175,f145]) ).

fof(f145,plain,
    ! [X0] : sK12(X0) = sK1(sK12(X0)),
    inference(resolution,[],[f143,f131]) ).

fof(f143,plain,
    ! [X0] :
      ( r1(X0)
      | sK1(X0) = X0 ),
    inference(subsumption_resolution,[],[f142,f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK1(X0) = 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(f26,plain,
    ! [X0] :
      ( ? [X2] :
          ( X0 = X2
          & ? [X3] :
              ( r2(X3,X2)
              & r1(X3) ) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f142,plain,
    ! [X0] :
      ( r1(X0)
      | sP0(X0)
      | sK1(X0) = X0 ),
    inference(superposition,[],[f66,f135]) ).

fof(f135,plain,
    ! [X0] :
      ( sK3(X0) = X0
      | sK1(X0) = X0 ),
    inference(resolution,[],[f65,f67]) ).

fof(f67,plain,
    ! [X0] :
      ( sP0(X0)
      | sK3(X0) = 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(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',nonzerosnononesexist) ).

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

fof(f175,plain,
    ! [X0] :
      ( r2(sK23,sK1(sK12(X0)))
      | ~ sP0(sK12(X0)) ),
    inference(superposition,[],[f64,f172]) ).

fof(f172,plain,
    ! [X0] : sK23 = sK2(sK12(X0)),
    inference(resolution,[],[f169,f131]) ).

fof(f169,plain,
    ! [X0] :
      ( r1(X0)
      | sK2(X0) = sK23 ),
    inference(subsumption_resolution,[],[f166,f118]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK2(X0) = sK23 ),
    inference(resolution,[],[f105,f63]) ).

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

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

fof(f166,plain,
    ! [X0] :
      ( r1(X0)
      | sP0(X0)
      | sK2(X0) = sK23 ),
    inference(superposition,[],[f66,f141]) ).

fof(f141,plain,
    ! [X0] :
      ( sK3(X0) = X0
      | sK2(X0) = sK23 ),
    inference(resolution,[],[f118,f67]) ).

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

fof(f697,plain,
    ! [X0,X1] :
      ( ~ r2(X0,sK12(X1))
      | X0 = X1 ),
    inference(resolution,[],[f110,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(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',axiom_2) ).

fof(f110,plain,
    ! [X3,X0,X1] :
      ( ~ r2(X1,X3)
      | X0 = X1
      | ~ 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',axiom_3a) ).

fof(f765,plain,
    ! [X0] :
      ( sP0(sK12(X0))
      | sK23 = X0 ),
    inference(subsumption_resolution,[],[f760,f131]) ).

fof(f760,plain,
    ! [X0] :
      ( r1(sK12(X0))
      | sP0(sK12(X0))
      | sK23 = X0 ),
    inference(superposition,[],[f66,f727]) ).

fof(f727,plain,
    ! [X0] :
      ( sK12(X0) = sK3(sK12(X0))
      | sK23 = X0 ),
    inference(resolution,[],[f697,f576]) ).

fof(f576,plain,
    ! [X0] :
      ( r2(sK23,sK12(X0))
      | sK12(X0) = sK3(sK12(X0)) ),
    inference(forward_demodulation,[],[f564,f172]) ).

fof(f564,plain,
    ! [X0] :
      ( r2(sK2(sK12(X0)),sK12(X0))
      | sK12(X0) = sK3(sK12(X0)) ),
    inference(superposition,[],[f530,f145]) ).

fof(f530,plain,
    ! [X0] :
      ( r2(sK2(X0),sK1(X0))
      | sK3(X0) = X0 ),
    inference(superposition,[],[f108,f429]) ).

fof(f429,plain,
    ! [X0] :
      ( sK1(X0) = sK12(sK2(X0))
      | sK3(X0) = X0 ),
    inference(resolution,[],[f215,f67]) ).

fof(f215,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK1(X0) = sK12(sK2(X0)) ),
    inference(resolution,[],[f81,f64]) ).

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

fof(f131,plain,
    ! [X0] : ~ r1(sK12(X0)),
    inference(resolution,[],[f109,f108]) ).

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',axiom_7a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% 0.10/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n019.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 18:53:53 EDT 2024
% 0.16/0.32  % CPUTime    : 
% 0.16/0.32  % (413)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (416)WARNING: value z3 for option sas not known
% 0.16/0.33  % (420)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.33  % (416)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.34  % (417)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34  % (414)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.34  % (418)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.34  % (415)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.34  % (419)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.34  TRYING [1]
% 0.16/0.34  TRYING [2]
% 0.16/0.34  TRYING [3]
% 0.16/0.34  TRYING [1]
% 0.16/0.34  TRYING [4]
% 0.16/0.34  TRYING [2]
% 0.16/0.35  TRYING [3]
% 0.16/0.35  TRYING [5]
% 0.16/0.36  % (416)First to succeed.
% 0.16/0.36  % (420)Also succeeded, but the first one will report.
% 0.16/0.36  % (416)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-413"
% 0.16/0.36  % (416)Refutation found. Thanks to Tanya!
% 0.16/0.36  % SZS status Theorem for theBenchmark
% 0.16/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.36  % (416)------------------------------
% 0.16/0.36  % (416)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.36  % (416)Termination reason: Refutation
% 0.16/0.36  
% 0.16/0.36  % (416)Memory used [KB]: 1115
% 0.16/0.36  % (416)Time elapsed: 0.025 s
% 0.16/0.36  % (416)Instructions burned: 43 (million)
% 0.16/0.36  % (413)Success in time 0.04 s
%------------------------------------------------------------------------------