TSTP Solution File: NUN066+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN066+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 : n023.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 14:40:19 EDT 2024

% Result   : Theorem 0.22s 0.41s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   77 (  13 unt;   0 def)
%            Number of atoms       :  221 (  89 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  238 (  94   ~;  85   |;  53   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  163 ( 131   !;  32   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1249,plain,
    $false,
    inference(resolution,[],[f1209,f1187]) ).

fof(f1187,plain,
    ! [X2,X1] : r2(X2,X1),
    inference(superposition,[],[f943,f1169]) ).

fof(f1169,plain,
    ! [X0,X1] : X0 = X1,
    inference(resolution,[],[f1128,f943]) ).

fof(f1128,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X2,sK13(X1))
      | X0 = X2 ),
    inference(resolution,[],[f112,f943]) ).

fof(f112,plain,
    ! [X3,X0,X1] :
      ( ~ r2(X1,X3)
      | ~ r2(X0,X3)
      | X0 = X1 ),
    inference(equality_resolution,[],[f86]) ).

fof(f86,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(f943,plain,
    ! [X0,X1] : r2(X0,sK13(X1)),
    inference(superposition,[],[f110,f916]) ).

fof(f916,plain,
    ! [X0,X1] : sK13(X0) = sK13(X1),
    inference(superposition,[],[f903,f903]) ).

fof(f903,plain,
    ! [X0] : sK13(X0) = sK13(sK13(sK24)),
    inference(resolution,[],[f899,f110]) ).

fof(f899,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK13(X0))
      | sK13(X0) = sK13(sK13(sK24)) ),
    inference(duplicate_literal_removal,[],[f887]) ).

fof(f887,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK13(X0))
      | sK13(X0) = sK13(sK13(sK24))
      | sK13(X0) = sK13(sK13(sK24)) ),
    inference(superposition,[],[f816,f818]) ).

fof(f818,plain,
    ! [X0] :
      ( sK13(X0) = sK4(sK13(X0))
      | sK13(X0) = sK13(sK13(sK24)) ),
    inference(backward_demodulation,[],[f338,f802]) ).

fof(f802,plain,
    ! [X0] : sK2(sK13(X0)) = sK13(sK24),
    inference(resolution,[],[f798,f110]) ).

fof(f798,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK13(X0))
      | sK2(sK13(X0)) = sK13(sK24) ),
    inference(duplicate_literal_removal,[],[f786]) ).

fof(f786,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK13(X0))
      | sK2(sK13(X0)) = sK13(sK24)
      | sK2(sK13(X0)) = sK13(sK24) ),
    inference(superposition,[],[f317,f319]) ).

fof(f319,plain,
    ! [X0] :
      ( sK13(X0) = sK4(sK13(X0))
      | sK2(sK13(X0)) = sK13(sK24) ),
    inference(resolution,[],[f294,f69]) ).

fof(f69,plain,
    ! [X0] :
      ( sP0(X0)
      | sK4(X0) = X0 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ( sK4(X0) = X0
        & r1(sK4(X0)) )
      | sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & r1(X1) )
     => ( sK4(X0) = X0
        & r1(sK4(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)
              & ? [X4] :
                  ( r2(X4,X3)
                  & r1(X4) ) ) )
      | ~ 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)
              & ? [X4] :
                  ( r2(X4,X3)
                  & r1(X4) ) ) ) ),
    inference(ennf_transformation,[],[f14]) ).

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

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

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

fof(f294,plain,
    ! [X0] :
      ( ~ sP0(sK13(X0))
      | sK2(sK13(X0)) = sK13(sK24) ),
    inference(resolution,[],[f83,f188]) ).

fof(f188,plain,
    ! [X0] :
      ( r2(sK24,sK2(sK13(X0)))
      | ~ sP0(sK13(X0)) ),
    inference(superposition,[],[f65,f180]) ).

fof(f180,plain,
    ! [X0] : sK24 = sK3(sK13(X0)),
    inference(resolution,[],[f178,f110]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK3(X0) = sK24 ),
    inference(duplicate_literal_removal,[],[f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK3(X0) = sK24
      | sK3(X0) = sK24 ),
    inference(superposition,[],[f159,f161]) ).

fof(f161,plain,
    ! [X0] :
      ( sK4(X0) = X0
      | sK3(X0) = sK24 ),
    inference(resolution,[],[f123,f69]) ).

fof(f123,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK3(X0) = sK24 ),
    inference(resolution,[],[f107,f64]) ).

fof(f64,plain,
    ! [X0] :
      ( r1(sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ( sK1(X0) = X0
        & r2(sK2(X0),sK1(X0))
        & r2(sK3(X0),sK2(X0))
        & r1(sK3(X0)) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f29,f32,f31,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r2(X2,X1)
              & ? [X3] :
                  ( r2(X3,X2)
                  & r1(X3) ) ) )
     => ( sK1(X0) = X0
        & ? [X2] :
            ( r2(X2,sK1(X0))
            & ? [X3] :
                ( r2(X3,X2)
                & r1(X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0] :
      ( ? [X2] :
          ( r2(X2,sK1(X0))
          & ? [X3] :
              ( r2(X3,X2)
              & r1(X3) ) )
     => ( r2(sK2(X0),sK1(X0))
        & ? [X3] :
            ( r2(X3,sK2(X0))
            & r1(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0] :
      ( ? [X3] :
          ( r2(X3,sK2(X0))
          & r1(X3) )
     => ( r2(sK3(X0),sK2(X0))
        & r1(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r2(X2,X1)
              & ? [X3] :
                  ( r2(X3,X2)
                  & r1(X3) ) ) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ? [X2] :
          ( X0 = X2
          & ? [X3] :
              ( r2(X3,X2)
              & ? [X4] :
                  ( r2(X4,X3)
                  & r1(X4) ) ) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f107,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK24 = X1 ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X1] :
      ( ( sK24 = X1
        & r1(X1) )
      | ( sK24 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1,f62]) ).

fof(f62,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 = X1
          & r1(X1) )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( sK24 = X1
          & r1(X1) )
        | ( sK24 != 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(f159,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK4(X0))
      | sK3(X0) = sK24 ),
    inference(resolution,[],[f123,f137]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( sP0(X1)
      | ~ r2(X0,sK4(X1)) ),
    inference(resolution,[],[f111,f68]) ).

fof(f68,plain,
    ! [X0] :
      ( r1(sK4(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f111,plain,
    ! [X2,X0] :
      ( ~ r1(X2)
      | ~ r2(X0,X2) ),
    inference(equality_resolution,[],[f85]) ).

fof(f85,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) ).

fof(f65,plain,
    ! [X0] :
      ( r2(sK3(X0),sK2(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f83,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK13(X0) = X2 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X2] :
      ( ( sK13(X0) = X2
        & r2(X0,X2) )
      | ( sK13(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK13(X0) = X2
            & r2(X0,X2) )
          | ( sK13(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(f317,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK4(sK13(X0)))
      | sK2(sK13(X0)) = sK13(sK24) ),
    inference(resolution,[],[f294,f137]) ).

fof(f338,plain,
    ! [X0] :
      ( sK13(X0) = sK13(sK2(sK13(X0)))
      | sK13(X0) = sK4(sK13(X0)) ),
    inference(resolution,[],[f291,f69]) ).

fof(f291,plain,
    ! [X0] :
      ( ~ sP0(sK13(X0))
      | sK13(X0) = sK13(sK2(sK13(X0))) ),
    inference(resolution,[],[f83,f216]) ).

fof(f216,plain,
    ! [X0] :
      ( r2(sK2(sK13(X0)),sK13(X0))
      | ~ sP0(sK13(X0)) ),
    inference(superposition,[],[f66,f145]) ).

fof(f145,plain,
    ! [X0] : sK13(X0) = sK1(sK13(X0)),
    inference(resolution,[],[f144,f110]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK1(X0) = X0 ),
    inference(duplicate_literal_removal,[],[f143]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | sK1(X0) = X0
      | sK1(X0) = X0 ),
    inference(superposition,[],[f139,f141]) ).

fof(f141,plain,
    ! [X0] :
      ( sK4(X0) = X0
      | sK1(X0) = X0 ),
    inference(resolution,[],[f67,f69]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | sK1(X0) = X0 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK4(X0))
      | sK1(X0) = X0 ),
    inference(resolution,[],[f67,f137]) ).

fof(f66,plain,
    ! [X0] :
      ( r2(sK2(X0),sK1(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f816,plain,
    ! [X0,X1] :
      ( ~ r2(X1,sK4(sK13(X0)))
      | sK13(X0) = sK13(sK13(sK24)) ),
    inference(backward_demodulation,[],[f336,f802]) ).

fof(f336,plain,
    ! [X0,X1] :
      ( sK13(X0) = sK13(sK2(sK13(X0)))
      | ~ r2(X1,sK4(sK13(X0))) ),
    inference(resolution,[],[f291,f137]) ).

fof(f110,plain,
    ! [X0] : r2(X0,sK13(X0)),
    inference(equality_resolution,[],[f82]) ).

fof(f82,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK13(X0) != X2 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f1209,plain,
    ! [X0,X1] : ~ r2(X1,X0),
    inference(superposition,[],[f138,f1169]) ).

fof(f138,plain,
    ! [X0] : ~ r2(X0,sK24),
    inference(resolution,[],[f111,f118]) ).

fof(f118,plain,
    r1(sK24),
    inference(equality_resolution,[],[f106]) ).

fof(f106,plain,
    ! [X1] :
      ( r1(X1)
      | sK24 != X1 ),
    inference(cnf_transformation,[],[f63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n023.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 02:45:10 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (15452)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (15456)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (15455)WARNING: value z3 for option sas not known
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  % (15453)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (15457)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)
% 0.14/0.37  % (15455)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)
% 0.14/0.37  % (15459)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)
% 0.14/0.37  % (15458)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)
% 0.14/0.37  % (15454)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.39  TRYING [5]
% 0.22/0.39  TRYING [3]
% 0.22/0.40  TRYING [6]
% 0.22/0.41  % (15458)First to succeed.
% 0.22/0.41  % (15458)Refutation found. Thanks to Tanya!
% 0.22/0.41  % SZS status Theorem for theBenchmark
% 0.22/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41  % (15458)------------------------------
% 0.22/0.41  % (15458)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41  % (15458)Termination reason: Refutation
% 0.22/0.41  
% 0.22/0.41  % (15458)Memory used [KB]: 1108
% 0.22/0.41  % (15458)Time elapsed: 0.036 s
% 0.22/0.41  % (15458)Instructions burned: 60 (million)
% 0.22/0.41  % (15458)------------------------------
% 0.22/0.41  % (15458)------------------------------
% 0.22/0.41  % (15452)Success in time 0.053 s
%------------------------------------------------------------------------------