TSTP Solution File: NUM460+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM460+2 : TPTP v8.1.2. Released v4.0.0.
% 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 08:28:29 EDT 2024

% Result   : Theorem 2.37s 0.73s
% Output   : Refutation 2.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   41 (  12 unt;   0 def)
%            Number of atoms       :  141 (  45 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  148 (  48   ~;  36   |;  56   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   55 (  38   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6266,plain,
    $false,
    inference(resolution,[],[f6265,f74]) ).

fof(f74,plain,
    aNaturalNumber0(sK0),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ( ~ sdtlseqdt0(xm,xl)
    & ! [X0] :
        ( xl != sdtpldt0(xm,X0)
        | ~ aNaturalNumber0(X0) )
    & sdtlseqdt0(xn,xl)
    & xl = sdtpldt0(xn,sK0)
    & aNaturalNumber0(sK0)
    & sdtlseqdt0(xm,xn)
    & xn = sdtpldt0(xm,sK1)
    & aNaturalNumber0(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f61,f63,f62]) ).

fof(f62,plain,
    ( ? [X1] :
        ( xl = sdtpldt0(xn,X1)
        & aNaturalNumber0(X1) )
   => ( xl = sdtpldt0(xn,sK0)
      & aNaturalNumber0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ( ? [X2] :
        ( xn = sdtpldt0(xm,X2)
        & aNaturalNumber0(X2) )
   => ( xn = sdtpldt0(xm,sK1)
      & aNaturalNumber0(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ( ~ sdtlseqdt0(xm,xl)
    & ! [X0] :
        ( xl != sdtpldt0(xm,X0)
        | ~ aNaturalNumber0(X0) )
    & sdtlseqdt0(xn,xl)
    & ? [X1] :
        ( xl = sdtpldt0(xn,X1)
        & aNaturalNumber0(X1) )
    & sdtlseqdt0(xm,xn)
    & ? [X2] :
        ( xn = sdtpldt0(xm,X2)
        & aNaturalNumber0(X2) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ( ~ sdtlseqdt0(xm,xl)
    & ! [X2] :
        ( xl != sdtpldt0(xm,X2)
        | ~ aNaturalNumber0(X2) )
    & sdtlseqdt0(xn,xl)
    & ? [X0] :
        ( xl = sdtpldt0(xn,X0)
        & aNaturalNumber0(X0) )
    & sdtlseqdt0(xm,xn)
    & ? [X1] :
        ( xn = sdtpldt0(xm,X1)
        & aNaturalNumber0(X1) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ( ~ sdtlseqdt0(xm,xl)
    & ! [X2] :
        ( xl != sdtpldt0(xm,X2)
        | ~ aNaturalNumber0(X2) )
    & sdtlseqdt0(xn,xl)
    & ? [X0] :
        ( xl = sdtpldt0(xn,X0)
        & aNaturalNumber0(X0) )
    & sdtlseqdt0(xm,xn)
    & ? [X1] :
        ( xn = sdtpldt0(xm,X1)
        & aNaturalNumber0(X1) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ~ ( ( sdtlseqdt0(xn,xl)
        & ? [X0] :
            ( xl = sdtpldt0(xn,X0)
            & aNaturalNumber0(X0) )
        & sdtlseqdt0(xm,xn)
        & ? [X1] :
            ( xn = sdtpldt0(xm,X1)
            & aNaturalNumber0(X1) ) )
     => ( sdtlseqdt0(xm,xl)
        | ? [X2] :
            ( xl = sdtpldt0(xm,X2)
            & aNaturalNumber0(X2) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ( ( sdtlseqdt0(xn,xl)
        & ? [X0] :
            ( xl = sdtpldt0(xn,X0)
            & aNaturalNumber0(X0) )
        & sdtlseqdt0(xm,xn)
        & ? [X0] :
            ( xn = sdtpldt0(xm,X0)
            & aNaturalNumber0(X0) ) )
     => ( sdtlseqdt0(xm,xl)
        | ? [X0] :
            ( xl = sdtpldt0(xm,X0)
            & aNaturalNumber0(X0) ) ) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ( ( sdtlseqdt0(xn,xl)
      & ? [X0] :
          ( xl = sdtpldt0(xn,X0)
          & aNaturalNumber0(X0) )
      & sdtlseqdt0(xm,xn)
      & ? [X0] :
          ( xn = sdtpldt0(xm,X0)
          & aNaturalNumber0(X0) ) )
   => ( sdtlseqdt0(xm,xl)
      | ? [X0] :
          ( xl = sdtpldt0(xm,X0)
          & aNaturalNumber0(X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f6265,plain,
    ~ aNaturalNumber0(sK0),
    inference(resolution,[],[f6264,f71]) ).

fof(f71,plain,
    aNaturalNumber0(sK1),
    inference(cnf_transformation,[],[f64]) ).

fof(f6264,plain,
    ( ~ aNaturalNumber0(sK1)
    | ~ aNaturalNumber0(sK0) ),
    inference(resolution,[],[f6263,f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(f6263,plain,
    ~ aNaturalNumber0(sdtpldt0(sK0,sK1)),
    inference(trivial_inequality_removal,[],[f6254]) ).

fof(f6254,plain,
    ( xl != xl
    | ~ aNaturalNumber0(sdtpldt0(sK0,sK1)) ),
    inference(superposition,[],[f77,f6002]) ).

fof(f6002,plain,
    xl = sdtpldt0(xm,sdtpldt0(sK0,sK1)),
    inference(forward_demodulation,[],[f6001,f75]) ).

fof(f75,plain,
    xl = sdtpldt0(xn,sK0),
    inference(cnf_transformation,[],[f64]) ).

fof(f6001,plain,
    sdtpldt0(xn,sK0) = sdtpldt0(xm,sdtpldt0(sK0,sK1)),
    inference(forward_demodulation,[],[f5987,f303]) ).

fof(f303,plain,
    sdtpldt0(sK1,sK0) = sdtpldt0(sK0,sK1),
    inference(resolution,[],[f253,f71]) ).

fof(f253,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtpldt0(X0,sK0) = sdtpldt0(sK0,X0) ),
    inference(resolution,[],[f97,f74]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(f5987,plain,
    sdtpldt0(xn,sK0) = sdtpldt0(xm,sdtpldt0(sK1,sK0)),
    inference(resolution,[],[f3006,f74]) ).

fof(f3006,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK1,X0)) ),
    inference(forward_demodulation,[],[f2982,f72]) ).

fof(f72,plain,
    xn = sdtpldt0(xm,sK1),
    inference(cnf_transformation,[],[f64]) ).

fof(f2982,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtpldt0(sdtpldt0(xm,sK1),X0) = sdtpldt0(xm,sdtpldt0(sK1,X0)) ),
    inference(resolution,[],[f1077,f79]) ).

fof(f79,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xn)
    & aNaturalNumber0(xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).

fof(f1077,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sdtpldt0(sdtpldt0(X1,sK1),X0) = sdtpldt0(X1,sdtpldt0(sK1,X0)) ),
    inference(resolution,[],[f109,f71]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

fof(f77,plain,
    ! [X0] :
      ( xl != sdtpldt0(xm,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM460+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35  % Computer : n019.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Fri May  3 15:11:38 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.12/0.35  % (18222)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37  % (18227)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)
% 0.12/0.37  % (18225)WARNING: value z3 for option sas not known
% 0.12/0.37  % (18226)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37  % (18229)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)
% 0.12/0.37  % (18224)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37  % (18225)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)
% 0.12/0.37  % (18228)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)
% 0.12/0.37  TRYING [1]
% 0.12/0.37  % (18223)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37  TRYING [2]
% 0.12/0.37  TRYING [3]
% 0.12/0.37  TRYING [1]
% 0.12/0.37  TRYING [2]
% 0.12/0.38  TRYING [3]
% 0.19/0.38  TRYING [4]
% 0.19/0.38  TRYING [4]
% 0.19/0.43  TRYING [5]
% 0.19/0.43  TRYING [5]
% 1.36/0.54  TRYING [6]
% 1.36/0.55  TRYING [6]
% 1.51/0.60  TRYING [1]
% 1.51/0.60  TRYING [2]
% 1.51/0.60  TRYING [3]
% 1.51/0.61  TRYING [4]
% 2.08/0.65  TRYING [5]
% 2.37/0.73  % (18228)First to succeed.
% 2.37/0.73  % (18228)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18222"
% 2.37/0.73  % (18228)Refutation found. Thanks to Tanya!
% 2.37/0.73  % SZS status Theorem for theBenchmark
% 2.37/0.73  % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.73  % (18228)------------------------------
% 2.37/0.73  % (18228)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.37/0.73  % (18228)Termination reason: Refutation
% 2.37/0.73  
% 2.37/0.73  % (18228)Memory used [KB]: 5088
% 2.37/0.73  % (18228)Time elapsed: 0.360 s
% 2.37/0.73  % (18228)Instructions burned: 716 (million)
% 2.37/0.73  % (18222)Success in time 0.365 s
%------------------------------------------------------------------------------