TSTP Solution File: RNG109+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG109+4 : 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 : 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 : Sun May  5 08:57:29 EDT 2024

% Result   : Theorem 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   46 (  15 unt;   0 def)
%            Number of atoms       :  179 (  77 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  179 (  46   ~;  33   |;  77   &)
%                                         (  12 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   69 (  36   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f949,plain,
    $false,
    inference(trivial_inequality_removal,[],[f948]) ).

fof(f948,plain,
    xa != xa,
    inference(superposition,[],[f937,f516]) ).

fof(f516,plain,
    sz00 = xa,
    inference(forward_demodulation,[],[f515,f440]) ).

fof(f440,plain,
    xa = sdtpldt0(xa,sz00),
    inference(resolution,[],[f288,f265]) ).

fof(f265,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ( aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).

fof(f288,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).

fof(f515,plain,
    sz00 = sdtpldt0(xa,sz00),
    inference(resolution,[],[f510,f272]) ).

fof(f272,plain,
    aElementOf0(xa,slsdtgt0(xa)),
    inference(cnf_transformation,[],[f161]) ).

fof(f161,plain,
    ( aElementOf0(xb,slsdtgt0(xb))
    & xb = sdtasdt0(xb,sK22)
    & aElement0(sK22)
    & aElementOf0(sz00,slsdtgt0(xb))
    & sz00 = sdtasdt0(xb,sK23)
    & aElement0(sK23)
    & aElementOf0(xa,slsdtgt0(xa))
    & xa = sdtasdt0(xa,sK24)
    & aElement0(sK24)
    & aElementOf0(sz00,slsdtgt0(xa))
    & sz00 = sdtasdt0(xa,sK25)
    & aElement0(sK25) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25])],[f49,f160,f159,f158,f157]) ).

fof(f157,plain,
    ( ? [X0] :
        ( xb = sdtasdt0(xb,X0)
        & aElement0(X0) )
   => ( xb = sdtasdt0(xb,sK22)
      & aElement0(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ( ? [X1] :
        ( sz00 = sdtasdt0(xb,X1)
        & aElement0(X1) )
   => ( sz00 = sdtasdt0(xb,sK23)
      & aElement0(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ( ? [X2] :
        ( xa = sdtasdt0(xa,X2)
        & aElement0(X2) )
   => ( xa = sdtasdt0(xa,sK24)
      & aElement0(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ( ? [X3] :
        ( sz00 = sdtasdt0(xa,X3)
        & aElement0(X3) )
   => ( sz00 = sdtasdt0(xa,sK25)
      & aElement0(sK25) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ( aElementOf0(xb,slsdtgt0(xb))
    & ? [X0] :
        ( xb = sdtasdt0(xb,X0)
        & aElement0(X0) )
    & aElementOf0(sz00,slsdtgt0(xb))
    & ? [X1] :
        ( sz00 = sdtasdt0(xb,X1)
        & aElement0(X1) )
    & aElementOf0(xa,slsdtgt0(xa))
    & ? [X2] :
        ( xa = sdtasdt0(xa,X2)
        & aElement0(X2) )
    & aElementOf0(sz00,slsdtgt0(xa))
    & ? [X3] :
        ( sz00 = sdtasdt0(xa,X3)
        & aElement0(X3) ) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ( aElementOf0(xb,slsdtgt0(xb))
    & ? [X0] :
        ( xb = sdtasdt0(xb,X0)
        & aElement0(X0) )
    & aElementOf0(sz00,slsdtgt0(xb))
    & ? [X0] :
        ( sz00 = sdtasdt0(xb,X0)
        & aElement0(X0) )
    & aElementOf0(xa,slsdtgt0(xa))
    & ? [X0] :
        ( xa = sdtasdt0(xa,X0)
        & aElement0(X0) )
    & aElementOf0(sz00,slsdtgt0(xa))
    & ? [X0] :
        ( sz00 = sdtasdt0(xa,X0)
        & aElement0(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).

fof(f510,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,slsdtgt0(xa))
      | sz00 = sdtpldt0(X0,sz00) ),
    inference(resolution,[],[f381,f275]) ).

fof(f275,plain,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(cnf_transformation,[],[f161]) ).

fof(f381,plain,
    ! [X2,X1] :
      ( ~ aElementOf0(X2,slsdtgt0(xb))
      | ~ aElementOf0(X1,slsdtgt0(xa))
      | sz00 = sdtpldt0(X1,X2) ),
    inference(equality_resolution,[],[f228]) ).

fof(f228,plain,
    ! [X2,X0,X1] :
      ( sz00 = X0
      | sdtpldt0(X1,X2) != X0
      | ~ aElementOf0(X2,slsdtgt0(xb))
      | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X1,X2] :
            ( sdtpldt0(X1,X2) != X0
            | ~ aElementOf0(X2,slsdtgt0(xb))
            | ~ aElementOf0(X1,slsdtgt0(xa)) )
        & sP1
        & sP0 ) ),
    inference(rectify,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X5,X6] :
            ( sdtpldt0(X5,X6) != X0
            | ~ aElementOf0(X6,slsdtgt0(xb))
            | ~ aElementOf0(X5,slsdtgt0(xa)) )
        & sP1
        & sP0 ) ),
    inference(definition_folding,[],[f60,f114,f113]) ).

fof(f113,plain,
    ( ! [X1] :
        ( aElementOf0(X1,slsdtgt0(xa))
      <=> ? [X2] :
            ( sdtasdt0(xa,X2) = X1
            & aElement0(X2) ) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f114,plain,
    ( ! [X3] :
        ( aElementOf0(X3,slsdtgt0(xb))
      <=> ? [X4] :
            ( sdtasdt0(xb,X4) = X3
            & aElement0(X4) ) )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f60,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X5,X6] :
            ( sdtpldt0(X5,X6) != X0
            | ~ aElementOf0(X6,slsdtgt0(xb))
            | ~ aElementOf0(X5,slsdtgt0(xa)) )
        & ! [X3] :
            ( aElementOf0(X3,slsdtgt0(xb))
          <=> ? [X4] :
                ( sdtasdt0(xb,X4) = X3
                & aElement0(X4) ) )
        & ! [X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
          <=> ? [X2] :
                ( sdtasdt0(xa,X2) = X1
                & aElement0(X2) ) ) ) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( sz00 = X0
      | ( ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ! [X5,X6] :
            ( sdtpldt0(X5,X6) != X0
            | ~ aElementOf0(X6,slsdtgt0(xb))
            | ~ aElementOf0(X5,slsdtgt0(xa)) )
        & ! [X3] :
            ( aElementOf0(X3,slsdtgt0(xb))
          <=> ? [X4] :
                ( sdtasdt0(xb,X4) = X3
                & aElement0(X4) ) )
        & ! [X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
          <=> ? [X2] :
                ( sdtasdt0(xa,X2) = X1
                & aElement0(X2) ) ) ) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ~ ? [X0] :
        ( sz00 != X0
        & ( ! [X1] :
              ( aElementOf0(X1,slsdtgt0(xa))
            <=> ? [X2] :
                  ( sdtasdt0(xa,X2) = X1
                  & aElement0(X2) ) )
         => ( ! [X3] :
                ( aElementOf0(X3,slsdtgt0(xb))
              <=> ? [X4] :
                    ( sdtasdt0(xb,X4) = X3
                    & aElement0(X4) ) )
           => ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
              | ? [X5,X6] :
                  ( sdtpldt0(X5,X6) = X0
                  & aElementOf0(X6,slsdtgt0(xb))
                  & aElementOf0(X5,slsdtgt0(xa)) ) ) ) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ? [X0] :
        ( sz00 != X0
        & ( ! [X1] :
              ( aElementOf0(X1,slsdtgt0(xa))
            <=> ? [X2] :
                  ( sdtasdt0(xa,X2) = X1
                  & aElement0(X2) ) )
         => ( ! [X1] :
                ( aElementOf0(X1,slsdtgt0(xb))
              <=> ? [X2] :
                    ( sdtasdt0(xb,X2) = X1
                    & aElement0(X2) ) )
           => ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
              | ? [X1,X2] :
                  ( sdtpldt0(X1,X2) = X0
                  & aElementOf0(X2,slsdtgt0(xb))
                  & aElementOf0(X1,slsdtgt0(xa)) ) ) ) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ? [X0] :
      ( sz00 != X0
      & ( ! [X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
          <=> ? [X2] :
                ( sdtasdt0(xa,X2) = X1
                & aElement0(X2) ) )
       => ( ! [X1] :
              ( aElementOf0(X1,slsdtgt0(xb))
            <=> ? [X2] :
                  ( sdtasdt0(xb,X2) = X1
                  & aElement0(X2) ) )
         => ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
            | ? [X1,X2] :
                ( sdtpldt0(X1,X2) = X0
                & aElementOf0(X2,slsdtgt0(xb))
                & aElementOf0(X1,slsdtgt0(xa)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f937,plain,
    sz00 != xa,
    inference(trivial_inequality_removal,[],[f890]) ).

fof(f890,plain,
    ( xa != xa
    | sz00 != xa ),
    inference(backward_demodulation,[],[f394,f871]) ).

fof(f871,plain,
    xa = xb,
    inference(backward_demodulation,[],[f596,f868]) ).

fof(f868,plain,
    xa = sdtpldt0(xa,xb),
    inference(resolution,[],[f614,f272]) ).

fof(f614,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,slsdtgt0(xa))
      | xa = sdtpldt0(X0,xb) ),
    inference(backward_demodulation,[],[f511,f516]) ).

fof(f511,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,slsdtgt0(xa))
      | sz00 = sdtpldt0(X0,xb) ),
    inference(resolution,[],[f381,f278]) ).

fof(f278,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cnf_transformation,[],[f161]) ).

fof(f596,plain,
    xb = sdtpldt0(xa,xb),
    inference(backward_demodulation,[],[f459,f516]) ).

fof(f459,plain,
    xb = sdtpldt0(sz00,xb),
    inference(resolution,[],[f289,f266]) ).

fof(f266,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f39]) ).

fof(f289,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtpldt0(sz00,X0) = X0 ),
    inference(cnf_transformation,[],[f68]) ).

fof(f394,plain,
    ( xa != xb
    | sz00 != xa ),
    inference(inner_rewriting,[],[f393]) ).

fof(f393,plain,
    ( sz00 != xb
    | xa != xb ),
    inference(inner_rewriting,[],[f279]) ).

fof(f279,plain,
    ( sz00 != xb
    | sz00 != xa ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    ( sz00 != xb
    | sz00 != xa ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2110) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n006.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   : Fri May  3 18:19:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (13306)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (13309)WARNING: value z3 for option sas not known
% 0.14/0.38  % (13310)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (13309)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)
% 0.14/0.38  % (13308)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (13311)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)
% 0.14/0.38  % (13312)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)
% 0.14/0.38  % (13313)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)
% 0.14/0.38  % (13307)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.20/0.41  TRYING [3]
% 0.20/0.41  % (13312)First to succeed.
% 0.20/0.41  % (13312)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13306"
% 0.20/0.41  % (13312)Refutation found. Thanks to Tanya!
% 0.20/0.41  % SZS status Theorem for theBenchmark
% 0.20/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41  % (13312)------------------------------
% 0.20/0.41  % (13312)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.41  % (13312)Termination reason: Refutation
% 0.20/0.41  
% 0.20/0.41  % (13312)Memory used [KB]: 1419
% 0.20/0.41  % (13312)Time elapsed: 0.034 s
% 0.20/0.41  % (13312)Instructions burned: 54 (million)
% 0.20/0.41  % (13306)Success in time 0.052 s
%------------------------------------------------------------------------------