TSTP Solution File: NUM423+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM423+1 : 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 : n017.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 08:26:54 EDT 2024

% Result   : Theorem 0.15s 0.41s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   51 (  14 unt;   0 def)
%            Number of atoms       :  193 (  59 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  236 (  94   ~;  92   |;  38   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   61 (  54   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f873,plain,
    $false,
    inference(trivial_inequality_removal,[],[f872]) ).

fof(f872,plain,
    sz00 != sz00,
    inference(superposition,[],[f63,f749]) ).

fof(f749,plain,
    sz00 = xq,
    inference(resolution,[],[f747,f65]) ).

fof(f65,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).

fof(f747,plain,
    ( ~ aInteger0(sz00)
    | sz00 = xq ),
    inference(resolution,[],[f745,f61]) ).

fof(f61,plain,
    aInteger0(xa),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,axiom,
    ( sz00 != xq
    & aInteger0(xq)
    & aInteger0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).

fof(f745,plain,
    ( ~ aInteger0(xa)
    | sz00 = xq
    | ~ aInteger0(sz00) ),
    inference(resolution,[],[f744,f62]) ).

fof(f62,plain,
    aInteger0(xq),
    inference(cnf_transformation,[],[f20]) ).

fof(f744,plain,
    ( ~ aInteger0(xq)
    | ~ aInteger0(xa)
    | sz00 = xq
    | ~ aInteger0(sz00) ),
    inference(duplicate_literal_removal,[],[f742]) ).

fof(f742,plain,
    ( ~ aInteger0(xa)
    | ~ aInteger0(xq)
    | sz00 = xq
    | ~ aInteger0(sz00)
    | ~ aInteger0(sz00)
    | sz00 = xq
    | ~ aInteger0(xq) ),
    inference(resolution,[],[f741,f460]) ).

fof(f460,plain,
    ( sP0(sz00,xq)
    | ~ aInteger0(sz00)
    | sz00 = xq
    | ~ aInteger0(xq) ),
    inference(superposition,[],[f96,f102]) ).

fof(f102,plain,
    sz00 = sdtasdt0(xq,sz00),
    inference(resolution,[],[f67,f62]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sz00 = sdtasdt0(X0,sz00) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

fof(f96,plain,
    ! [X2,X1] :
      ( sP0(sdtasdt0(X1,X2),X1)
      | ~ aInteger0(X2)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(equality_resolution,[],[f83]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1)
      | sdtasdt0(X1,X2) != X0
      | ~ aInteger0(X2)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( sdtasdt0(X1,X2) != X0
            | ~ aInteger0(X2) )
        | sz00 = X1
        | ~ aInteger0(X1) )
      & ( ( sdtasdt0(X1,sK2(X0,X1)) = X0
          & aInteger0(sK2(X0,X1))
          & sz00 != X1
          & aInteger0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f56,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X1,X3) = X0
          & aInteger0(X3) )
     => ( sdtasdt0(X1,sK2(X0,X1)) = X0
        & aInteger0(sK2(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( sdtasdt0(X1,X2) != X0
            | ~ aInteger0(X2) )
        | sz00 = X1
        | ~ aInteger0(X1) )
      & ( ( ? [X3] :
              ( sdtasdt0(X1,X3) = X0
              & aInteger0(X3) )
          & sz00 != X1
          & aInteger0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( sdtasdt0(X1,X2) != X0
            | ~ aInteger0(X2) )
        | sz00 = X1
        | ~ aInteger0(X1) )
      & ( ( ? [X2] :
              ( sdtasdt0(X1,X2) = X0
              & aInteger0(X2) )
          & sz00 != X1
          & aInteger0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( sdtasdt0(X1,X2) != X0
            | ~ aInteger0(X2) )
        | sz00 = X1
        | ~ aInteger0(X1) )
      & ( ( ? [X2] :
              ( sdtasdt0(X1,X2) = X0
              & aInteger0(X2) )
          & sz00 != X1
          & aInteger0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ( ? [X2] :
            ( sdtasdt0(X1,X2) = X0
            & aInteger0(X2) )
        & sz00 != X1
        & aInteger0(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f741,plain,
    ( ~ sP0(sz00,xq)
    | ~ aInteger0(xa)
    | ~ aInteger0(xq)
    | sz00 = xq
    | ~ aInteger0(sz00) ),
    inference(resolution,[],[f740,f84]) ).

fof(f84,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ aInteger0(X0) ),
    inference(definition_folding,[],[f31,f51,f50]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> sP0(X0,X1) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f31,plain,
    ! [X0] :
      ( ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & sz00 != X1
            & aInteger0(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).

fof(f740,plain,
    ( ~ sP1(sz00)
    | ~ aInteger0(xq)
    | ~ aInteger0(xa)
    | ~ sP0(sz00,xq)
    | sz00 = xq ),
    inference(resolution,[],[f739,f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( aDivisorOf0(X1,X0)
      | ~ sP0(X0,X1)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ~ sP0(X0,X1) )
          & ( sP0(X0,X1)
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f739,plain,
    ( ~ aDivisorOf0(xq,sz00)
    | sz00 = xq
    | ~ aInteger0(xq)
    | ~ aInteger0(xa) ),
    inference(forward_demodulation,[],[f738,f137]) ).

fof(f137,plain,
    sz00 = sdtpldt0(xa,smndt0(xa)),
    inference(resolution,[],[f73,f61]) ).

fof(f73,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sz00 = sdtpldt0(X0,smndt0(X0)) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

fof(f738,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
    | sz00 = xq
    | ~ aInteger0(xq)
    | ~ aInteger0(xa) ),
    inference(duplicate_literal_removal,[],[f737]) ).

fof(f737,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
    | sz00 = xq
    | ~ aInteger0(xq)
    | ~ aInteger0(xa)
    | ~ aInteger0(xa) ),
    inference(resolution,[],[f91,f60]) ).

fof(f60,plain,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(flattening,[],[f22]) ).

fof(f22,negated_conjecture,
    ~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
    inference(negated_conjecture,[],[f21]) ).

fof(f21,conjecture,
    sdteqdtlpzmzozddtrp0(xa,xa,xq),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      | ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
          | ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
        & ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
          | ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
      | sz00 = X2
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1,X2] :
      ( ( sz00 != X2
        & aInteger0(X2)
        & aInteger0(X1)
        & aInteger0(X0) )
     => ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
      <=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).

fof(f63,plain,
    sz00 != xq,
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 14:11:23 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (29018)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (29019)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (29022)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (29023)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)
% 0.15/0.37  % (29025)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)
% 0.15/0.37  % (29020)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (29024)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)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  % (29021)WARNING: value z3 for option sas not known
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (29021)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)
% 0.15/0.38  TRYING [3]
% 0.15/0.39  TRYING [4]
% 0.15/0.40  TRYING [4]
% 0.15/0.41  % (29024)First to succeed.
% 0.15/0.41  % (29024)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29018"
% 0.15/0.41  % (29024)Refutation found. Thanks to Tanya!
% 0.15/0.41  % SZS status Theorem for theBenchmark
% 0.15/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41  % (29024)------------------------------
% 0.15/0.41  % (29024)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.41  % (29024)Termination reason: Refutation
% 0.15/0.41  
% 0.15/0.41  % (29024)Memory used [KB]: 1298
% 0.15/0.41  % (29024)Time elapsed: 0.034 s
% 0.15/0.41  % (29024)Instructions burned: 53 (million)
% 0.15/0.41  % (29018)Success in time 0.05 s
%------------------------------------------------------------------------------