TSTP Solution File: NUM500+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -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 : Wed Aug 31 18:00:08 EDT 2022

% Result   : Theorem 1.66s 0.61s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   48 (  11 unt;   0 def)
%            Number of atoms       :  219 (  80 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  247 (  76   ~;  75   |;  88   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   56 (  31   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f652,plain,
    $false,
    inference(subsumption_resolution,[],[f651,f519]) ).

fof(f519,plain,
    isPrime0(sK8(xk)),
    inference(subsumption_resolution,[],[f518,f388]) ).

fof(f388,plain,
    ~ sQ16_eqProxy(sz00,xk),
    inference(equality_proxy_replacement,[],[f274,f350]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( sQ16_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ16_eqProxy])]) ).

fof(f274,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f47]) ).

fof(f47,axiom,
    ( sz00 != xk
    & sz10 != xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).

fof(f518,plain,
    ( isPrime0(sK8(xk))
    | sQ16_eqProxy(sz00,xk) ),
    inference(subsumption_resolution,[],[f504,f225]) ).

fof(f225,plain,
    aNaturalNumber0(xk),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    ( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
    & aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

fof(f504,plain,
    ( ~ aNaturalNumber0(xk)
    | sQ16_eqProxy(sz00,xk)
    | isPrime0(sK8(xk)) ),
    inference(resolution,[],[f352,f399]) ).

fof(f399,plain,
    ! [X0] :
      ( sQ16_eqProxy(sz10,X0)
      | ~ aNaturalNumber0(X0)
      | isPrime0(sK8(X0))
      | sQ16_eqProxy(sz00,X0) ),
    inference(equality_proxy_replacement,[],[f287,f350,f350]) ).

fof(f287,plain,
    ! [X0] :
      ( isPrime0(sK8(X0))
      | sz00 = X0
      | sz10 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ( isPrime0(sK8(X0))
        & aNaturalNumber0(sK8(X0))
        & doDivides0(sK8(X0),X0) )
      | sz00 = X0
      | sz10 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f147,f178]) ).

fof(f178,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aNaturalNumber0(X1)
          & doDivides0(X1,X0) )
     => ( isPrime0(sK8(X0))
        & aNaturalNumber0(sK8(X0))
        & doDivides0(sK8(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aNaturalNumber0(X1)
          & doDivides0(X1,X0) )
      | sz00 = X0
      | sz10 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aNaturalNumber0(X1)
          & doDivides0(X1,X0) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0)
      | sz10 = X0 ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ( sz00 != X0
        & aNaturalNumber0(X0)
        & sz10 != X0 )
     => ? [X1] :
          ( isPrime0(X1)
          & aNaturalNumber0(X1)
          & doDivides0(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).

fof(f352,plain,
    ~ sQ16_eqProxy(sz10,xk),
    inference(equality_proxy_replacement,[],[f219,f350]) ).

fof(f219,plain,
    sz10 != xk,
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ( sz10 != xk
    & sz00 != xk ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ~ ( sz00 = xk
      | sz10 = xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).

fof(f651,plain,
    ~ isPrime0(sK8(xk)),
    inference(resolution,[],[f646,f237]) ).

fof(f237,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ~ isPrime0(X0) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f159,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( sz10 = X0
          | sz00 = X0
          | ( doDivides0(sK3(X0),X0)
            & sK3(X0) != X0
            & sz10 != sK3(X0)
            & aNaturalNumber0(sK3(X0))
            & aNaturalNumber0(sK4(X0))
            & sdtasdt0(sK3(X0),sK4(X0)) = X0 ) ) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f156,f158,f157]) ).

fof(f157,plain,
    ! [X0] :
      ( ? [X1] :
          ( doDivides0(X1,X0)
          & X0 != X1
          & sz10 != X1
          & aNaturalNumber0(X1)
          & ? [X2] :
              ( aNaturalNumber0(X2)
              & sdtasdt0(X1,X2) = X0 ) )
     => ( doDivides0(sK3(X0),X0)
        & sK3(X0) != X0
        & sz10 != sK3(X0)
        & aNaturalNumber0(sK3(X0))
        & ? [X2] :
            ( aNaturalNumber0(X2)
            & sdtasdt0(sK3(X0),X2) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X2] :
          ( aNaturalNumber0(X2)
          & sdtasdt0(sK3(X0),X2) = X0 )
     => ( aNaturalNumber0(sK4(X0))
        & sdtasdt0(sK3(X0),sK4(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f156,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( sz10 = X0
          | sz00 = X0
          | ? [X1] :
              ( doDivides0(X1,X0)
              & X0 != X1
              & sz10 != X1
              & aNaturalNumber0(X1)
              & ? [X2] :
                  ( aNaturalNumber0(X2)
                  & sdtasdt0(X1,X2) = X0 ) ) ) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( sz10 = X0
          | sz00 = X0
          | ? [X1] :
              ( doDivides0(X1,X0)
              & X0 != X1
              & sz10 != X1
              & aNaturalNumber0(X1)
              & ? [X2] :
                  ( aNaturalNumber0(X2)
                  & sdtasdt0(X1,X2) = X0 ) ) ) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f646,plain,
    sP0(sK8(xk)),
    inference(subsumption_resolution,[],[f633,f523]) ).

fof(f523,plain,
    aNaturalNumber0(sK8(xk)),
    inference(subsumption_resolution,[],[f522,f225]) ).

fof(f522,plain,
    ( aNaturalNumber0(sK8(xk))
    | ~ aNaturalNumber0(xk) ),
    inference(subsumption_resolution,[],[f505,f388]) ).

fof(f505,plain,
    ( aNaturalNumber0(sK8(xk))
    | sQ16_eqProxy(sz00,xk)
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[],[f352,f400]) ).

fof(f400,plain,
    ! [X0] :
      ( sQ16_eqProxy(sz10,X0)
      | sQ16_eqProxy(sz00,X0)
      | aNaturalNumber0(sK8(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_proxy_replacement,[],[f286,f350,f350]) ).

fof(f286,plain,
    ! [X0] :
      ( aNaturalNumber0(sK8(X0))
      | sz00 = X0
      | sz10 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f633,plain,
    ( sP0(sK8(xk))
    | ~ aNaturalNumber0(sK8(xk)) ),
    inference(resolution,[],[f521,f238]) ).

fof(f238,plain,
    ! [X0] :
      ( ~ doDivides0(X0,xk)
      | sP0(X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( sP0(X0)
      | ( ! [X1] :
            ( sdtasdt0(X0,X1) != xk
            | ~ aNaturalNumber0(X1) )
        & ~ doDivides0(X0,xk) )
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f149]) ).

fof(f149,plain,
    ! [X0] :
      ( sP0(X0)
      | ( ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) )
        & ~ doDivides0(X0,xk) )
      | ~ aNaturalNumber0(X0) ),
    inference(definition_folding,[],[f120,f148]) ).

fof(f120,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( sz10 = X0
          | sz00 = X0
          | ? [X1] :
              ( doDivides0(X1,X0)
              & X0 != X1
              & sz10 != X1
              & aNaturalNumber0(X1)
              & ? [X2] :
                  ( aNaturalNumber0(X2)
                  & sdtasdt0(X1,X2) = X0 ) ) ) )
      | ( ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) )
        & ~ doDivides0(X0,xk) )
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ( ( sz00 = X0
          | ? [X1] :
              ( sz10 != X1
              & X0 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( aNaturalNumber0(X2)
                  & sdtasdt0(X1,X2) = X0 )
              & aNaturalNumber0(X1) )
          | sz10 = X0 )
        & ~ isPrime0(X0) )
      | ( ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) )
        & ~ doDivides0(X0,xk) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ~ ? [X0] :
        ( ( ( sz00 != X0
            & ! [X1] :
                ( ( doDivides0(X1,X0)
                  & ? [X2] :
                      ( aNaturalNumber0(X2)
                      & sdtasdt0(X1,X2) = X0 )
                  & aNaturalNumber0(X1) )
               => ( sz10 = X1
                  | X0 = X1 ) )
            & sz10 != X0 )
          | isPrime0(X0) )
        & ( ? [X3] :
              ( aNaturalNumber0(X3)
              & xk = sdtasdt0(X0,X3) )
          | doDivides0(X0,xk) )
        & aNaturalNumber0(X0) ),
    inference(rectify,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ? [X0] :
        ( aNaturalNumber0(X0)
        & ( ( sz00 != X0
            & ! [X1] :
                ( ( doDivides0(X1,X0)
                  & ? [X2] :
                      ( aNaturalNumber0(X2)
                      & sdtasdt0(X1,X2) = X0 )
                  & aNaturalNumber0(X1) )
               => ( sz10 = X1
                  | X0 = X1 ) )
            & sz10 != X0 )
          | isPrime0(X0) )
        & ( ? [X1] :
              ( sdtasdt0(X0,X1) = xk
              & aNaturalNumber0(X1) )
          | doDivides0(X0,xk) ) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ? [X0] :
      ( aNaturalNumber0(X0)
      & ( ( sz00 != X0
          & ! [X1] :
              ( ( doDivides0(X1,X0)
                & ? [X2] :
                    ( aNaturalNumber0(X2)
                    & sdtasdt0(X1,X2) = X0 )
                & aNaturalNumber0(X1) )
             => ( sz10 = X1
                | X0 = X1 ) )
          & sz10 != X0 )
        | isPrime0(X0) )
      & ( ? [X1] :
            ( sdtasdt0(X0,X1) = xk
            & aNaturalNumber0(X1) )
        | doDivides0(X0,xk) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f521,plain,
    doDivides0(sK8(xk),xk),
    inference(subsumption_resolution,[],[f520,f388]) ).

fof(f520,plain,
    ( doDivides0(sK8(xk),xk)
    | sQ16_eqProxy(sz00,xk) ),
    inference(subsumption_resolution,[],[f506,f225]) ).

fof(f506,plain,
    ( ~ aNaturalNumber0(xk)
    | doDivides0(sK8(xk),xk)
    | sQ16_eqProxy(sz00,xk) ),
    inference(resolution,[],[f352,f401]) ).

fof(f401,plain,
    ! [X0] :
      ( sQ16_eqProxy(sz10,X0)
      | ~ aNaturalNumber0(X0)
      | sQ16_eqProxy(sz00,X0)
      | doDivides0(sK8(X0),X0) ),
    inference(equality_proxy_replacement,[],[f285,f350,f350]) ).

fof(f285,plain,
    ! [X0] :
      ( doDivides0(sK8(X0),X0)
      | sz00 = X0
      | sz10 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f179]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 07:08:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.19/0.56  % (17485)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.56  % (17508)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.56  % (17500)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.57  % (17491)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.57  % (17495)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.58  % (17503)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.58  % (17500)Instruction limit reached!
% 0.19/0.58  % (17500)------------------------------
% 0.19/0.58  % (17500)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59  % (17500)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59  % (17500)Termination reason: Unknown
% 0.19/0.59  % (17500)Termination phase: Naming
% 0.19/0.59  % (17497)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.59  
% 0.19/0.59  % (17500)Memory used [KB]: 1535
% 0.19/0.59  % (17500)Time elapsed: 0.005 s
% 0.19/0.59  % (17500)Instructions burned: 3 (million)
% 0.19/0.59  % (17500)------------------------------
% 0.19/0.59  % (17500)------------------------------
% 0.19/0.59  % (17482)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.59  % (17497)Instruction limit reached!
% 0.19/0.59  % (17497)------------------------------
% 0.19/0.59  % (17497)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59  % (17497)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59  % (17497)Termination reason: Unknown
% 0.19/0.59  % (17497)Termination phase: Property scanning
% 0.19/0.59  
% 0.19/0.59  % (17497)Memory used [KB]: 1535
% 0.19/0.59  % (17497)Time elapsed: 0.004 s
% 0.19/0.59  % (17497)Instructions burned: 4 (million)
% 0.19/0.59  % (17497)------------------------------
% 0.19/0.59  % (17497)------------------------------
% 1.66/0.60  % (17486)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.66/0.60  % (17487)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.66/0.60  % (17483)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.66/0.60  % (17488)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.66/0.60  % (17502)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.66/0.61  % (17495)First to succeed.
% 1.66/0.61  % (17506)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.66/0.61  % (17495)Refutation found. Thanks to Tanya!
% 1.66/0.61  % SZS status Theorem for theBenchmark
% 1.66/0.61  % SZS output start Proof for theBenchmark
% See solution above
% 1.66/0.61  % (17495)------------------------------
% 1.66/0.61  % (17495)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.66/0.61  % (17495)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.66/0.61  % (17495)Termination reason: Refutation
% 1.66/0.61  
% 1.66/0.61  % (17495)Memory used [KB]: 1918
% 1.66/0.61  % (17495)Time elapsed: 0.164 s
% 1.66/0.61  % (17495)Instructions burned: 14 (million)
% 1.66/0.61  % (17495)------------------------------
% 1.66/0.61  % (17495)------------------------------
% 1.66/0.61  % (17481)Success in time 0.252 s
%------------------------------------------------------------------------------