TSTP Solution File: SWV488+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWV488+2 : 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 : n007.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 18:50:11 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   49 (  14 unt;   0 def)
%            Number of atoms       :  209 (  51 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  258 (  98   ~;  87   |;  50   &)
%                                         (   6 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   57 (  51   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f127,plain,
    $false,
    inference(avatar_sat_refutation,[],[f79,f96,f100,f116,f120,f122,f126]) ).

fof(f126,plain,
    ( ~ spl3_8
    | ~ spl3_1 ),
    inference(avatar_split_clause,[],[f124,f74,f113]) ).

fof(f113,plain,
    ( spl3_8
  <=> int_leq(sK1,n) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f74,plain,
    ( spl3_1
  <=> ! [X0] :
        ( ~ int_leq(X0,n)
        | ~ int_leq(int_one,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f124,plain,
    ( ~ int_leq(sK1,n)
    | ~ spl3_1 ),
    inference(resolution,[],[f75,f65]) ).

fof(f65,plain,
    int_leq(int_one,sK1),
    inference(definition_unfolding,[],[f45,f46]) ).

fof(f46,plain,
    sK0 = sK1,
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( int_leq(sK1,n)
    & sK0 = sK1
    & int_leq(int_one,sK0)
    & real_zero = a(sK0,sK1)
    & int_leq(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( int_leq(X1,n)
        & X0 = X1
        & int_leq(int_one,X0)
        & real_zero = a(X0,X1)
        & int_leq(X0,X1) )
   => ( int_leq(sK1,n)
      & sK0 = sK1
      & int_leq(int_one,sK0)
      & real_zero = a(sK0,sK1)
      & int_leq(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ? [X0,X1] :
      ( int_leq(X1,n)
      & X0 = X1
      & int_leq(int_one,X0)
      & real_zero = a(X0,X1)
      & int_leq(X0,X1) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ? [X1,X0] :
      ( real_zero = a(X0,X1)
      & X0 = X1
      & int_leq(X0,X1)
      & int_leq(X1,n)
      & int_leq(int_one,X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X1,X0] :
        ( ( int_leq(X0,X1)
          & int_leq(X1,n)
          & int_leq(int_one,X0) )
       => ( X0 = X1
         => real_zero != a(X0,X1) ) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X1,X0] :
      ( ( int_leq(X0,X1)
        & int_leq(X1,n)
        & int_leq(int_one,X0) )
     => ( X0 = X1
       => real_zero != a(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lti) ).

fof(f45,plain,
    int_leq(int_one,sK0),
    inference(cnf_transformation,[],[f31]) ).

fof(f75,plain,
    ( ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f122,plain,
    spl3_8,
    inference(avatar_contradiction_clause,[],[f121]) ).

fof(f121,plain,
    ( $false
    | spl3_8 ),
    inference(resolution,[],[f115,f47]) ).

fof(f47,plain,
    int_leq(sK1,n),
    inference(cnf_transformation,[],[f31]) ).

fof(f115,plain,
    ( ~ int_leq(sK1,n)
    | spl3_8 ),
    inference(avatar_component_clause,[],[f113]) ).

fof(f120,plain,
    ( ~ spl3_3
    | spl3_4
    | spl3_5
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f117,f77,f91,f87,f83]) ).

fof(f83,plain,
    ( spl3_3
  <=> int_leq(int_one,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f87,plain,
    ( spl3_4
  <=> real_zero = real_one ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f91,plain,
    ( spl3_5
  <=> ! [X0] :
        ( ~ int_leq(sK1,X0)
        | ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f77,plain,
    ( spl3_2
  <=> ! [X6,X1] :
        ( ~ int_leq(X6,X1)
        | ~ int_leq(int_one,X6)
        | real_one = a(X6,X6)
        | ~ int_leq(int_one,X1)
        | ~ int_leq(X1,n) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f117,plain,
    ( ! [X0] :
        ( ~ int_leq(sK1,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(int_one,X0)
        | real_zero = real_one
        | ~ int_leq(int_one,sK1) )
    | ~ spl3_2 ),
    inference(superposition,[],[f78,f66]) ).

fof(f66,plain,
    real_zero = a(sK1,sK1),
    inference(definition_unfolding,[],[f44,f46]) ).

fof(f44,plain,
    real_zero = a(sK0,sK1),
    inference(cnf_transformation,[],[f31]) ).

fof(f78,plain,
    ( ! [X1,X6] :
        ( real_one = a(X6,X6)
        | ~ int_leq(int_one,X6)
        | ~ int_leq(X1,n)
        | ~ int_leq(X6,X1)
        | ~ int_leq(int_one,X1) )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f116,plain,
    ( ~ spl3_8
    | ~ spl3_3
    | ~ spl3_5 ),
    inference(avatar_split_clause,[],[f102,f91,f83,f113]) ).

fof(f102,plain,
    ( ~ int_leq(int_one,sK1)
    | ~ int_leq(sK1,n)
    | ~ spl3_5 ),
    inference(resolution,[],[f92,f67]) ).

fof(f67,plain,
    int_leq(sK1,sK1),
    inference(definition_unfolding,[],[f43,f46]) ).

fof(f43,plain,
    int_leq(sK0,sK1),
    inference(cnf_transformation,[],[f31]) ).

fof(f92,plain,
    ( ! [X0] :
        ( ~ int_leq(sK1,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(int_one,X0) )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f100,plain,
    ~ spl3_4,
    inference(avatar_contradiction_clause,[],[f99]) ).

fof(f99,plain,
    ( $false
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f98]) ).

fof(f98,plain,
    ( real_zero != real_zero
    | ~ spl3_4 ),
    inference(superposition,[],[f42,f89]) ).

fof(f89,plain,
    ( real_zero = real_one
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f87]) ).

fof(f42,plain,
    real_zero != real_one,
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    real_zero != real_one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).

fof(f96,plain,
    spl3_3,
    inference(avatar_contradiction_clause,[],[f95]) ).

fof(f95,plain,
    ( $false
    | spl3_3 ),
    inference(resolution,[],[f85,f65]) ).

fof(f85,plain,
    ( ~ int_leq(int_one,sK1)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f79,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f60,f77,f74]) ).

fof(f60,plain,
    ! [X0,X1,X6] :
      ( ~ int_leq(X6,X1)
      | ~ int_leq(X1,n)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X1)
      | real_one = a(X6,X6)
      | ~ int_leq(int_one,X6)
      | ~ int_leq(int_one,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( plus(X1,X2) != X0
            | ! [X3] :
                ( a(plus(X3,X2),X3) = lu(plus(X3,X2),X3)
                | ~ int_leq(int_one,X3)
                | ~ int_leq(X3,X1) )
            | ~ int_less(int_zero,X2) )
        & ! [X4] :
            ( plus(X0,X4) != X1
            | ! [X5] :
                ( ~ int_leq(int_one,X5)
                | real_zero = a(X5,plus(X5,X4))
                | ~ int_leq(X5,X0) )
            | ~ int_less(int_zero,X4) )
        & ! [X6] :
            ( ~ int_leq(int_one,X6)
            | ~ int_leq(X6,X1)
            | real_one = a(X6,X6) ) )
      | ~ int_leq(X1,n)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0)
      | ~ int_leq(int_one,X1) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ! [X5] :
            ( plus(X1,X5) != X0
            | ! [X6] :
                ( a(plus(X6,X5),X6) = lu(plus(X6,X5),X6)
                | ~ int_leq(int_one,X6)
                | ~ int_leq(X6,X1) )
            | ~ int_less(int_zero,X5) )
        & ! [X2] :
            ( plus(X0,X2) != X1
            | ! [X3] :
                ( ~ int_leq(int_one,X3)
                | real_zero = a(X3,plus(X3,X2))
                | ~ int_leq(X3,X0) )
            | ~ int_less(int_zero,X2) )
        & ! [X4] :
            ( ~ int_leq(int_one,X4)
            | ~ int_leq(X4,X1)
            | real_one = a(X4,X4) ) )
      | ~ int_leq(X1,n)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0)
      | ~ int_leq(int_one,X1) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ! [X3] :
                ( real_zero = a(X3,plus(X3,X2))
                | ~ int_leq(X3,X0)
                | ~ int_leq(int_one,X3) )
            | plus(X0,X2) != X1
            | ~ int_less(int_zero,X2) )
        & ! [X5] :
            ( ! [X6] :
                ( a(plus(X6,X5),X6) = lu(plus(X6,X5),X6)
                | ~ int_leq(int_one,X6)
                | ~ int_leq(X6,X1) )
            | ~ int_less(int_zero,X5)
            | plus(X1,X5) != X0 )
        & ! [X4] :
            ( real_one = a(X4,X4)
            | ~ int_leq(int_one,X4)
            | ~ int_leq(X4,X1) ) )
      | ~ int_leq(X0,n)
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(int_one,X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ( int_leq(X0,n)
        & int_leq(X1,n)
        & int_leq(int_one,X1)
        & int_leq(int_one,X0) )
     => ( ! [X2] :
            ( ( plus(X0,X2) = X1
              & int_less(int_zero,X2) )
           => ! [X3] :
                ( ( int_leq(X3,X0)
                  & int_leq(int_one,X3) )
               => real_zero = a(X3,plus(X3,X2)) ) )
        & ! [X5] :
            ( ( int_less(int_zero,X5)
              & plus(X1,X5) = X0 )
           => ! [X6] :
                ( ( int_leq(int_one,X6)
                  & int_leq(X6,X1) )
               => a(plus(X6,X5),X6) = lu(plus(X6,X5),X6) ) )
        & ! [X4] :
            ( ( int_leq(int_one,X4)
              & int_leq(X4,X1) )
           => real_one = a(X4,X4) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( ( int_leq(X0,n)
        & int_leq(X1,n)
        & int_leq(int_one,X1)
        & int_leq(int_one,X0) )
     => ( ! [X7] :
            ( ( int_less(int_zero,X7)
              & plus(X0,X7) = X1 )
           => ! [X2] :
                ( ( int_leq(X2,X0)
                  & int_leq(int_one,X2) )
               => real_zero = a(X2,plus(X2,X7)) ) )
        & ! [X2] :
            ( ( int_leq(int_one,X2)
              & int_leq(X2,X1) )
           => real_one = a(X2,X2) )
        & ! [X7] :
            ( ( plus(X1,X7) = X0
              & int_less(int_zero,X7) )
           => ! [X2] :
                ( ( int_leq(int_one,X2)
                  & int_leq(X2,X1) )
               => a(plus(X2,X7),X2) = lu(plus(X2,X7),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qil) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWV488+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14  % 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 : n007.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 19:17:31 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  % (18915)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51  % (18902)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)
% 0.20/0.51  % (18903)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)
% 0.20/0.52  % (18898)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.52  % (18915)Instruction limit reached!
% 0.20/0.52  % (18915)------------------------------
% 0.20/0.52  % (18915)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (18920)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.52  % (18901)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)
% 0.20/0.52  % (18923)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)
% 0.20/0.52  % (18912)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)
% 0.20/0.53  % (18907)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)
% 0.20/0.53  % (18915)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (18915)Termination reason: Unknown
% 0.20/0.53  % (18915)Termination phase: Finite model building preprocessing
% 0.20/0.53  
% 0.20/0.53  % (18915)Memory used [KB]: 1407
% 0.20/0.53  % (18915)Time elapsed: 0.005 s
% 0.20/0.53  % (18915)Instructions burned: 3 (million)
% 0.20/0.53  % (18915)------------------------------
% 0.20/0.53  % (18915)------------------------------
% 0.20/0.53  % (18920)First to succeed.
% 0.20/0.53  % (18904)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)
% 0.20/0.53  % (18912)Instruction limit reached!
% 0.20/0.53  % (18912)------------------------------
% 0.20/0.53  % (18912)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (18907)Also succeeded, but the first one will report.
% 0.20/0.53  % (18926)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.53  % (18912)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (18912)Termination reason: Unknown
% 0.20/0.53  % (18912)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (18912)Memory used [KB]: 6012
% 0.20/0.53  % (18912)Time elapsed: 0.082 s
% 0.20/0.53  % (18920)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (18920)------------------------------
% 0.20/0.53  % (18920)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (18920)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (18920)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (18920)Memory used [KB]: 6012
% 0.20/0.53  % (18920)Time elapsed: 0.084 s
% 0.20/0.53  % (18920)Instructions burned: 3 (million)
% 0.20/0.53  % (18920)------------------------------
% 0.20/0.53  % (18920)------------------------------
% 0.20/0.53  % (18897)Success in time 0.172 s
%------------------------------------------------------------------------------