TSTP Solution File: SWV376+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n020.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 18:45:22 EDT 2022

% Result   : Theorem 0.21s 0.56s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (   7 unt;   0 def)
%            Number of atoms       :  105 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  127 (  55   ~;  27   |;  24   &)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  12 con; 0-3 aty)
%            Number of variables   :  141 (  93   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f114,plain,
    $false,
    inference(subsumption_resolution,[],[f113,f87]) ).

fof(f87,plain,
    ~ ok(triple(sK4,sK2,sK0)),
    inference(subsumption_resolution,[],[f86,f74]) ).

fof(f74,plain,
    ok(triple(sK10,sK11,sK9)),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ( ~ ok(triple(sK7,sK8,sK6))
    & succ_cpq(triple(sK7,sK8,sK6),triple(sK10,sK11,sK9))
    & ok(triple(sK10,sK11,sK9)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f63,f65,f64]) ).

fof(f64,plain,
    ( ? [X0,X1,X2] :
        ( ~ ok(triple(X1,X2,X0))
        & ? [X3,X4,X5] :
            ( succ_cpq(triple(X1,X2,X0),triple(X4,X5,X3))
            & ok(triple(X4,X5,X3)) ) )
   => ( ~ ok(triple(sK7,sK8,sK6))
      & ? [X5,X4,X3] :
          ( succ_cpq(triple(sK7,sK8,sK6),triple(X4,X5,X3))
          & ok(triple(X4,X5,X3)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ( ? [X5,X4,X3] :
        ( succ_cpq(triple(sK7,sK8,sK6),triple(X4,X5,X3))
        & ok(triple(X4,X5,X3)) )
   => ( succ_cpq(triple(sK7,sK8,sK6),triple(sK10,sK11,sK9))
      & ok(triple(sK10,sK11,sK9)) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ? [X0,X1,X2] :
      ( ~ ok(triple(X1,X2,X0))
      & ? [X3,X4,X5] :
          ( succ_cpq(triple(X1,X2,X0),triple(X4,X5,X3))
          & ok(triple(X4,X5,X3)) ) ),
    inference(rectify,[],[f54]) ).

fof(f54,plain,
    ? [X2,X0,X1] :
      ( ~ ok(triple(X0,X1,X2))
      & ? [X5,X4,X3] :
          ( succ_cpq(triple(X0,X1,X2),triple(X4,X3,X5))
          & ok(triple(X4,X3,X5)) ) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,plain,
    ~ ! [X0,X2,X1] :
        ( ~ ok(triple(X0,X1,X2))
       => ! [X3,X4,X5] :
            ( succ_cpq(triple(X0,X1,X2),triple(X4,X3,X5))
           => ~ ok(triple(X4,X3,X5)) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ~ ok(triple(X0,X1,X2))
       => ! [X4,X3,X5] :
            ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
           => ~ ok(triple(X3,X4,X5)) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => ! [X4,X3,X5] :
          ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
         => ~ ok(triple(X3,X4,X5)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_co) ).

fof(f86,plain,
    ( ~ ok(triple(sK10,sK11,sK9))
    | ~ ok(triple(sK4,sK2,sK0)) ),
    inference(subsumption_resolution,[],[f81,f76]) ).

fof(f76,plain,
    ~ ok(triple(sK7,sK8,sK6)),
    inference(cnf_transformation,[],[f66]) ).

fof(f81,plain,
    ( ~ ok(triple(sK4,sK2,sK0))
    | ok(triple(sK7,sK8,sK6))
    | ~ ok(triple(sK10,sK11,sK9)) ),
    inference(resolution,[],[f75,f70]) ).

fof(f70,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ succ_cpq(triple(X0,X1,X2),triple(X4,X3,X5))
      | ~ ok(triple(X4,X3,X5))
      | ok(triple(X0,X1,X2))
      | ~ ok(triple(sK4,sK2,sK0)) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ( ! [X0,X1,X2] :
        ( ! [X3,X4,X5] :
            ( ~ succ_cpq(triple(X0,X1,X2),triple(X4,X3,X5))
            | ~ ok(triple(X4,X3,X5)) )
        | ok(triple(X0,X1,X2)) )
    | ( succ_cpq(triple(sK5,sK3,sK1),triple(sK4,sK2,sK0))
      & ~ ok(triple(sK4,sK2,sK0))
      & ok(im_succ_cpq(triple(sK4,sK2,sK0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f59,f60]) ).

fof(f60,plain,
    ( ? [X6,X7,X8,X9,X10,X11] :
        ( succ_cpq(triple(X11,X9,X7),triple(X10,X8,X6))
        & ~ ok(triple(X10,X8,X6))
        & ok(im_succ_cpq(triple(X10,X8,X6))) )
   => ( succ_cpq(triple(sK5,sK3,sK1),triple(sK4,sK2,sK0))
      & ~ ok(triple(sK4,sK2,sK0))
      & ok(im_succ_cpq(triple(sK4,sK2,sK0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ( ! [X0,X1,X2] :
        ( ! [X3,X4,X5] :
            ( ~ succ_cpq(triple(X0,X1,X2),triple(X4,X3,X5))
            | ~ ok(triple(X4,X3,X5)) )
        | ok(triple(X0,X1,X2)) )
    | ? [X6,X7,X8,X9,X10,X11] :
        ( succ_cpq(triple(X11,X9,X7),triple(X10,X8,X6))
        & ~ ok(triple(X10,X8,X6))
        & ok(im_succ_cpq(triple(X10,X8,X6))) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ( ! [X6,X7,X8] :
        ( ! [X11,X9,X10] :
            ( ~ succ_cpq(triple(X6,X7,X8),triple(X9,X11,X10))
            | ~ ok(triple(X9,X11,X10)) )
        | ok(triple(X6,X7,X8)) )
    | ? [X4,X2,X3,X5,X1,X0] :
        ( succ_cpq(triple(X0,X5,X2),triple(X1,X3,X4))
        & ~ ok(triple(X1,X3,X4))
        & ok(im_succ_cpq(triple(X1,X3,X4))) ) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ( ! [X6,X7,X8] :
        ( ! [X11,X9,X10] :
            ( ~ succ_cpq(triple(X6,X7,X8),triple(X9,X11,X10))
            | ~ ok(triple(X9,X11,X10)) )
        | ok(triple(X6,X7,X8)) )
    | ? [X0,X2,X4,X3,X5,X1] :
        ( ok(im_succ_cpq(triple(X1,X3,X4)))
        & ~ ok(triple(X1,X3,X4))
        & succ_cpq(triple(X0,X5,X2),triple(X1,X3,X4)) ) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ( ! [X0,X2,X4,X3,X5,X1] :
        ( succ_cpq(triple(X0,X5,X2),triple(X1,X3,X4))
       => ( ~ ok(triple(X1,X3,X4))
         => ~ ok(im_succ_cpq(triple(X1,X3,X4))) ) )
   => ! [X6,X8,X7] :
        ( ~ ok(triple(X6,X7,X8))
       => ! [X10,X9,X11] :
            ( succ_cpq(triple(X6,X7,X8),triple(X9,X11,X10))
           => ~ ok(triple(X9,X11,X10)) ) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ( ! [X0,X3,X2,X4,X5,X1] :
        ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
       => ( ~ ok(triple(X3,X4,X5))
         => ~ ok(im_succ_cpq(triple(X3,X4,X5))) ) )
   => ! [X6,X7,X8] :
        ( ~ ok(triple(X6,X7,X8))
       => ! [X9,X11,X10] :
            ( succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11))
           => ~ ok(triple(X9,X10,X11)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_induction) ).

fof(f75,plain,
    succ_cpq(triple(sK7,sK8,sK6),triple(sK10,sK11,sK9)),
    inference(cnf_transformation,[],[f66]) ).

fof(f113,plain,
    ok(triple(sK4,sK2,sK0)),
    inference(resolution,[],[f73,f83]) ).

fof(f83,plain,
    ok(im_succ_cpq(triple(sK4,sK2,sK0))),
    inference(subsumption_resolution,[],[f82,f74]) ).

fof(f82,plain,
    ( ok(im_succ_cpq(triple(sK4,sK2,sK0)))
    | ~ ok(triple(sK10,sK11,sK9)) ),
    inference(subsumption_resolution,[],[f80,f76]) ).

fof(f80,plain,
    ( ok(triple(sK7,sK8,sK6))
    | ~ ok(triple(sK10,sK11,sK9))
    | ok(im_succ_cpq(triple(sK4,sK2,sK0))) ),
    inference(resolution,[],[f75,f69]) ).

fof(f69,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ succ_cpq(triple(X0,X1,X2),triple(X4,X3,X5))
      | ~ ok(triple(X4,X3,X5))
      | ok(im_succ_cpq(triple(sK4,sK2,sK0)))
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ok(triple(X0,X1,X2)) ),
    inference(rectify,[],[f53]) ).

fof(f53,plain,
    ! [X1,X0,X2] :
      ( ~ ok(im_succ_cpq(triple(X1,X0,X2)))
      | ok(triple(X1,X0,X2)) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X2,X1] :
      ( ~ ok(triple(X1,X0,X2))
     => ~ ok(im_succ_cpq(triple(X1,X0,X2))) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ! [X1,X0,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => ~ ok(im_succ_cpq(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_l13) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWV376+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14  % 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 : n020.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 19:26:15 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.53  % (26343)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)
% 0.21/0.55  % (26350)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)
% 0.21/0.55  % (26366)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)
% 0.21/0.55  % (26343)First to succeed.
% 0.21/0.55  % (26366)Also succeeded, but the first one will report.
% 0.21/0.55  % (26358)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)
% 0.21/0.56  % (26343)Refutation found. Thanks to Tanya!
% 0.21/0.56  % SZS status Theorem for theBenchmark
% 0.21/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56  % (26343)------------------------------
% 0.21/0.56  % (26343)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.56  % (26343)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.56  % (26343)Termination reason: Refutation
% 0.21/0.56  
% 0.21/0.56  % (26343)Memory used [KB]: 1535
% 0.21/0.56  % (26343)Time elapsed: 0.134 s
% 0.21/0.56  % (26343)Instructions burned: 3 (million)
% 0.21/0.56  % (26343)------------------------------
% 0.21/0.56  % (26343)------------------------------
% 0.21/0.56  % (26337)Success in time 0.199 s
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