TSTP Solution File: SET797+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET797+4 : TPTP v8.1.0. Released v3.2.0.
% 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 : n013.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 18:22:17 EDT 2022

% Result   : Theorem 1.69s 0.60s
% Output   : Refutation 1.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (   7 unt;   0 def)
%            Number of atoms       :  147 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  156 (  46   ~;  29   |;  57   &)
%                                         (   6 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :  107 (  78   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f239,plain,
    $false,
    inference(subsumption_resolution,[],[f233,f135]) ).

fof(f135,plain,
    member(sK0(sK3,sK1,sK5),sK3),
    inference(resolution,[],[f105,f91]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( upper_bound(X2,X1,X0)
      | member(sK0(X0,X1,X2),X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X1,X0)
        | ( ~ apply(X1,sK0(X0,X1,X2),X2)
          & member(sK0(X0,X1,X2),X0) ) )
      & ( ! [X4] :
            ( apply(X1,X4,X2)
            | ~ member(X4,X0) )
        | ~ upper_bound(X2,X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f57,f58]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X1,X3,X2)
          & member(X3,X0) )
     => ( ~ apply(X1,sK0(X0,X1,X2),X2)
        & member(sK0(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X1,X0)
        | ? [X3] :
            ( ~ apply(X1,X3,X2)
            & member(X3,X0) ) )
      & ( ! [X4] :
            ( apply(X1,X4,X2)
            | ~ member(X4,X0) )
        | ~ upper_bound(X2,X1,X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ! [X1,X0,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X3,X2)
            & member(X3,X1) ) )
      & ( ! [X3] :
            ( apply(X0,X3,X2)
            | ~ member(X3,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X1,X0,X2] :
      ( upper_bound(X2,X0,X1)
    <=> ! [X3] :
          ( apply(X0,X3,X2)
          | ~ member(X3,X1) ) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X2,X1] :
      ( upper_bound(X2,X0,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X0,X3,X2) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X5,X3,X7] :
      ( upper_bound(X7,X5,X3)
    <=> ! [X2] :
          ( member(X2,X3)
         => apply(X5,X2,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_bound) ).

fof(f105,plain,
    ~ upper_bound(sK5,sK1,sK3),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ( subset(sK3,sK2)
    & subset(sK4,sK2)
    & ~ upper_bound(sK5,sK1,sK3)
    & upper_bound(sK5,sK1,sK4)
    & subset(sK3,sK4)
    & order(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f52,f66,f65,f64]) ).

fof(f64,plain,
    ( ? [X0,X1] :
        ( ? [X2,X3] :
            ( subset(X2,X1)
            & subset(X3,X1)
            & ? [X4] :
                ( ~ upper_bound(X4,X0,X2)
                & upper_bound(X4,X0,X3) )
            & subset(X2,X3) )
        & order(X0,X1) )
   => ( ? [X3,X2] :
          ( subset(X2,sK2)
          & subset(X3,sK2)
          & ? [X4] :
              ( ~ upper_bound(X4,sK1,X2)
              & upper_bound(X4,sK1,X3) )
          & subset(X2,X3) )
      & order(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ( ? [X3,X2] :
        ( subset(X2,sK2)
        & subset(X3,sK2)
        & ? [X4] :
            ( ~ upper_bound(X4,sK1,X2)
            & upper_bound(X4,sK1,X3) )
        & subset(X2,X3) )
   => ( subset(sK3,sK2)
      & subset(sK4,sK2)
      & ? [X4] :
          ( ~ upper_bound(X4,sK1,sK3)
          & upper_bound(X4,sK1,sK4) )
      & subset(sK3,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ( ? [X4] :
        ( ~ upper_bound(X4,sK1,sK3)
        & upper_bound(X4,sK1,sK4) )
   => ( ~ upper_bound(sK5,sK1,sK3)
      & upper_bound(sK5,sK1,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( subset(X2,X1)
          & subset(X3,X1)
          & ? [X4] :
              ( ~ upper_bound(X4,X0,X2)
              & upper_bound(X4,X0,X3) )
          & subset(X2,X3) )
      & order(X0,X1) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ? [X1,X0] :
      ( ? [X2,X3] :
          ( ? [X4] :
              ( ~ upper_bound(X4,X0,X2)
              & upper_bound(X4,X0,X3) )
          & subset(X3,X1)
          & subset(X2,X1)
          & subset(X2,X3) )
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ~ ! [X1,X0] :
        ( order(X0,X1)
       => ! [X2,X3] :
            ( ( subset(X3,X1)
              & subset(X2,X1)
              & subset(X2,X3) )
           => ! [X4] :
                ( upper_bound(X4,X0,X3)
               => upper_bound(X4,X0,X2) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [X5,X3] :
        ( order(X5,X3)
       => ! [X2,X4] :
            ( ( subset(X2,X3)
              & subset(X2,X4)
              & subset(X4,X3) )
           => ! [X7] :
                ( upper_bound(X7,X5,X4)
               => upper_bound(X7,X5,X2) ) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [X5,X3] :
      ( order(X5,X3)
     => ! [X2,X4] :
          ( ( subset(X2,X3)
            & subset(X2,X4)
            & subset(X4,X3) )
         => ! [X7] :
              ( upper_bound(X7,X5,X4)
             => upper_bound(X7,X5,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV9) ).

fof(f233,plain,
    ~ member(sK0(sK3,sK1,sK5),sK3),
    inference(resolution,[],[f159,f131]) ).

fof(f131,plain,
    ! [X0] :
      ( member(X0,sK4)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f103,f122]) ).

fof(f122,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | member(X3,X1)
      | ~ member(X3,X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK8(X0,X1),X1)
          & member(sK8(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f84,f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK8(X0,X1),X1)
        & member(sK8(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f83]) ).

fof(f83,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) ) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

fof(f103,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f67]) ).

fof(f159,plain,
    ~ member(sK0(sK3,sK1,sK5),sK4),
    inference(resolution,[],[f136,f105]) ).

fof(f136,plain,
    ! [X0] :
      ( upper_bound(sK5,sK1,X0)
      | ~ member(sK0(X0,sK1,sK5),sK4) ),
    inference(resolution,[],[f134,f92]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( ~ apply(X1,sK0(X0,X1,X2),X2)
      | upper_bound(X2,X1,X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f134,plain,
    ! [X0] :
      ( apply(sK1,X0,sK5)
      | ~ member(X0,sK4) ),
    inference(resolution,[],[f104,f90]) ).

fof(f90,plain,
    ! [X2,X0,X1,X4] :
      ( ~ upper_bound(X2,X1,X0)
      | apply(X1,X4,X2)
      | ~ member(X4,X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f104,plain,
    upper_bound(sK5,sK1,sK4),
    inference(cnf_transformation,[],[f67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET797+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 14:16:47 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 1.48/0.56  % (21953)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.48/0.56  % (21970)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.69/0.57  % (21968)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)
% 1.69/0.58  % (21962)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.69/0.58  % (21977)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)
% 1.69/0.59  % (21970)First to succeed.
% 1.69/0.59  % (21956)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)
% 1.69/0.59  % (21966)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)
% 1.69/0.59  % (21967)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.69/0.59  % (21979)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)
% 1.69/0.60  % (21960)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)
% 1.69/0.60  % (21970)Refutation found. Thanks to Tanya!
% 1.69/0.60  % SZS status Theorem for theBenchmark
% 1.69/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.69/0.60  % (21970)------------------------------
% 1.69/0.60  % (21970)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.60  % (21970)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.60  % (21970)Termination reason: Refutation
% 1.69/0.60  
% 1.69/0.60  % (21970)Memory used [KB]: 6268
% 1.69/0.60  % (21970)Time elapsed: 0.163 s
% 1.69/0.60  % (21970)Instructions burned: 8 (million)
% 1.69/0.60  % (21970)------------------------------
% 1.69/0.60  % (21970)------------------------------
% 1.69/0.60  % (21952)Success in time 0.242 s
%------------------------------------------------------------------------------