TSTP Solution File: SET798+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n031.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 : Tue Apr 30 15:13:13 EDT 2024

% Result   : Theorem 0.19s 0.39s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   36 (   8 unt;   0 def)
%            Number of atoms       :  143 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  155 (  48   ~;  28   |;  57   &)
%                                         (   5 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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   :  103 (  74   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f530,plain,
    $false,
    inference(resolution,[],[f527,f87]) ).

fof(f87,plain,
    ~ lower_bound(sK4,sK0,sK2),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ( ~ lower_bound(sK4,sK0,sK2)
    & lower_bound(sK4,sK0,sK3)
    & subset(sK2,sK3)
    & subset(sK3,sK1)
    & subset(sK2,sK1)
    & order(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f46,f54,f53,f52]) ).

fof(f52,plain,
    ( ? [X0,X1] :
        ( ? [X2,X3] :
            ( ? [X4] :
                ( ~ lower_bound(X4,X0,X2)
                & lower_bound(X4,X0,X3) )
            & subset(X2,X3)
            & subset(X3,X1)
            & subset(X2,X1) )
        & order(X0,X1) )
   => ( ? [X3,X2] :
          ( ? [X4] :
              ( ~ lower_bound(X4,sK0,X2)
              & lower_bound(X4,sK0,X3) )
          & subset(X2,X3)
          & subset(X3,sK1)
          & subset(X2,sK1) )
      & order(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ( ? [X3,X2] :
        ( ? [X4] :
            ( ~ lower_bound(X4,sK0,X2)
            & lower_bound(X4,sK0,X3) )
        & subset(X2,X3)
        & subset(X3,sK1)
        & subset(X2,sK1) )
   => ( ? [X4] :
          ( ~ lower_bound(X4,sK0,sK2)
          & lower_bound(X4,sK0,sK3) )
      & subset(sK2,sK3)
      & subset(sK3,sK1)
      & subset(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ( ? [X4] :
        ( ~ lower_bound(X4,sK0,sK2)
        & lower_bound(X4,sK0,sK3) )
   => ( ~ lower_bound(sK4,sK0,sK2)
      & lower_bound(sK4,sK0,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4] :
              ( ~ lower_bound(X4,X0,X2)
              & lower_bound(X4,X0,X3) )
          & subset(X2,X3)
          & subset(X3,X1)
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4] :
              ( ~ lower_bound(X4,X0,X2)
              & lower_bound(X4,X0,X3) )
          & subset(X2,X3)
          & subset(X3,X1)
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ~ ! [X0,X1] :
        ( order(X0,X1)
       => ! [X2,X3] :
            ( ( subset(X2,X3)
              & subset(X3,X1)
              & subset(X2,X1) )
           => ! [X4] :
                ( lower_bound(X4,X0,X3)
               => lower_bound(X4,X0,X2) ) ) ),
    inference(rectify,[],[f23]) ).

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

fof(f22,conjecture,
    ! [X5,X3] :
      ( order(X5,X3)
     => ! [X2,X4] :
          ( ( subset(X2,X4)
            & subset(X4,X3)
            & subset(X2,X3) )
         => ! [X7] :
              ( lower_bound(X7,X5,X4)
             => lower_bound(X7,X5,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV10) ).

fof(f527,plain,
    lower_bound(sK4,sK0,sK2),
    inference(resolution,[],[f511,f106]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( member(sK8(X0,X1,X2),X1)
      | lower_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X2,X0,X1)
        | ( ~ apply(X0,X2,sK8(X0,X1,X2))
          & member(sK8(X0,X1,X2),X1) ) )
      & ( ! [X4] :
            ( apply(X0,X2,X4)
            | ~ member(X4,X1) )
        | ~ lower_bound(X2,X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f71,f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X0,X2,X3)
          & member(X3,X1) )
     => ( ~ apply(X0,X2,sK8(X0,X1,X2))
        & member(sK8(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) ) )
      & ( ! [X4] :
            ( apply(X0,X2,X4)
            | ~ member(X4,X1) )
        | ~ lower_bound(X2,X0,X1) ) ),
    inference(rectify,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) ) )
      & ( ! [X3] :
            ( apply(X0,X2,X3)
            | ~ member(X3,X1) )
        | ~ lower_bound(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( lower_bound(X2,X0,X1)
    <=> ! [X3] :
          ( apply(X0,X2,X3)
          | ~ member(X3,X1) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( lower_bound(X2,X0,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X0,X2,X3) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X5,X3,X7] :
      ( lower_bound(X7,X5,X3)
    <=> ! [X2] :
          ( member(X2,X3)
         => apply(X5,X7,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_bound) ).

fof(f511,plain,
    ~ member(sK8(sK0,sK2,sK4),sK2),
    inference(resolution,[],[f510,f85]) ).

fof(f85,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f55]) ).

fof(f510,plain,
    ! [X0] :
      ( ~ subset(X0,sK3)
      | ~ member(sK8(sK0,sK2,sK4),X0) ),
    inference(resolution,[],[f500,f92]) ).

fof(f92,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK5(X0,X1),X1)
          & member(sK5(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f57,f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK5(X0,X1),X1)
        & member(sK5(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,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,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f500,plain,
    ~ member(sK8(sK0,sK2,sK4),sK3),
    inference(resolution,[],[f499,f86]) ).

fof(f86,plain,
    lower_bound(sK4,sK0,sK3),
    inference(cnf_transformation,[],[f55]) ).

fof(f499,plain,
    ! [X0] :
      ( ~ lower_bound(sK4,sK0,X0)
      | ~ member(sK8(sK0,sK2,sK4),X0) ),
    inference(resolution,[],[f498,f105]) ).

fof(f105,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X0,X2,X4)
      | ~ member(X4,X1)
      | ~ lower_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f498,plain,
    ~ apply(sK0,sK4,sK8(sK0,sK2,sK4)),
    inference(resolution,[],[f107,f87]) ).

fof(f107,plain,
    ! [X2,X0,X1] :
      ( lower_bound(X2,X0,X1)
      | ~ apply(X0,X2,sK8(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f73]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n031.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 02:09:43 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (21531)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (21534)WARNING: value z3 for option sas not known
% 0.14/0.37  % (21533)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (21535)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (21534)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)
% 0.14/0.37  % (21532)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (21537)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)
% 0.14/0.37  % (21536)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)
% 0.14/0.37  % (21538)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)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [3]
% 0.19/0.38  TRYING [1]
% 0.19/0.38  TRYING [4]
% 0.19/0.38  TRYING [2]
% 0.19/0.38  % (21537)First to succeed.
% 0.19/0.39  % (21537)Refutation found. Thanks to Tanya!
% 0.19/0.39  % SZS status Theorem for theBenchmark
% 0.19/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.39  % (21537)------------------------------
% 0.19/0.39  % (21537)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.39  % (21537)Termination reason: Refutation
% 0.19/0.39  
% 0.19/0.39  % (21537)Memory used [KB]: 1137
% 0.19/0.39  % (21537)Time elapsed: 0.016 s
% 0.19/0.39  % (21537)Instructions burned: 22 (million)
% 0.19/0.39  % (21537)------------------------------
% 0.19/0.39  % (21537)------------------------------
% 0.19/0.39  % (21531)Success in time 0.021 s
%------------------------------------------------------------------------------