TSTP Solution File: SET790+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET790+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 : n025.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 : Sun May  5 09:18:57 EDT 2024

% Result   : Theorem 0.13s 0.36s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   36 (   8 unt;   0 def)
%            Number of atoms       :  171 (  19 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  204 (  69   ~;  54   |;  49   &)
%                                         (   4 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  101 (  87   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f64,plain,
    $false,
    inference(subsumption_resolution,[],[f63,f33]) ).

fof(f33,plain,
    order(sK0,sK1),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ( sK2 != sK3
    & least(sK3,sK0,sK1)
    & least(sK2,sK0,sK1)
    & order(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f26,f31,f30]) ).

fof(f30,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3] :
            ( X2 != X3
            & least(X3,X0,X1) )
        & least(X2,X0,X1)
        & order(X0,X1) )
   => ( ? [X3] :
          ( sK2 != X3
          & least(X3,sK0,sK1) )
      & least(sK2,sK0,sK1)
      & order(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ( ? [X3] :
        ( sK2 != X3
        & least(X3,sK0,sK1) )
   => ( sK2 != sK3
      & least(sK3,sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( ? [X3] :
          ( X2 != X3
          & least(X3,X0,X1) )
      & least(X2,X0,X1)
      & order(X0,X1) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ? [X0,X1,X2] :
      ( ? [X3] :
          ( X2 != X3
          & least(X3,X0,X1) )
      & least(X2,X0,X1)
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ~ ! [X0,X1,X2] :
        ( ( least(X2,X0,X1)
          & order(X0,X1) )
       => ! [X3] :
            ( least(X3,X0,X1)
           => X2 = X3 ) ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X5] :
        ( ( least(X5,X0,X1)
          & order(X0,X1) )
       => ! [X2] :
            ( least(X2,X0,X1)
           => X2 = X5 ) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1,X5] :
      ( ( least(X5,X0,X1)
        & order(X0,X1) )
     => ! [X2] :
          ( least(X2,X0,X1)
         => X2 = X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV2) ).

fof(f63,plain,
    ~ order(sK0,sK1),
    inference(subsumption_resolution,[],[f62,f42]) ).

fof(f42,plain,
    member(sK2,sK1),
    inference(resolution,[],[f40,f34]) ).

fof(f34,plain,
    least(sK2,sK0,sK1),
    inference(cnf_transformation,[],[f32]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( ~ least(X2,X0,X1)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( apply(X0,X2,X3)
            | ~ member(X3,X1) )
        & member(X2,X1) )
      | ~ least(X2,X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( least(X2,X0,X1)
     => ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X2,X3) )
        & member(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( least(X2,X0,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X2,X3) )
        & member(X2,X1) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X5] :
      ( least(X5,X0,X1)
    <=> ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X5,X2) )
        & member(X5,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least) ).

fof(f62,plain,
    ( ~ member(sK2,sK1)
    | ~ order(sK0,sK1) ),
    inference(resolution,[],[f57,f43]) ).

fof(f43,plain,
    member(sK3,sK1),
    inference(resolution,[],[f40,f35]) ).

fof(f35,plain,
    least(sK3,sK0,sK1),
    inference(cnf_transformation,[],[f32]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ member(sK3,X0)
      | ~ member(sK2,X0)
      | ~ order(sK0,X0) ),
    inference(subsumption_resolution,[],[f56,f42]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ member(sK2,X0)
      | ~ member(sK3,X0)
      | ~ order(sK0,X0)
      | ~ member(sK2,sK1) ),
    inference(subsumption_resolution,[],[f55,f43]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ member(sK2,X0)
      | ~ member(sK3,X0)
      | ~ order(sK0,X0)
      | ~ member(sK3,sK1)
      | ~ member(sK2,sK1) ),
    inference(subsumption_resolution,[],[f51,f36]) ).

fof(f36,plain,
    sK2 != sK3,
    inference(cnf_transformation,[],[f32]) ).

fof(f51,plain,
    ! [X0] :
      ( sK2 = sK3
      | ~ member(sK2,X0)
      | ~ member(sK3,X0)
      | ~ order(sK0,X0)
      | ~ member(sK3,sK1)
      | ~ member(sK2,sK1) ),
    inference(resolution,[],[f47,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( apply(sK0,sK3,X0)
      | ~ member(X0,sK1) ),
    inference(resolution,[],[f41,f35]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1] :
      ( ~ least(X2,X0,X1)
      | ~ member(X3,X1)
      | apply(X0,X2,X3) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ apply(sK0,X0,sK2)
      | sK2 = X0
      | ~ member(sK2,X1)
      | ~ member(X0,X1)
      | ~ order(sK0,X1)
      | ~ member(X0,sK1) ),
    inference(resolution,[],[f38,f44]) ).

fof(f44,plain,
    ! [X0] :
      ( apply(sK0,sK2,X0)
      | ~ member(X0,sK1) ),
    inference(resolution,[],[f41,f34]) ).

fof(f38,plain,
    ! [X0,X1,X6,X5] :
      ( ~ apply(X0,X6,X5)
      | X5 = X6
      | ~ apply(X0,X5,X6)
      | ~ member(X6,X1)
      | ~ member(X5,X1)
      | ~ order(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( apply(X0,X2,X4)
            | ~ apply(X0,X3,X4)
            | ~ apply(X0,X2,X3)
            | ~ member(X4,X1)
            | ~ member(X3,X1)
            | ~ member(X2,X1) )
        & ! [X5,X6] :
            ( X5 = X6
            | ~ apply(X0,X6,X5)
            | ~ apply(X0,X5,X6)
            | ~ member(X6,X1)
            | ~ member(X5,X1) )
        & ! [X7] :
            ( apply(X0,X7,X7)
            | ~ member(X7,X1) ) )
      | ~ order(X0,X1) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( apply(X0,X2,X4)
            | ~ apply(X0,X3,X4)
            | ~ apply(X0,X2,X3)
            | ~ member(X4,X1)
            | ~ member(X3,X1)
            | ~ member(X2,X1) )
        & ! [X5,X6] :
            ( X5 = X6
            | ~ apply(X0,X6,X5)
            | ~ apply(X0,X5,X6)
            | ~ member(X6,X1)
            | ~ member(X5,X1) )
        & ! [X7] :
            ( apply(X0,X7,X7)
            | ~ member(X7,X1) ) )
      | ~ order(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( order(X0,X1)
     => ( ! [X2,X3,X4] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X1)
              & member(X5,X1) )
           => ( ( apply(X0,X6,X5)
                & apply(X0,X5,X6) )
             => X5 = X6 ) )
        & ! [X7] :
            ( member(X7,X1)
           => apply(X0,X7,X7) ) ) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( order(X0,X1)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X1)
              & member(X5,X1) )
           => ( ( apply(X0,X6,X5)
                & apply(X0,X5,X6) )
             => X5 = X6 ) )
        & ! [X7] :
            ( member(X7,X1)
           => apply(X0,X7,X7) ) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( order(X0,X1)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X2,X3] :
            ( ( member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X2)
                & apply(X0,X2,X3) )
             => X2 = X3 ) )
        & ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n025.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri May  3 16:36:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (19258)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (19262)WARNING: value z3 for option sas not known
% 0.13/0.36  % (19262)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)
% 0.13/0.36  % (19262)First to succeed.
% 0.13/0.36  % (19262)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19258"
% 0.13/0.36  % (19262)Refutation found. Thanks to Tanya!
% 0.13/0.36  % SZS status Theorem for theBenchmark
% 0.13/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.36  % (19262)------------------------------
% 0.13/0.36  % (19262)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36  % (19262)Termination reason: Refutation
% 0.13/0.36  
% 0.13/0.36  % (19262)Memory used [KB]: 852
% 0.13/0.36  % (19262)Time elapsed: 0.004 s
% 0.13/0.36  % (19262)Instructions burned: 5 (million)
% 0.13/0.36  % (19258)Success in time 0.013 s
%------------------------------------------------------------------------------