TSTP Solution File: SET642+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 09:14:47 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   30 (   7 unt;   0 def)
%            Number of atoms       :  143 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  180 (  67   ~;  47   |;  43   &)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   64 (  40   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f176,plain,
    $false,
    inference(resolution,[],[f175,f92]) ).

fof(f92,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).

fof(f175,plain,
    ~ ilf_type(sK2,set_type),
    inference(resolution,[],[f174,f92]) ).

fof(f174,plain,
    ( ~ ilf_type(sK3,set_type)
    | ~ ilf_type(sK2,set_type) ),
    inference(resolution,[],[f171,f92]) ).

fof(f171,plain,
    ( ~ ilf_type(sK4,set_type)
    | ~ ilf_type(sK3,set_type)
    | ~ ilf_type(sK2,set_type) ),
    inference(resolution,[],[f164,f89]) ).

fof(f89,plain,
    ilf_type(sK5,relation_type(sK3,sK4)),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ( ~ ilf_type(sK2,relation_type(sK3,sK4))
    & subset(sK2,sK5)
    & ilf_type(sK5,relation_type(sK3,sK4))
    & ilf_type(sK4,set_type)
    & ilf_type(sK3,set_type)
    & ilf_type(sK2,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f24,f57,f56,f55,f54]) ).

fof(f54,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ ilf_type(X0,relation_type(X1,X2))
                    & subset(X0,X3)
                    & ilf_type(X3,relation_type(X1,X2)) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(sK2,relation_type(X1,X2))
                  & subset(sK2,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK2,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ ilf_type(sK2,relation_type(X1,X2))
                & subset(sK2,X3)
                & ilf_type(X3,relation_type(X1,X2)) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ ilf_type(sK2,relation_type(sK3,X2))
              & subset(sK2,X3)
              & ilf_type(X3,relation_type(sK3,X2)) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK3,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ ilf_type(sK2,relation_type(sK3,X2))
            & subset(sK2,X3)
            & ilf_type(X3,relation_type(sK3,X2)) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ~ ilf_type(sK2,relation_type(sK3,sK4))
          & subset(sK2,X3)
          & ilf_type(X3,relation_type(sK3,sK4)) )
      & ilf_type(sK4,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ( ? [X3] :
        ( ~ ilf_type(sK2,relation_type(sK3,sK4))
        & subset(sK2,X3)
        & ilf_type(X3,relation_type(sK3,sK4)) )
   => ( ~ ilf_type(sK2,relation_type(sK3,sK4))
      & subset(sK2,sK5)
      & ilf_type(sK5,relation_type(sK3,sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X0,relation_type(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X0,relation_type(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X1,X2))
                   => ( subset(X0,X3)
                     => ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_4) ).

fof(f164,plain,
    ( ~ ilf_type(sK5,relation_type(sK3,sK4))
    | ~ ilf_type(sK4,set_type)
    | ~ ilf_type(sK3,set_type)
    | ~ ilf_type(sK2,set_type) ),
    inference(resolution,[],[f163,f90]) ).

fof(f90,plain,
    subset(sK2,sK5),
    inference(cnf_transformation,[],[f58]) ).

fof(f163,plain,
    ! [X0] :
      ( ~ subset(sK2,X0)
      | ~ ilf_type(X0,relation_type(sK3,sK4))
      | ~ ilf_type(sK4,set_type)
      | ~ ilf_type(sK3,set_type)
      | ~ ilf_type(sK2,set_type) ),
    inference(duplicate_literal_removal,[],[f162]) ).

fof(f162,plain,
    ! [X0] :
      ( ~ subset(sK2,X0)
      | ~ ilf_type(X0,relation_type(sK3,sK4))
      | ~ ilf_type(sK4,set_type)
      | ~ ilf_type(sK3,set_type)
      | ~ ilf_type(sK2,set_type)
      | ~ ilf_type(sK4,set_type)
      | ~ ilf_type(sK3,set_type)
      | ~ ilf_type(sK2,set_type) ),
    inference(resolution,[],[f123,f153]) ).

fof(f153,plain,
    ( ~ subset(sK2,cross_product(sK3,sK4))
    | ~ ilf_type(sK4,set_type)
    | ~ ilf_type(sK3,set_type)
    | ~ ilf_type(sK2,set_type) ),
    inference(resolution,[],[f122,f91]) ).

fof(f91,plain,
    ~ ilf_type(sK2,relation_type(sK3,sK4)),
    inference(cnf_transformation,[],[f58]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X0,relation_type(X1,X2))
      | ~ subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( subset(X0,cross_product(X1,X2))
               => ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f123,plain,
    ! [X2,X3,X0,X1] :
      ( subset(X0,cross_product(X1,X2))
      | ~ subset(X0,X3)
      | ~ ilf_type(X3,relation_type(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(X0,cross_product(X1,X2))
                  | ~ subset(X0,X3)
                  | ~ ilf_type(X3,relation_type(X1,X2)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(X0,cross_product(X1,X2))
                  | ~ subset(X0,X3)
                  | ~ ilf_type(X3,relation_type(X1,X2)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => subset(X0,cross_product(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 16:38:38 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (3271)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (3274)WARNING: value z3 for option sas not known
% 0.15/0.39  % (3272)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (3273)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (3275)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (3276)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)
% 0.15/0.39  % (3277)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)
% 0.15/0.39  % (3274)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)
% 0.15/0.39  % (3278)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)
% 0.15/0.39  % (3277)First to succeed.
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (3277)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3271"
% 0.15/0.39  % (3277)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (3277)------------------------------
% 0.15/0.39  % (3277)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (3277)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (3277)Memory used [KB]: 927
% 0.15/0.39  % (3277)Time elapsed: 0.008 s
% 0.15/0.39  % (3277)Instructions burned: 9 (million)
% 0.15/0.39  % (3271)Success in time 0.024 s
%------------------------------------------------------------------------------