TSTP Solution File: SET974+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n029.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 May 21 03:14:09 EDT 2024

% Result   : Theorem 0.53s 0.73s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   35 (   5 unt;   0 def)
%            Number of atoms       :   91 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   96 (  40   ~;  26   |;  23   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-5 aty)
%            Number of variables   :   83 (  67   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f100,plain,
    $false,
    inference(avatar_sat_refutation,[],[f63,f81,f99]) ).

fof(f99,plain,
    ~ spl10_1,
    inference(avatar_contradiction_clause,[],[f97]) ).

fof(f97,plain,
    ( $false
    | ~ spl10_1 ),
    inference(resolution,[],[f87,f66]) ).

fof(f66,plain,
    in(sK8(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),set_intersection2(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))),
    inference(resolution,[],[f44,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( in(sK8(X0,X1),set_intersection2(X0,X1))
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( in(sK8(X0,X1),set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X3] : in(X3,set_intersection2(X0,X1))
     => in(sK8(X0,X1),set_intersection2(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( ? [X3] : in(X3,set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(f44,plain,
    ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))
    & ( disjoint(sK6,sK7)
      | disjoint(sK4,sK5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f19,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
        & ( disjoint(X2,X3)
          | disjoint(X0,X1) ) )
   => ( ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))
      & ( disjoint(sK6,sK7)
        | disjoint(sK4,sK5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0,X1,X2,X3] :
      ( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      & ( disjoint(X2,X3)
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( disjoint(X2,X3)
          | disjoint(X0,X1) )
       => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( disjoint(X2,X3)
        | disjoint(X0,X1) )
     => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).

fof(f87,plain,
    ( ! [X2,X0,X1] : ~ in(X0,set_intersection2(cartesian_product2(sK4,X1),cartesian_product2(sK5,X2)))
    | ~ spl10_1 ),
    inference(resolution,[],[f82,f41]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
        & in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
        & ordered_pair(sK2(X0,X1,X2,X3,X4),sK3(X0,X1,X2,X3,X4)) = X0 )
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f18,f25]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X2,X4))
          & in(X5,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0 )
     => ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
        & in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
        & ordered_pair(sK2(X0,X1,X2,X3,X4),sK3(X0,X1,X2,X3,X4)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X2,X4))
          & in(X5,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0 )
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1,X2,X3,X4] :
      ~ ( ! [X5,X6] :
            ~ ( in(X6,set_intersection2(X2,X4))
              & in(X5,set_intersection2(X1,X3))
              & ordered_pair(X5,X6) = X0 )
        & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

fof(f82,plain,
    ( ! [X0] : ~ in(X0,set_intersection2(sK4,sK5))
    | ~ spl10_1 ),
    inference(resolution,[],[f58,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( ~ disjoint(X0,X1)
      | ~ in(X2,set_intersection2(X0,X1)) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f58,plain,
    ( disjoint(sK4,sK5)
    | ~ spl10_1 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl10_1
  <=> disjoint(sK4,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).

fof(f81,plain,
    ~ spl10_2,
    inference(avatar_contradiction_clause,[],[f79]) ).

fof(f79,plain,
    ( $false
    | ~ spl10_2 ),
    inference(resolution,[],[f68,f66]) ).

fof(f68,plain,
    ( ! [X2,X0,X1] : ~ in(X0,set_intersection2(cartesian_product2(X1,sK6),cartesian_product2(X2,sK7)))
    | ~ spl10_2 ),
    inference(resolution,[],[f64,f42]) ).

fof(f42,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f64,plain,
    ( ! [X0] : ~ in(X0,set_intersection2(sK6,sK7))
    | ~ spl10_2 ),
    inference(resolution,[],[f62,f46]) ).

fof(f62,plain,
    ( disjoint(sK6,sK7)
    | ~ spl10_2 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl10_2
  <=> disjoint(sK6,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).

fof(f63,plain,
    ( spl10_1
    | spl10_2 ),
    inference(avatar_split_clause,[],[f43,f60,f56]) ).

fof(f43,plain,
    ( disjoint(sK6,sK7)
    | disjoint(sK4,sK5) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem    : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% 0.05/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34  % Computer : n029.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   : Mon May 20 12:34:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.34  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.73  % (4314)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.53/0.73  % (4315)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.53/0.73  % (4316)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.53/0.73  % (4317)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.53/0.73  % (4318)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.53/0.73  % (4319)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.53/0.73  % (4312)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.53/0.73  % (4317)Refutation not found, incomplete strategy% (4317)------------------------------
% 0.53/0.73  % (4317)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.53/0.73  % (4317)Termination reason: Refutation not found, incomplete strategy
% 0.53/0.73  
% 0.53/0.73  % (4317)Memory used [KB]: 972
% 0.53/0.73  % (4317)Time elapsed: 0.003 s
% 0.53/0.73  % (4317)Instructions burned: 2 (million)
% 0.53/0.73  % (4317)------------------------------
% 0.53/0.73  % (4317)------------------------------
% 0.53/0.73  % (4319)Also succeeded, but the first one will report.
% 0.53/0.73  % (4316)First to succeed.
% 0.53/0.73  % (4318)Also succeeded, but the first one will report.
% 0.53/0.73  % (4312)Also succeeded, but the first one will report.
% 0.53/0.73  % (4316)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4311"
% 0.53/0.73  % (4315)Also succeeded, but the first one will report.
% 0.53/0.73  % (4314)Also succeeded, but the first one will report.
% 0.53/0.73  % (4316)Refutation found. Thanks to Tanya!
% 0.53/0.73  % SZS status Theorem for theBenchmark
% 0.53/0.73  % SZS output start Proof for theBenchmark
% See solution above
% 0.53/0.73  % (4316)------------------------------
% 0.53/0.73  % (4316)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.53/0.73  % (4316)Termination reason: Refutation
% 0.53/0.73  
% 0.53/0.73  % (4316)Memory used [KB]: 1062
% 0.53/0.73  % (4316)Time elapsed: 0.004 s
% 0.53/0.73  % (4316)Instructions burned: 5 (million)
% 0.53/0.73  % (4311)Success in time 0.375 s
% 0.53/0.73  % Vampire---4.8 exiting
%------------------------------------------------------------------------------