TSTP Solution File: SET628+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET628+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 : n023.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 09:14:33 EDT 2024

% Result   : Theorem 0.19s 0.37s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   8 unt;   0 def)
%            Number of atoms       :  132 (  21 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  149 (  56   ~;  58   |;  25   &)
%                                         (   6 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   62 (  52   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f76,plain,
    $false,
    inference(resolution,[],[f75,f66]) ).

fof(f66,plain,
    ! [X0] : ~ intersect(sK0,X0),
    inference(backward_demodulation,[],[f43,f62]) ).

fof(f62,plain,
    empty_set = sK0,
    inference(duplicate_literal_removal,[],[f59]) ).

fof(f59,plain,
    ( empty_set = sK0
    | empty_set = sK0 ),
    inference(resolution,[],[f58,f25]) ).

fof(f25,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f58,plain,
    ! [X0] :
      ( member(sK1(X0,sK0),X0)
      | sK0 = X0
      | empty_set = sK0 ),
    inference(resolution,[],[f29,f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | empty_set = sK0 ),
    inference(duplicate_literal_removal,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | ~ member(X0,sK0)
      | empty_set = sK0 ),
    inference(resolution,[],[f35,f41]) ).

fof(f41,plain,
    ( ~ intersect(sK0,sK0)
    | empty_set = sK0 ),
    inference(resolution,[],[f32,f24]) ).

fof(f24,plain,
    ( ~ not_equal(sK0,empty_set)
    | ~ intersect(sK0,sK0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ( ~ not_equal(sK0,empty_set)
      | ~ intersect(sK0,sK0) )
    & ( not_equal(sK0,empty_set)
      | intersect(sK0,sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0] :
        ( ( ~ not_equal(X0,empty_set)
          | ~ intersect(X0,X0) )
        & ( not_equal(X0,empty_set)
          | intersect(X0,X0) ) )
   => ( ( ~ not_equal(sK0,empty_set)
        | ~ intersect(sK0,sK0) )
      & ( not_equal(sK0,empty_set)
        | intersect(sK0,sK0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0] :
      ( ( ~ not_equal(X0,empty_set)
        | ~ intersect(X0,X0) )
      & ( not_equal(X0,empty_set)
        | intersect(X0,X0) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ? [X0] :
      ( intersect(X0,X0)
    <~> not_equal(X0,empty_set) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0] :
        ( intersect(X0,X0)
      <=> not_equal(X0,empty_set) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0] :
      ( intersect(X0,X0)
    <=> not_equal(X0,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).

fof(f32,plain,
    ! [X0,X1] :
      ( not_equal(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( not_equal(X0,X1)
        | X0 = X1 )
      & ( X0 != X1
        | ~ not_equal(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( not_equal(X0,X1)
    <=> X0 != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( intersect(X0,X1)
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ( member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) )
        | ~ intersect(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & member(X3,X0) )
     => ( member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & member(X3,X0) )
        | ~ intersect(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
        | ~ intersect(X0,X1) ) ),
    inference(nnf_transformation,[],[f1]) ).

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

fof(f29,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X1)
      | X0 = X1
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK1(X0,X1),X1)
            | ~ member(sK1(X0,X1),X0) )
          & ( member(sK1(X0,X1),X1)
            | member(sK1(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK1(X0,X1),X1)
          | ~ member(sK1(X0,X1),X0) )
        & ( member(sK1(X0,X1),X1)
          | member(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f43,plain,
    ! [X0] : ~ intersect(empty_set,X0),
    inference(resolution,[],[f33,f25]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | ~ intersect(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f75,plain,
    intersect(sK0,sK0),
    inference(resolution,[],[f63,f38]) ).

fof(f38,plain,
    ! [X1] : ~ not_equal(X1,X1),
    inference(equality_resolution,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ not_equal(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f63,plain,
    ( not_equal(sK0,sK0)
    | intersect(sK0,sK0) ),
    inference(backward_demodulation,[],[f23,f62]) ).

fof(f23,plain,
    ( not_equal(sK0,empty_set)
    | intersect(sK0,sK0) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET628+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 16:57:08 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (24336)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (24341)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.36  TRYING [1]
% 0.19/0.36  TRYING [2]
% 0.19/0.36  TRYING [3]
% 0.19/0.36  % (24340)WARNING: value z3 for option sas not known
% 0.19/0.36  TRYING [4]
% 0.19/0.36  % (24339)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.37  % (24338)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.37  % (24340)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)
% 0.19/0.37  TRYING [5]
% 0.19/0.37  % (24343)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)
% 0.19/0.37  % (24344)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)
% 0.19/0.37  % (24342)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)
% 0.19/0.37  TRYING [1]
% 0.19/0.37  % (24343)First to succeed.
% 0.19/0.37  % (24344)Also succeeded, but the first one will report.
% 0.19/0.37  TRYING [6]
% 0.19/0.37  TRYING [2]
% 0.19/0.37  % (24343)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24336"
% 0.19/0.37  TRYING [1]
% 0.19/0.37  TRYING [2]
% 0.19/0.37  % (24340)Also succeeded, but the first one will report.
% 0.19/0.37  % (24343)Refutation found. Thanks to Tanya!
% 0.19/0.37  % SZS status Theorem for theBenchmark
% 0.19/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.37  % (24343)------------------------------
% 0.19/0.37  % (24343)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.37  % (24343)Termination reason: Refutation
% 0.19/0.37  
% 0.19/0.37  % (24343)Memory used [KB]: 768
% 0.19/0.37  % (24343)Time elapsed: 0.005 s
% 0.19/0.37  % (24343)Instructions burned: 4 (million)
% 0.19/0.37  % (24336)Success in time 0.021 s
%------------------------------------------------------------------------------