TSTP Solution File: SET600+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.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 03:19:36 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   47 (  10 unt;   0 def)
%            Number of atoms       :  150 (  76 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  160 (  57   ~;  63   |;  30   &)
%                                         (   6 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   68 (  57   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f163,plain,
    $false,
    inference(unit_resulting_resolution,[],[f35,f35,f97,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

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

fof(f97,plain,
    member(sK4(union(empty_set,empty_set),empty_set),union(empty_set,empty_set)),
    inference(unit_resulting_resolution,[],[f91,f63]) ).

fof(f63,plain,
    ! [X0] :
      ( member(sK4(X0,empty_set),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f61,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,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,[],[f26]) ).

fof(f26,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,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f61,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(resolution,[],[f40,f58]) ).

fof(f58,plain,
    ! [X0] : subset(empty_set,X0),
    inference(unit_resulting_resolution,[],[f35,f48]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

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

fof(f91,plain,
    empty_set != union(empty_set,empty_set),
    inference(unit_resulting_resolution,[],[f80,f90,f57]) ).

fof(f57,plain,
    ( empty_set != union(empty_set,empty_set)
    | empty_set != sK1
    | empty_set != sK2 ),
    inference(inner_rewriting,[],[f56]) ).

fof(f56,plain,
    ( empty_set != sK2
    | empty_set != sK1
    | empty_set != union(sK1,empty_set) ),
    inference(inner_rewriting,[],[f34]) ).

fof(f34,plain,
    ( empty_set != sK2
    | empty_set != sK1
    | empty_set != union(sK1,sK2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( empty_set != sK2
      | empty_set != sK1
      | empty_set != union(sK1,sK2) )
    & ( ( empty_set = sK2
        & empty_set = sK1 )
      | empty_set = union(sK1,sK2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0,X1] :
        ( ( empty_set != X1
          | empty_set != X0
          | union(X0,X1) != empty_set )
        & ( ( empty_set = X1
            & empty_set = X0 )
          | union(X0,X1) = empty_set ) )
   => ( ( empty_set != sK2
        | empty_set != sK1
        | empty_set != union(sK1,sK2) )
      & ( ( empty_set = sK2
          & empty_set = sK1 )
        | empty_set = union(sK1,sK2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1] :
      ( ( empty_set != X1
        | empty_set != X0
        | union(X0,X1) != empty_set )
      & ( ( empty_set = X1
          & empty_set = X0 )
        | union(X0,X1) = empty_set ) ),
    inference(flattening,[],[f15]) ).

fof(f15,plain,
    ? [X0,X1] :
      ( ( empty_set != X1
        | empty_set != X0
        | union(X0,X1) != empty_set )
      & ( ( empty_set = X1
          & empty_set = X0 )
        | union(X0,X1) = empty_set ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ? [X0,X1] :
      ( union(X0,X1) = empty_set
    <~> ( empty_set = X1
        & empty_set = X0 ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( union(X0,X1) = empty_set
      <=> ( empty_set = X1
          & empty_set = X0 ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] :
      ( union(X0,X1) = empty_set
    <=> ( empty_set = X1
        & empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).

fof(f90,plain,
    empty_set = sK1,
    inference(subsumption_resolution,[],[f89,f35]) ).

fof(f89,plain,
    ( member(sK4(sK1,empty_set),empty_set)
    | empty_set = sK1 ),
    inference(duplicate_literal_removal,[],[f88]) ).

fof(f88,plain,
    ( member(sK4(sK1,empty_set),empty_set)
    | empty_set = sK1
    | empty_set = sK1 ),
    inference(superposition,[],[f68,f83]) ).

fof(f83,plain,
    ( empty_set = union(empty_set,sK1)
    | empty_set = sK1 ),
    inference(superposition,[],[f82,f37]) ).

fof(f37,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f82,plain,
    ( empty_set = union(sK1,empty_set)
    | empty_set = sK1 ),
    inference(superposition,[],[f32,f80]) ).

fof(f32,plain,
    ( empty_set = union(sK1,sK2)
    | empty_set = sK1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( member(sK4(X0,empty_set),union(X1,X0))
      | empty_set = X0 ),
    inference(resolution,[],[f63,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f80,plain,
    empty_set = sK2,
    inference(subsumption_resolution,[],[f79,f35]) ).

fof(f79,plain,
    ( member(sK4(sK2,empty_set),empty_set)
    | empty_set = sK2 ),
    inference(duplicate_literal_removal,[],[f77]) ).

fof(f77,plain,
    ( member(sK4(sK2,empty_set),empty_set)
    | empty_set = sK2
    | empty_set = sK2 ),
    inference(superposition,[],[f68,f33]) ).

fof(f33,plain,
    ( empty_set = union(sK1,sK2)
    | empty_set = sK2 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f35,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n015.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon May 20 11:31:38 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.38  % (7157)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (7160)WARNING: value z3 for option sas not known
% 0.15/0.39  % (7158)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (7159)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  % (7164)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  % (7162)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  % (7161)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (7163)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  % (7160)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)
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [2]
% 0.15/0.40  TRYING [3]
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [2]
% 0.15/0.40  TRYING [4]
% 0.15/0.40  % (7164)First to succeed.
% 0.15/0.40  % (7164)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7157"
% 0.15/0.40  % (7163)Also succeeded, but the first one will report.
% 0.15/0.40  % (7164)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (7164)------------------------------
% 0.15/0.40  % (7164)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40  % (7164)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (7164)Memory used [KB]: 834
% 0.15/0.40  % (7164)Time elapsed: 0.007 s
% 0.15/0.40  % (7164)Instructions burned: 9 (million)
% 0.15/0.40  % (7157)Success in time 0.024 s
%------------------------------------------------------------------------------