TSTP Solution File: SET941+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET941+1 : 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 : 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 : Tue Apr 30 15:14:03 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   42 (  10 unt;   0 def)
%            Number of atoms       :  150 (   5 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  171 (  63   ~;  57   |;  34   &)
%                                         (   8 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   94 (  79   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f86,plain,
    $false,
    inference(subsumption_resolution,[],[f84,f73]) ).

fof(f73,plain,
    in(sK4(union(sK2),sK3),sK6(sK2,sK4(union(sK2),sK3))),
    inference(unit_resulting_resolution,[],[f70,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | in(X1,sK6(X0,X1)) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | ~ in(X1,X2) ) )
      & ( ( in(sK6(X0,X1),X0)
          & in(X1,sK6(X0,X1)) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X0)
          & in(X1,X3) )
     => ( in(sK6(X0,X1),X0)
        & in(X1,sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | ~ in(X1,X2) ) )
      & ( ? [X3] :
            ( in(X3,X0)
            & in(X1,X3) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X2] :
      ( ( sP0(X0,X2)
        | ! [X3] :
            ( ~ in(X3,X0)
            | ~ in(X2,X3) ) )
      & ( ? [X3] :
            ( in(X3,X0)
            & in(X2,X3) )
        | ~ sP0(X0,X2) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X2] :
      ( sP0(X0,X2)
    <=> ? [X3] :
          ( in(X3,X0)
          & in(X2,X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f70,plain,
    sP0(sK2,sK4(union(sK2),sK3)),
    inference(unit_resulting_resolution,[],[f57,f53,f42]) ).

fof(f42,plain,
    ! [X3,X0,X1] :
      ( ~ sP1(X0,X1)
      | ~ in(X3,X1)
      | sP0(X0,X3) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( ( ~ sP0(X0,sK5(X0,X1))
            | ~ in(sK5(X0,X1),X1) )
          & ( sP0(X0,sK5(X0,X1))
            | in(sK5(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ sP0(X0,X3) )
            & ( sP0(X0,X3)
              | ~ in(X3,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f23,f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ sP0(X0,X2)
            | ~ in(X2,X1) )
          & ( sP0(X0,X2)
            | in(X2,X1) ) )
     => ( ( ~ sP0(X0,sK5(X0,X1))
          | ~ in(sK5(X0,X1),X1) )
        & ( sP0(X0,sK5(X0,X1))
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] :
            ( ( ~ sP0(X0,X2)
              | ~ in(X2,X1) )
            & ( sP0(X0,X2)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ sP0(X0,X3) )
            & ( sP0(X0,X3)
              | ~ in(X3,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] :
            ( ( ~ sP0(X0,X2)
              | ~ in(X2,X1) )
            & ( sP0(X0,X2)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ sP0(X0,X2) )
            & ( sP0(X0,X2)
              | ~ in(X2,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> sP0(X0,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f53,plain,
    ! [X0] : sP1(X0,union(X0)),
    inference(equality_resolution,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f3,f14,f13]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).

fof(f57,plain,
    in(sK4(union(sK2),sK3),union(sK2)),
    inference(unit_resulting_resolution,[],[f36,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f36,plain,
    ~ subset(union(sK2),sK3),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( ~ subset(union(sK2),sK3)
    & ! [X2] :
        ( subset(X2,sK3)
        | ~ in(X2,sK2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f16]) ).

fof(f16,plain,
    ( ? [X0,X1] :
        ( ~ subset(union(X0),X1)
        & ! [X2] :
            ( subset(X2,X1)
            | ~ in(X2,X0) ) )
   => ( ~ subset(union(sK2),sK3)
      & ! [X2] :
          ( subset(X2,sK3)
          | ~ in(X2,sK2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0,X1] :
      ( ~ subset(union(X0),X1)
      & ! [X2] :
          ( subset(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( ! [X2] :
            ( in(X2,X0)
           => subset(X2,X1) )
       => subset(union(X0),X1) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
         => subset(X2,X1) )
     => subset(union(X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).

fof(f84,plain,
    ~ in(sK4(union(sK2),sK3),sK6(sK2,sK4(union(sK2),sK3))),
    inference(unit_resulting_resolution,[],[f62,f78,f39]) ).

fof(f39,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f78,plain,
    subset(sK6(sK2,sK4(union(sK2),sK3)),sK3),
    inference(unit_resulting_resolution,[],[f72,f35]) ).

fof(f35,plain,
    ! [X2] :
      ( ~ in(X2,sK2)
      | subset(X2,sK3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f72,plain,
    in(sK6(sK2,sK4(union(sK2),sK3)),sK2),
    inference(unit_resulting_resolution,[],[f70,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | in(sK6(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f62,plain,
    ~ in(sK4(union(sK2),sK3),sK3),
    inference(unit_resulting_resolution,[],[f36,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % 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   : Tue Apr 30 01:01:43 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (19137)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (19138)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (19139)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  % (19140)WARNING: value z3 for option sas not known
% 0.15/0.39  % (19144)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  % (19143)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  TRYING [1]
% 0.15/0.39  % (19142)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  % (19140)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  TRYING [2]
% 0.15/0.39  % (19144)First to succeed.
% 0.15/0.39  % (19141)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [1]
% 0.15/0.39  % (19144)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  % (19144)------------------------------
% 0.15/0.39  % (19144)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (19144)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (19144)Memory used [KB]: 825
% 0.15/0.39  % (19144)Time elapsed: 0.005 s
% 0.15/0.39  % (19144)Instructions burned: 5 (million)
% 0.15/0.39  % (19144)------------------------------
% 0.15/0.39  % (19144)------------------------------
% 0.15/0.39  % (19137)Success in time 0.025 s
%------------------------------------------------------------------------------