TSTP Solution File: SEU746_8 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU746_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 04:06:35 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (   7 unt;   1 typ;   0 def)
%            Number of atoms       :  285 (  34 equ)
%            Maximal formula atoms :   18 (  11 avg)
%            Number of connectives :  171 (  42   ~;  34   |;  51   &)
%                                         (   1 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  173 ( 140 fml;  33 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   12 (   9 usr;   8 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   66 (  41   !;  25   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_7,type,
    sK3: $o ).

tff(f94,plain,
    $false,
    inference(unit_resulting_resolution,[],[f27,f28,f22,f29]) ).

tff(f29,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ in(X2,binunion(X0,X1))
      | in(X2,X0)
      | in(X2,X1) ),
    inference(subsumption_resolution,[],[f26,f18]) ).

tff(f18,plain,
    binunionE,
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ( ( $true != sK3 )
    & ( ( $true = sK3 )
      | ~ in(sK4,sK2) )
    & ( ( $true = sK3 )
      | ~ in(sK4,sK1) )
    & in(sK4,binunion(sK1,sK2))
    & in(sK4,sK0)
    & in(sK2,powerset(sK0))
    & in(sK1,powerset(sK0))
    & binunionE ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f11,f16,f15,f14]) ).

tff(f14,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ? [X3: $o,X4] :
                ( ( $true != (X3) )
                & ( ( $true = (X3) )
                  | ~ in(X4,X2) )
                & ( ( $true = (X3) )
                  | ~ in(X4,X1) )
                & in(X4,binunion(X1,X2))
                & in(X4,X0) )
            & in(X2,powerset(X0)) )
        & in(X1,powerset(X0)) )
   => ( ? [X2] :
          ( ? [X4,X3: $o] :
              ( ( $true != (X3) )
              & ( ( $true = (X3) )
                | ~ in(X4,X2) )
              & ( ( $true = (X3) )
                | ~ in(X4,sK1) )
              & in(X4,binunion(sK1,X2))
              & in(X4,sK0) )
          & in(X2,powerset(sK0)) )
      & in(sK1,powerset(sK0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f15,plain,
    ( ? [X2] :
        ( ? [X4,X3: $o] :
            ( ( $true != (X3) )
            & ( ( $true = (X3) )
              | ~ in(X4,X2) )
            & ( ( $true = (X3) )
              | ~ in(X4,sK1) )
            & in(X4,binunion(sK1,X2))
            & in(X4,sK0) )
        & in(X2,powerset(sK0)) )
   => ( ? [X4,X3: $o] :
          ( ( $true != (X3) )
          & ( ( $true = (X3) )
            | ~ in(X4,sK2) )
          & ( ( $true = (X3) )
            | ~ in(X4,sK1) )
          & in(X4,binunion(sK1,sK2))
          & in(X4,sK0) )
      & in(sK2,powerset(sK0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ( ? [X4,X3: $o] :
        ( ( $true != (X3) )
        & ( ( $true = (X3) )
          | ~ in(X4,sK2) )
        & ( ( $true = (X3) )
          | ~ in(X4,sK1) )
        & in(X4,binunion(sK1,sK2))
        & in(X4,sK0) )
   => ( ( $true != sK3 )
      & ( ( $true = sK3 )
        | ~ in(sK4,sK2) )
      & ( ( $true = sK3 )
        | ~ in(sK4,sK1) )
      & in(sK4,binunion(sK1,sK2))
      & in(sK4,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ? [X3: $o,X4] :
                ( ( $true != (X3) )
                & ( ( $true = (X3) )
                  | ~ in(X4,X2) )
                & ( ( $true = (X3) )
                  | ~ in(X4,X1) )
                & in(X4,binunion(X1,X2))
                & in(X4,X0) )
            & in(X2,powerset(X0)) )
        & in(X1,powerset(X0)) )
    & binunionE ),
    inference(flattening,[],[f10]) ).

tff(f10,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ? [X3: $o,X4] :
                ( ( $true != (X3) )
                & ( ( $true = (X3) )
                  | ~ in(X4,X2) )
                & ( ( $true = (X3) )
                  | ~ in(X4,X1) )
                & in(X4,binunion(X1,X2))
                & in(X4,X0) )
            & in(X2,powerset(X0)) )
        & in(X1,powerset(X0)) )
    & binunionE ),
    inference(ennf_transformation,[],[f7]) ).

tff(f7,plain,
    ~ ( binunionE
     => ! [X0,X1] :
          ( in(X1,powerset(X0))
         => ! [X2] :
              ( in(X2,powerset(X0))
             => ! [X3: $o,X4] :
                  ( in(X4,X0)
                 => ( in(X4,binunion(X1,X2))
                   => ( ( in(X4,X1)
                       => ( $true = (X3) ) )
                     => ( ( in(X4,X2)
                         => ( $true = (X3) ) )
                       => ( $true = (X3) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f6]) ).

tff(f6,plain,
    ~ ( binunionE
     => ! [X0,X1] :
          ( in(X1,powerset(X0))
         => ! [X2] :
              ( in(X2,powerset(X0))
             => ! [X3: $o,X4] :
                  ( in(X4,X0)
                 => ( in(X4,binunion(X1,X2))
                   => ( ( in(X4,X1)
                       => (X3) )
                     => ( ( in(X4,X2)
                         => (X3) )
                       => (X3) ) ) ) ) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,negated_conjecture,
    ~ ( binunionE
     => ! [X0,X3] :
          ( in(X3,powerset(X0))
         => ! [X4] :
              ( in(X4,powerset(X0))
             => ! [X5: $o,X2] :
                  ( in(X2,X0)
                 => ( in(X2,binunion(X3,X4))
                   => ( ( in(X2,X3)
                       => (X5) )
                     => ( ( in(X2,X4)
                         => (X5) )
                       => (X5) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f2]) ).

tff(f2,conjecture,
    ( binunionE
   => ! [X0,X3] :
        ( in(X3,powerset(X0))
       => ! [X4] :
            ( in(X4,powerset(X0))
           => ! [X5: $o,X2] :
                ( in(X2,X0)
               => ( in(X2,binunion(X3,X4))
                 => ( ( in(X2,X3)
                     => (X5) )
                   => ( ( in(X2,X4)
                       => (X5) )
                     => (X5) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTE) ).

tff(f26,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( in(X2,X1)
      | in(X2,X0)
      | ~ in(X2,binunion(X0,X1))
      | ~ binunionE ),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ( ! [X0,X1,X2] :
        ( in(X2,X1)
        | in(X2,X0)
        | ~ in(X2,binunion(X0,X1)) )
    | ~ binunionE ),
    inference(flattening,[],[f12]) ).

tff(f12,plain,
    ( ! [X0,X1,X2] :
        ( in(X2,X1)
        | in(X2,X0)
        | ~ in(X2,binunion(X0,X1)) )
    | ~ binunionE ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,plain,
    ( binunionE
   => ! [X0,X1,X2] :
        ( in(X2,binunion(X0,X1))
       => ( in(X2,X1)
          | in(X2,X0) ) ) ),
    inference(unused_predicate_definition_removal,[],[f8]) ).

tff(f8,plain,
    ( binunionE
  <=> ! [X0,X1,X2] :
        ( in(X2,binunion(X0,X1))
       => ( in(X2,X1)
          | in(X2,X0) ) ) ),
    inference(fool_elimination,[],[f1]) ).

tff(f1,axiom,
    ( binunionE
    = ( ! [X0,X1,X2] :
          ( in(X2,binunion(X0,X1))
         => ( in(X2,X1)
            | in(X2,X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).

tff(f22,plain,
    in(sK4,binunion(sK1,sK2)),
    inference(cnf_transformation,[],[f17]) ).

tff(f28,plain,
    ~ in(sK4,sK1),
    inference(subsumption_resolution,[],[f23,f25]) ).

tff(f25,plain,
    $true != sK3,
    inference(cnf_transformation,[],[f17]) ).

tff(f23,plain,
    ( ( $true = sK3 )
    | ~ in(sK4,sK1) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f27,plain,
    ~ in(sK4,sK2),
    inference(subsumption_resolution,[],[f24,f25]) ).

tff(f24,plain,
    ( ( $true = sK3 )
    | ~ in(sK4,sK2) ),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU746_8 : TPTP v8.2.0. Released v8.0.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n021.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun May 19 15:37:53 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (23025)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (23032)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)
% 0.15/0.37  % (23031)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)
% 0.15/0.37  % (23029)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (23030)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)
% 0.15/0.37  % (23028)WARNING: value z3 for option sas not known
% 0.15/0.37  Detected minimum model sizes of [1,1]
% 0.15/0.37  Detected maximum model sizes of [max,3]
% 0.15/0.37  TRYING [1,1]
% 0.15/0.37  TRYING [1,2]
% 0.15/0.37  TRYING [2,2]
% 0.15/0.37  % (23032)First to succeed.
% 0.15/0.37  TRYING [1,3]
% 0.15/0.37  % (23026)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (23027)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  TRYING [2,3]
% 0.15/0.37  % (23031)Also succeeded, but the first one will report.
% 0.15/0.37  % (23030)Also succeeded, but the first one will report.
% 0.15/0.37  TRYING [3,2]
% 0.15/0.37  % (23032)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23025"
% 0.15/0.37  % (23028)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)
% 0.15/0.38  % (23032)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (23032)------------------------------
% 0.15/0.38  % (23032)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (23032)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (23032)Memory used [KB]: 757
% 0.15/0.38  % (23032)Time elapsed: 0.005 s
% 0.15/0.38  % (23032)Instructions burned: 5 (million)
% 0.15/0.38  % (23025)Success in time 0.005 s
%------------------------------------------------------------------------------