TSTP Solution File: SEU633_8 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU633_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n004.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 15:35:10 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   32 (   9 unt;   2 typ;   0 def)
%            Number of atoms       :  165 (  20 equ)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :  113 (  37   ~;  25   |;  25   &)
%                                         (   1 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   99 (  63 fml;  36 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   2   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   6 usr;   5 prp; 0-3 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 3-3 aty)
%            Number of variables   :   76 (  63   !;  13   ?;  25   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_5,type,
    sK3: ( $o * $i * $i ) > $i ).

tff(pred_def_3,type,
    sP0: ( $o * $i * $i ) > $o ).

tff(f101,plain,
    $false,
    inference(unit_resulting_resolution,[],[f74,f86,f25]) ).

tff(f25,plain,
    ! [X2: $i,X0: $o,X1: $i] :
      ( ~ sP0((X0),X1,X2)
      | in(sK3((X0),X1,X2),X1) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,plain,
    ! [X0: $o,X1,X2] :
      ( ( ( $true != (X0) )
        & in(sK3((X0),X1,X2),X1)
        & in(X2,sK3((X0),X1,X2)) )
      | ~ sP0((X0),X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f18,f19]) ).

tff(f19,plain,
    ! [X0: $o,X1,X2] :
      ( ? [X3] :
          ( ( $true != (X0) )
          & in(X3,X1)
          & in(X2,X3) )
     => ( ( $true != (X0) )
        & in(sK3((X0),X1,X2),X1)
        & in(X2,sK3((X0),X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ! [X0: $o,X1,X2] :
      ( ? [X3] :
          ( ( $true != (X0) )
          & in(X3,X1)
          & in(X2,X3) )
      | ~ sP0((X0),X1,X2) ),
    inference(rectify,[],[f17]) ).

tff(f17,plain,
    ! [X2: $o,X0,X1] :
      ( ? [X3] :
          ( ( $true != (X2) )
          & in(X3,X0)
          & in(X1,X3) )
      | ~ sP0((X2),X0,X1) ),
    inference(nnf_transformation,[],[f13]) ).

tff(f13,plain,
    ! [X2: $o,X0,X1] :
      ( ? [X3] :
          ( ( $true != (X2) )
          & in(X3,X0)
          & in(X1,X3) )
      | ~ sP0((X2),X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f86,plain,
    ~ in(sK3($false,sK1,sK2),sK1),
    inference(unit_resulting_resolution,[],[f82,f23]) ).

tff(f23,plain,
    ! [X2: $i] :
      ( ~ in(sK2,X2)
      | ~ in(X2,sK1) ),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,plain,
    ( ! [X2] :
        ( ~ in(sK2,X2)
        | ~ in(X2,sK1) )
    & in(sK2,setunion(sK1))
    & setunionE ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f15]) ).

tff(f15,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
            ( ~ in(X1,X2)
            | ~ in(X2,X0) )
        & in(X1,setunion(X0)) )
   => ( ! [X2] :
          ( ~ in(sK2,X2)
          | ~ in(X2,sK1) )
      & in(sK2,setunion(sK1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f10,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
            ( ~ in(X1,X2)
            | ~ in(X2,X0) )
        & in(X1,setunion(X0)) )
    & setunionE ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ~ ( setunionE
     => ! [X0,X1] :
          ( in(X1,setunion(X0))
         => ? [X2] :
              ( in(X1,X2)
              & in(X2,X0) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,negated_conjecture,
    ~ ( setunionE
     => ! [X0,X1] :
          ( in(X1,setunion(X0))
         => ? [X4] :
              ( in(X1,X4)
              & in(X4,X0) ) ) ),
    inference(negated_conjecture,[],[f2]) ).

tff(f2,conjecture,
    ( setunionE
   => ! [X0,X1] :
        ( in(X1,setunion(X0))
       => ? [X4] :
            ( in(X1,X4)
            & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).

tff(f82,plain,
    in(sK2,sK3($false,sK1,sK2)),
    inference(unit_resulting_resolution,[],[f74,f24]) ).

tff(f24,plain,
    ! [X2: $i,X0: $o,X1: $i] :
      ( ~ sP0((X0),X1,X2)
      | in(X2,sK3((X0),X1,X2)) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f74,plain,
    sP0($false,sK1,sK2),
    inference(unit_resulting_resolution,[],[f4,f22,f29]) ).

tff(f29,plain,
    ! [X2: $o,X0: $i,X1: $i] :
      ( ~ in(X1,setunion(X0))
      | sP0((X2),X0,X1)
      | ( $true = (X2) ) ),
    inference(subsumption_resolution,[],[f27,f21]) ).

tff(f21,plain,
    setunionE,
    inference(cnf_transformation,[],[f16]) ).

tff(f27,plain,
    ! [X2: $o,X0: $i,X1: $i] :
      ( ( $true = (X2) )
      | sP0((X2),X0,X1)
      | ~ in(X1,setunion(X0))
      | ~ setunionE ),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,plain,
    ( ! [X0,X1] :
        ( ! [X2: $o] :
            ( ( $true = (X2) )
            | sP0((X2),X0,X1) )
        | ~ in(X1,setunion(X0)) )
    | ~ setunionE ),
    inference(definition_folding,[],[f12,f13]) ).

tff(f12,plain,
    ( ! [X0,X1] :
        ( ! [X2: $o] :
            ( ( $true = (X2) )
            | ? [X3] :
                ( ( $true != (X2) )
                & in(X3,X0)
                & in(X1,X3) ) )
        | ~ in(X1,setunion(X0)) )
    | ~ setunionE ),
    inference(flattening,[],[f11]) ).

tff(f11,plain,
    ( ! [X0,X1] :
        ( ! [X2: $o] :
            ( ( $true = (X2) )
            | ? [X3] :
                ( ( $true != (X2) )
                & in(X3,X0)
                & in(X1,X3) ) )
        | ~ in(X1,setunion(X0)) )
    | ~ setunionE ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,plain,
    ( setunionE
   => ! [X0,X1] :
        ( in(X1,setunion(X0))
       => ! [X2: $o] :
            ( ! [X3] :
                ( in(X1,X3)
               => ( in(X3,X0)
                 => ( $true = (X2) ) ) )
           => ( $true = (X2) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f7]) ).

tff(f7,plain,
    ( setunionE
  <=> ! [X0,X1] :
        ( in(X1,setunion(X0))
       => ! [X2: $o] :
            ( ! [X3] :
                ( in(X1,X3)
               => ( in(X3,X0)
                 => ( $true = (X2) ) ) )
           => ( $true = (X2) ) ) ) ),
    inference(fool_elimination,[],[f6]) ).

tff(f6,plain,
    ( setunionE
    = ( ! [X0,X1] :
          ( in(X1,setunion(X0))
         => ! [X2: $o] :
              ( ! [X3] :
                  ( in(X1,X3)
                 => ( in(X3,X0)
                   => (X2) ) )
             => (X2) ) ) ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ( setunionE
    = ( ! [X0,X1] :
          ( in(X1,setunion(X0))
         => ! [X2: $o] :
              ( ! [X3] :
                  ( in(X1,X3)
                 => ( in(X3,X0)
                   => (X2) ) )
             => (X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).

tff(f22,plain,
    in(sK2,setunion(sK1)),
    inference(cnf_transformation,[],[f16]) ).

tff(f4,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEU633_8 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n004.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   : Mon Apr 29 20:59:18 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (24995)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (24998)WARNING: value z3 for option sas not known
% 0.15/0.38  % (24999)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (24997)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (25000)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)
% 0.15/0.38  % (24998)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  % (25001)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)
% 0.15/0.38  % (24996)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (25002)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)
% 0.15/0.38  Detected minimum model sizes of [1,1]
% 0.15/0.38  Detected maximum model sizes of [max,2]
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  TRYING [1,2]
% 0.15/0.38  TRYING [2,2]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3,2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (25002)First to succeed.
% 0.15/0.38  TRYING [4,2]
% 0.15/0.38  % (25000)Also succeeded, but the first one will report.
% 0.15/0.39  TRYING [4]
% 0.15/0.39  % (24998)Also succeeded, but the first one will report.
% 0.15/0.39  % (25002)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  % (25002)------------------------------
% 0.15/0.39  % (25002)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (25002)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (25002)Memory used [KB]: 759
% 0.15/0.39  % (25002)Time elapsed: 0.005 s
% 0.15/0.39  % (25002)Instructions burned: 6 (million)
% 0.15/0.39  % (25002)------------------------------
% 0.15/0.39  % (25002)------------------------------
% 0.15/0.39  % (24995)Success in time 0.022 s
%------------------------------------------------------------------------------