TSTP Solution File: SEU531_8 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU531_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 : n010.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 04:05:48 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (  14 unt;   1 typ;   0 def)
%            Number of atoms       :  239 (  60 equ)
%            Maximal formula atoms :    7 (   6 avg)
%            Number of connectives :  143 (  46   ~;  34   |;  24   &)
%                                         (   3 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  142 ( 109 fml;  33 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   1   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  10 usr;   8 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   86 (  77   !;   9   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_4,type,
    sP0: ( $o * $i * $i ) > $o ).

tff(f112,plain,
    $false,
    inference(unit_resulting_resolution,[],[f25,f92,f52,f27,f38]) ).

tff(f38,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ sP4(X0,X2)
      | ~ in(X2,setadjoin(X0,X1))
      | ~ setadjoinE
      | in(X2,X1) ),
    inference(general_splitting,[],[f33,f37_D]) ).

tff(f37,plain,
    ! [X2: $i,X3: $o,X0: $i] :
      ( sP0((X3),X2,X0)
      | ( $true = (X3) )
      | sP4(X0,X2) ),
    inference(cnf_transformation,[],[f37_D]) ).

tff(f37_D,plain,
    ! [X2,X0] :
      ( ! [X3] :
          ( sP0(X3,X2,X0)
          | ( $true = X3 ) )
    <=> ~ sP4(X0,X2) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).

tff(f33,plain,
    ! [X2: $i,X3: $o,X0: $i,X1: $i] :
      ( ( $true = (X3) )
      | in(X2,X1)
      | sP0((X3),X2,X0)
      | ~ in(X2,setadjoin(X0,X1))
      | ~ setadjoinE ),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,plain,
    ( ! [X0,X1,X2] :
        ( ! [X3: $o] :
            ( ( $true = (X3) )
            | ( ( $true != (X3) )
              & in(X2,X1) )
            | sP0((X3),X2,X0) )
        | ~ in(X2,setadjoin(X0,X1)) )
    | ~ setadjoinE ),
    inference(definition_folding,[],[f18,f19]) ).

tff(f19,plain,
    ! [X3: $o,X2,X0] :
      ( ( ( $true != (X3) )
        & ( X0 = X2 ) )
      | ~ sP0((X3),X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

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

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

tff(f13,plain,
    ( setadjoinE
   => ! [X0,X1,X2] :
        ( in(X2,setadjoin(X0,X1))
       => ! [X3: $o] :
            ( ( ( X0 = X2 )
             => ( $true = (X3) ) )
           => ( ( in(X2,X1)
               => ( $true = (X3) ) )
             => ( $true = (X3) ) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

tff(f10,plain,
    ( setadjoinE
  <=> ! [X0,X1,X2] :
        ( in(X2,setadjoin(X0,X1))
       => ! [X3: $o] :
            ( ( ( X0 = X2 )
             => ( $true = (X3) ) )
           => ( ( in(X2,X1)
               => ( $true = (X3) ) )
             => ( $true = (X3) ) ) ) ) ),
    inference(fool_elimination,[],[f9]) ).

tff(f9,plain,
    ( setadjoinE
    = ( ! [X0,X1,X2] :
          ( in(X2,setadjoin(X0,X1))
         => ! [X3: $o] :
              ( ( ( X0 = X2 )
               => (X3) )
             => ( ( in(X2,X1)
                 => (X3) )
               => (X3) ) ) ) ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ( setadjoinE
    = ( ! [X0,X1,X2] :
          ( in(X2,setadjoin(X0,X1))
         => ! [X3: $o] :
              ( ( ( X0 = X2 )
               => (X3) )
             => ( ( in(X2,X1)
                 => (X3) )
               => (X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).

tff(f27,plain,
    in(sK3,setadjoin(sK1,setadjoin(sK2,emptyset))),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ( ( sK2 != sK3 )
    & ( sK1 != sK3 )
    & in(sK3,setadjoin(sK1,setadjoin(sK2,emptyset)))
    & uniqinunit
    & setadjoinE ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f15,f21]) ).

tff(f21,plain,
    ( ? [X0,X1,X2] :
        ( ( X1 != X2 )
        & ( X0 != X2 )
        & in(X2,setadjoin(X0,setadjoin(X1,emptyset))) )
   => ( ( sK2 != sK3 )
      & ( sK1 != sK3 )
      & in(sK3,setadjoin(sK1,setadjoin(sK2,emptyset))) ) ),
    introduced(choice_axiom,[]) ).

tff(f15,plain,
    ( ? [X0,X1,X2] :
        ( ( X1 != X2 )
        & ( X0 != X2 )
        & in(X2,setadjoin(X0,setadjoin(X1,emptyset))) )
    & uniqinunit
    & setadjoinE ),
    inference(flattening,[],[f14]) ).

tff(f14,plain,
    ( ? [X0,X1,X2] :
        ( ( X1 != X2 )
        & ( X0 != X2 )
        & in(X2,setadjoin(X0,setadjoin(X1,emptyset))) )
    & uniqinunit
    & setadjoinE ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,plain,
    ~ ( setadjoinE
     => ( uniqinunit
       => ! [X0,X1,X2] :
            ( in(X2,setadjoin(X0,setadjoin(X1,emptyset)))
           => ( ( X1 = X2 )
              | ( X0 = X2 ) ) ) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,negated_conjecture,
    ~ ( setadjoinE
     => ( uniqinunit
       => ! [X0,X2,X4] :
            ( in(X4,setadjoin(X0,setadjoin(X2,emptyset)))
           => ( ( X2 = X4 )
              | ( X0 = X4 ) ) ) ) ),
    inference(negated_conjecture,[],[f3]) ).

tff(f3,conjecture,
    ( setadjoinE
   => ( uniqinunit
     => ! [X0,X2,X4] :
          ( in(X4,setadjoin(X0,setadjoin(X2,emptyset)))
         => ( ( X2 = X4 )
            | ( X0 = X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).

tff(f52,plain,
    ~ in(sK3,setadjoin(sK2,emptyset)),
    inference(unit_resulting_resolution,[],[f29,f39]) ).

tff(f39,plain,
    ! [X0: $i,X1: $i] :
      ( ~ in(X0,setadjoin(X1,emptyset))
      | ( X0 = X1 ) ),
    inference(subsumption_resolution,[],[f30,f26]) ).

tff(f26,plain,
    uniqinunit,
    inference(cnf_transformation,[],[f22]) ).

tff(f30,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ in(X0,setadjoin(X1,emptyset))
      | ~ uniqinunit ),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,plain,
    ( ! [X0,X1] :
        ( ( X0 = X1 )
        | ~ in(X0,setadjoin(X1,emptyset)) )
    | ~ uniqinunit ),
    inference(ennf_transformation,[],[f12]) ).

tff(f12,plain,
    ( uniqinunit
   => ! [X0,X1] :
        ( in(X0,setadjoin(X1,emptyset))
       => ( X0 = X1 ) ) ),
    inference(unused_predicate_definition_removal,[],[f8]) ).

tff(f8,plain,
    ( uniqinunit
  <=> ! [X0,X1] :
        ( in(X0,setadjoin(X1,emptyset))
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f7]) ).

tff(f7,plain,
    ( uniqinunit
    = ( ! [X0,X1] :
          ( in(X0,setadjoin(X1,emptyset))
         => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ( uniqinunit
    = ( ! [X0,X2] :
          ( in(X0,setadjoin(X2,emptyset))
         => ( X0 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

tff(f29,plain,
    sK2 != sK3,
    inference(cnf_transformation,[],[f22]) ).

tff(f92,plain,
    sP4(sK1,sK3),
    inference(unit_resulting_resolution,[],[f47,f5,f37]) ).

tff(f5,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

tff(f47,plain,
    ! [X0: $o] : ~ sP0((X0),sK3,sK1),
    inference(unit_resulting_resolution,[],[f28,f31]) ).

tff(f31,plain,
    ! [X2: $i,X0: $o,X1: $i] :
      ( ~ sP0((X0),X1,X2)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: $o,X1,X2] :
      ( ( ( $true != (X0) )
        & ( X1 = X2 ) )
      | ~ sP0((X0),X1,X2) ),
    inference(rectify,[],[f23]) ).

tff(f23,plain,
    ! [X3: $o,X2,X0] :
      ( ( ( $true != (X3) )
        & ( X0 = X2 ) )
      | ~ sP0((X3),X2,X0) ),
    inference(nnf_transformation,[],[f19]) ).

tff(f28,plain,
    sK1 != sK3,
    inference(cnf_transformation,[],[f22]) ).

tff(f25,plain,
    setadjoinE,
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU531_8 : TPTP v8.2.0. Released v8.0.0.
% 0.14/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n010.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   : Sun May 19 17:12:23 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (27651)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (27655)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (27657)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  % (27654)WARNING: value z3 for option sas not known
% 0.15/0.39  % (27658)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  % (27653)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  Detected minimum model sizes of [1,1]
% 0.15/0.39  Detected maximum model sizes of [max,2]
% 0.15/0.39  TRYING [1,1]
% 0.15/0.39  TRYING [1,2]
% 0.15/0.39  TRYING [2,2]
% 0.15/0.39  % (27654)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 [3,2]
% 0.15/0.39  % (27656)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  TRYING [4,2]
% 0.15/0.39  % (27658)First to succeed.
% 0.15/0.39  % (27658)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27651"
% 0.15/0.39  Detected minimum model sizes of [1,1]
% 0.15/0.39  Detected maximum model sizes of [max,2]
% 0.15/0.39  TRYING [1,1]
% 0.15/0.39  TRYING [1,2]
% 0.15/0.39  TRYING [2,2]
% 0.15/0.39  TRYING [5,2]
% 0.15/0.39  TRYING [3,2]
% 0.15/0.39  % (27658)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  % (27658)------------------------------
% 0.15/0.39  % (27658)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (27658)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (27658)Memory used [KB]: 827
% 0.15/0.39  % (27658)Time elapsed: 0.006 s
% 0.15/0.39  % (27658)Instructions burned: 6 (million)
% 0.15/0.39  % (27651)Success in time 0.021 s
%------------------------------------------------------------------------------