TSTP Solution File: DAT324^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT324^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Mon May 20 19:52:09 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   34 (   3 unt;  19 typ;   0 def)
%            Number of atoms       :  174 (  27 equ;   0 cnn)
%            Maximal formula atoms :    4 (  11 avg)
%            Number of connectives :   28 (  10   ~;   2   |;   8   &;   0   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   41 (  40   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;   2 con; 0-6 aty)
%            Number of variables   :   33 (   0   ^  18   !;   4   ?;  33   :)
%                                         (  11  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    'type/ind_types/list': $tType > $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    'type/nums/num': $tType ).

thf(type_def_8,type,
    sK0: $tType ).

thf(func_def_0,type,
    'type/nums/num': $tType ).

thf(func_def_1,type,
    'type/ind_types/list': $tType > $tType ).

thf(func_def_2,type,
    'const/sets/set_of_list': 
      !>[X0: $tType] : ( 'type/ind_types/list'(X0) > X0 > $o ) ).

thf(func_def_3,type,
    'const/sets/list_of_set': 
      !>[X0: $tType] : ( ( X0 > $o ) > 'type/ind_types/list'(X0) ) ).

thf(func_def_4,type,
    'const/sets/FINITE': 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_5,type,
    'const/sets/CARD': 
      !>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).

thf(func_def_6,type,
    'const/lists/LENGTH': 
      !>[X0: $tType] : ( 'type/ind_types/list'(X0) > 'type/nums/num' ) ).

thf(func_def_10,type,
    sK1: sK0 > $o ).

thf(func_def_11,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_12,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_13,type,
    vAND: $o > $o > $o ).

thf(func_def_14,type,
    vOR: $o > $o > $o ).

thf(func_def_15,type,
    vIMP: $o > $o > $o ).

thf(func_def_16,type,
    vNOT: $o > $o ).

thf(func_def_17,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f55,plain,
    $false,
    inference(unit_resulting_resolution,[],[f14,f15,f17]) ).

thf(f17,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) != $true )
      | ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
        & ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) )
      | ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f9]) ).

thf(f9,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
     => ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
        & ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) ) ),
    inference(fool_elimination,[],[f8]) ).

thf(f8,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
     => ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
        & ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
     => ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
        & ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/LIST_OF_SET_PROPERTIES_') ).

thf(f15,plain,
    vAPP('type/ind_types/list'(sK0),'type/nums/num','const/lists/LENGTH'(sK0),vAPP(sTfun(sK0,$o),'type/ind_types/list'(sK0),'const/sets/list_of_set'(sK0),sK1)) != vAPP(sTfun(sK0,$o),'type/nums/num','const/sets/CARD'(sK0),sK1),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ( vAPP('type/ind_types/list'(sK0),'type/nums/num','const/lists/LENGTH'(sK0),vAPP(sTfun(sK0,$o),'type/ind_types/list'(sK0),'const/sets/list_of_set'(sK0),sK1)) != vAPP(sTfun(sK0,$o),'type/nums/num','const/sets/CARD'(sK0),sK1) )
    & ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12]) ).

thf(f12,plain,
    ( ? [X0: $tType,X1: X0 > $o] :
        ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) != vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
        & ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) )
   => ( ( vAPP('type/ind_types/list'(sK0),'type/nums/num','const/lists/LENGTH'(sK0),vAPP(sTfun(sK0,$o),'type/ind_types/list'(sK0),'const/sets/list_of_set'(sK0),sK1)) != vAPP(sTfun(sK0,$o),'type/nums/num','const/sets/CARD'(sK0),sK1) )
      & ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ? [X0: $tType,X1: X0 > $o] :
      ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) != vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
      & ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ! [X0: $tType,X1: X0 > $o] :
        ( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
       => ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
    inference(fool_elimination,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: $tType,X1: X0 > $o] :
        ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
       => ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,negated_conjecture,
    ~ ! [X0: $tType,X1: X0 > $o] :
        ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
       => ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
    inference(negated_conjecture,[],[f2]) ).

thf(f2,conjecture,
    ! [X0: $tType,X1: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
     => ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/LENGTH_LIST_OF_SET_') ).

thf(f14,plain,
    $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : DAT324^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 23:09:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (7935)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (7940)WARNING: value z3 for option sas not known
% 0.14/0.38  % (7938)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (7939)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (7941)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (7940)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)
% 0.14/0.38  % (7943)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)
% 0.14/0.38  % (7944)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)
% 0.14/0.38  % Exception at run slice level% Exception at run slice level
% 0.14/0.38  
% 0.14/0.38  User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % (7944)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38  % (7942)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)
% 0.14/0.38  % (7944)First to succeed.
% 0.14/0.39  % (7940)Also succeeded, but the first one will report.
% 0.14/0.39  % (7943)Also succeeded, but the first one will report.
% 0.14/0.39  % (7944)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7935"
% 0.14/0.39  % (7944)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (7944)------------------------------
% 0.14/0.39  % (7944)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (7944)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (7944)Memory used [KB]: 764
% 0.14/0.39  % (7944)Time elapsed: 0.005 s
% 0.14/0.39  % (7944)Instructions burned: 5 (million)
% 0.14/0.39  % (7935)Success in time 0.02 s
%------------------------------------------------------------------------------