TSTP Solution File: SYO310^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYO310^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 09:10:53 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   29 (   3 unt;   9 typ;   0 def)
%            Number of atoms       :  432 (  56 equ;   0 cnn)
%            Maximal formula atoms :    6 (  21 avg)
%            Number of connectives :   94 (  36   ~;  31   |;  20   &;   0   @)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   46 (  45   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   2 con; 0-6 aty)
%            Number of variables   :   23 (   0   ^  10   !;   7   ?;  23   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_3,type,
    vIMP: $o > $o > $o ).

thf(func_def_4,type,
    sK0: $o > $o ).

thf(func_def_6,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_7,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_8,type,
    vAND: $o > $o > $o ).

thf(func_def_9,type,
    vOR: $o > $o > $o ).

thf(func_def_10,type,
    vNOT: $o > $o ).

thf(func_def_11,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f56,plain,
    $false,
    inference(trivial_inequality_removal,[],[f55]) ).

thf(f55,plain,
    $true = $false,
    inference(equality_proxy_clausification,[],[f54]) ).

thf(f54,plain,
    $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false),
    inference(trivial_inequality_removal,[],[f53]) ).

thf(f53,plain,
    ( ( $true = $false )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false) ) ),
    inference(equality_proxy_clausification,[],[f52]) ).

thf(f52,plain,
    ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$false),$true) )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false) ) ),
    inference(trivial_inequality_removal,[],[f51]) ).

thf(f51,plain,
    ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$false),$true) )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false) )
    | ( $true != $true ) ),
    inference(boolean_simplification,[],[f50]) ).

thf(f50,plain,
    ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$false),$true) )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false) )
    | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$true) ) ),
    inference(trivial_inequality_removal,[],[f49]) ).

thf(f49,plain,
    ( ( $true != $true )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$false),$true) )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false) )
    | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$true) ) ),
    inference(boolean_simplification,[],[f46]) ).

thf(f46,plain,
    ( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$false),$false) )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$false),$true) )
    | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$false) )
    | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vEQ($o),$true),$true) ) ),
    inference(primitive_instantiation,[],[f13]) ).

thf(f13,plain,
    ! [X1: $o > $o > $o] :
      ( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ),
    inference(trivial_inequality_removal,[],[f12]) ).

thf(f12,plain,
    ! [X1: $o > $o > $o] :
      ( ( vAPP($o,$o,sK0,$true) != vAPP($o,$o,sK0,$true) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ),
    inference(boolean_simplification,[],[f11]) ).

thf(f11,plain,
    ! [X1: $o > $o > $o] :
      ( ( vAPP($o,$o,sK0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) != vAPP($o,$o,sK0,$true) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( vAPP($o,$o,sK0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) != vAPP($o,$o,sK0,$true) )
    | ! [X1: $o > $o > $o] :
        ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
        | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).

thf(f9,plain,
    ( ? [X0: $o > $o] : ( vAPP($o,$o,X0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) != vAPP($o,$o,X0,$true) )
   => ( vAPP($o,$o,sK0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) != vAPP($o,$o,sK0,$true) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ? [X0: $o > $o] : ( vAPP($o,$o,X0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) != vAPP($o,$o,X0,$true) )
    | ! [X1: $o > $o > $o] :
        ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
        | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ( ! [X0: $o > $o] : ( vAPP($o,$o,X0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) = vAPP($o,$o,X0,$true) )
      & ? [X1: $o > $o > $o] :
          ( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
          & ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
          & ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
          & ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ~ ( ! [X0: $o > $o] : ( vAPP($o,$o,X0,vAPP($o,$o,vAPP($o,sTfun($o,$o),vIMP,$true),$true)) = vAPP($o,$o,X0,$true) )
      & ? [X1: $o > $o > $o] :
          ( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false) )
          & ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true) )
          & ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false) )
          & ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X0: $o > $o] :
          ( vAPP($o,$o,X0,$true)
        <=> vAPP($o,$o,X0,
              ( $true
             => $true )) )
      & ? [X1: $o > $o > $o] :
          ( ~ vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$false)
          & ~ vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$true)
          & vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$false),$false)
          & vAPP($o,$o,vAPP($o,sTfun($o,$o),X1,$true),$true) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ! [X1: $o > $o] :
          ( vAPP($o,$o,X1,$true)
        <=> vAPP($o,$o,X1,
              ( $true
             => $true )) )
      & ? [X0: $o > $o > $o] :
          ( ~ vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),$false)
          & ~ vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$false),$true)
          & vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$false),$false)
          & vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),$true) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ! [X1: $o > $o] :
        ( vAPP($o,$o,X1,$true)
      <=> vAPP($o,$o,X1,
            ( $true
           => $true )) )
    & ? [X0: $o > $o > $o] :
        ( ~ vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),$false)
        & ~ vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$false),$true)
        & vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$false),$false)
        & vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),$true) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cOMEGA_EXAMPLE) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SYO310^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n017.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   : Mon May 20 10:15:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (32335)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40  % (32336)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.40  % (32339)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.40  % (32337)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40  % (32338)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.40  % (32340)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.40  % (32341)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.40  % (32342)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.40  % (32339)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40  % (32338)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40  % Exception at run slice level
% 0.14/0.40  User error: % Exception at run slice levelFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40  % Exception at run slice level
% 0.14/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40  
% 0.14/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40  % Exception at run slice level
% 0.14/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40  % (32341)First to succeed.
% 0.14/0.40  % (32340)Also succeeded, but the first one will report.
% 0.14/0.40  % (32338)Also succeeded, but the first one will report.
% 0.14/0.40  % (32341)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32335"
% 0.14/0.40  % (32341)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (32341)------------------------------
% 0.14/0.40  % (32341)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40  % (32341)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (32341)Memory used [KB]: 762
% 0.14/0.40  % (32341)Time elapsed: 0.008 s
% 0.14/0.40  % (32341)Instructions burned: 5 (million)
% 0.14/0.40  % (32335)Success in time 0.032 s
%------------------------------------------------------------------------------