TSTP Solution File: NUM666^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Sun May  5 08:41:46 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   54 (  19 unt;  17 typ;   0 def)
%            Number of atoms       :  337 (  46 equ;   0 cnn)
%            Maximal formula atoms :    4 (   9 avg)
%            Number of connectives :   49 (  22   ~;  18   |;   0   &;   0   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   27 (  26   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   5 con; 0-6 aty)
%            Number of variables   :   51 (   9   ^  36   !;   0   ?;  51   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    nat: $tType ).

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

thf(func_def_0,type,
    nat: $tType ).

thf(func_def_1,type,
    x: nat ).

thf(func_def_2,type,
    y: nat ).

thf(func_def_3,type,
    z: nat ).

thf(func_def_4,type,
    some: ( nat > $o ) > $o ).

thf(func_def_5,type,
    diffprop: nat > nat > nat > $o ).

thf(func_def_7,type,
    moreis: nat > nat > $o ).

thf(func_def_8,type,
    lessis: nat > nat > $o ).

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

thf(func_def_13,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

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

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

thf(func_def_17,type,
    vNOT: $o > $o ).

thf(func_def_18,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f98,plain,
    $false,
    inference(trivial_inequality_removal,[],[f97]) ).

thf(f97,plain,
    $true = $false,
    inference(forward_demodulation,[],[f96,f57]) ).

thf(f57,plain,
    $false = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
    inference(trivial_inequality_removal,[],[f56]) ).

thf(f56,plain,
    ( ( $true != $true )
    | ( $false = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)) ) ),
    inference(superposition,[],[f23,f8]) ).

thf(f8,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f23,plain,
    $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
    inference(cnf_transformation,[],[f19]) ).

thf(f19,plain,
    $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
    inference(flattening,[],[f10]) ).

thf(f10,plain,
    $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
    inference(fool_elimination,[],[f9]) ).

thf(f9,plain,
    ~ vAPP(sTfun(nat,$o),$o,some,
        ^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z),X0)),
    inference(rectify,[],[f6]) ).

thf(f6,negated_conjecture,
    ~ vAPP(sTfun(nat,$o),$o,some,
        ^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z),X0)),
    inference(negated_conjecture,[],[f5]) ).

thf(f5,conjecture,
    vAPP(sTfun(nat,$o),$o,some,
      ^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z),X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16d) ).

thf(f96,plain,
    $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)),
    inference(trivial_inequality_removal,[],[f91]) ).

thf(f91,plain,
    ( ( $true != $true )
    | ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),z)) ) ),
    inference(superposition,[],[f90,f63]) ).

thf(f63,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,z),y),
    inference(trivial_inequality_removal,[],[f60]) ).

thf(f60,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,z),y) ) ),
    inference(superposition,[],[f24,f26]) ).

thf(f26,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z) = $true,
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z) = $true,
    inference(fool_elimination,[],[f15]) ).

thf(f15,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,y),z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).

thf(f24,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) ) ),
    inference(cnf_transformation,[],[f20]) ).

thf(f20,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1) ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) ) ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X0) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),moreis,X1),X2)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).

thf(f90,plain,
    ! [X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),y) )
      | ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),X0)) ) ),
    inference(equality_resolution,[],[f67]) ).

thf(f67,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y) != vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X1) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X2),X1) != $true )
      | ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X2)) ) ),
    inference(trivial_inequality_removal,[],[f64]) ).

thf(f64,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true != $true )
      | ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X2),X1) != $true )
      | ( vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y) != vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X0),X1) ) ),
    inference(constrained_superposition,[],[f25,f27]) ).

thf(f27,plain,
    $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y)),
    inference(cnf_transformation,[],[f18]) ).

thf(f18,plain,
    $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y)),
    inference(fool_elimination,[],[f17]) ).

thf(f17,plain,
    vAPP(sTfun(nat,$o),$o,some,
      ^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y),X0)),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    vAPP(sTfun(nat,$o),$o,some,
      ^ [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,x),y),X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(f25,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
      | ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) ) ),
    inference(cnf_transformation,[],[f22]) ).

thf(f22,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) )
      | ( $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) ) ),
    inference(flattening,[],[f21]) ).

thf(f21,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) )
      | ( $true != vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) ) ),
    inference(ennf_transformation,[],[f14]) ).

thf(f14,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1) )
     => ( ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1)) )
       => ( $true = vAPP(sTfun(nat,$o),$o,some,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0)) ) ) ),
    inference(fool_elimination,[],[f13]) ).

thf(f13,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X0),X1)
     => ( vAPP(sTfun(nat,$o),$o,some,
            ^ [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X1),X3))
       => vAPP(sTfun(nat,$o),$o,some,
            ^ [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X2),X0),X4)) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X1: nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),lessis,X1),X2)
     => ( vAPP(sTfun(nat,$o),$o,some,
            ^ [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X3),X2),X4))
       => vAPP(sTfun(nat,$o),$o,some,
            ^ [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),diffprop,X3),X1),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 15:02:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (7705)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (7706)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (7711)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (7709)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37  % (7708)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)
% 0.14/0.37  % (7707)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (7710)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (7712)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)
% 0.14/0.37  % (7709)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.37  % (7708)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.37  % Exception at run slice level% Exception at run slice level
% 0.14/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37  % Exception at run slice level
% 0.14/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37  % Exception at run slice level
% 0.14/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37  
% 0.14/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37  % (7711)First to succeed.
% 0.14/0.37  % (7710)Also succeeded, but the first one will report.
% 0.14/0.37  % (7708)Also succeeded, but the first one will report.
% 0.14/0.37  % (7711)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7705"
% 0.14/0.37  % (7711)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (7711)------------------------------
% 0.14/0.38  % (7711)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (7711)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (7711)Memory used [KB]: 778
% 0.14/0.38  % (7711)Time elapsed: 0.007 s
% 0.14/0.38  % (7711)Instructions burned: 9 (million)
% 0.14/0.38  % (7705)Success in time 0.01 s
%------------------------------------------------------------------------------