TSTP Solution File: NUM682^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM682^1 : 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 : n026.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 08:41:50 EDT 2024

% Result   : Theorem 0.12s 0.37s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   56 (  15 unt;  16 typ;   0 def)
%            Number of atoms       :  394 (  76 equ;   0 cnn)
%            Maximal formula atoms :    6 (   9 avg)
%            Number of connectives :  125 (  67   ~;  23   |;   4   &;   0   @)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   24 (  23   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   5 con; 0-6 aty)
%            Number of variables   :   58 (   0   ^  52   !;   0   ?;  58   :)
%                                         (   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,
    less: nat > nat > $o ).

thf(func_def_5,type,
    pl: nat > nat > nat ).

thf(func_def_7,type,
    more: nat > nat > $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(f132,plain,
    $false,
    inference(subsumption_resolution,[],[f129,f45]) ).

thf(f45,plain,
    ! [X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X1) ),
    inference(equality_resolution,[],[f40]) ).

thf(f40,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ),
    inference(cnf_transformation,[],[f32]) ).

thf(f32,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 != X1 )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
      & ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
      & ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
        | ( X0 != X1 ) ) ),
    inference(flattening,[],[f31]) ).

thf(f31,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 != X1 )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
      & ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
      & ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
        | ( X0 != X1 ) ) ),
    inference(ennf_transformation,[],[f26]) ).

thf(f26,plain,
    ! [X0: nat,X1: nat] :
      ~ ( ( ( X0 = X1 )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
       => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
           => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
         => ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
             => ( X0 != X1 ) ) ) ),
    inference(flattening,[],[f18]) ).

thf(f18,plain,
    ! [X0: nat,X1: nat] :
      ~ ( ( ( X0 = X1 )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) )
       => ~ ~ ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
               => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) )
             => ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
                 => ( X0 != X1 ) ) ) ),
    inference(fool_elimination,[],[f17]) ).

thf(f17,plain,
    ! [X0: nat,X1: nat] :
      ~ ( ( ( X0 = X1 )
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
       => ~ ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
               => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
             => ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1)
                 => ( X0 != X1 ) ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X1: nat,X2: nat] :
      ~ ( ( ( X1 = X2 )
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2) )
       => ~ ~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
               => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) )
             => ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2)
                 => ( X1 != X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10b) ).

thf(f129,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),
    inference(superposition,[],[f43,f127]) ).

thf(f127,plain,
    x = y,
    inference(subsumption_resolution,[],[f126,f35]) ).

thf(f35,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true,
    inference(cnf_transformation,[],[f23]) ).

thf(f23,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true,
    inference(flattening,[],[f12]) ).

thf(f12,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) != $true,
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y),
    inference(rectify,[],[f8]) ).

thf(f8,negated_conjecture,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y),
    inference(negated_conjecture,[],[f7]) ).

thf(f7,conjecture,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20c) ).

thf(f126,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true )
    | ( x = y ) ),
    inference(trivial_inequality_removal,[],[f122]) ).

thf(f122,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,x),y) = $true )
    | ( x = y ) ),
    inference(superposition,[],[f121,f37]) ).

thf(f37,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f29]) ).

thf(f29,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f25]) ).

thf(f25,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
    inference(flattening,[],[f16]) ).

thf(f16,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ) ),
    inference(fool_elimination,[],[f15]) ).

thf(f15,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    ! [X1: nat,X2: nat] :
      ( ( X1 != X2 )
     => ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X1),X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).

thf(f121,plain,
    $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y),
    inference(trivial_inequality_removal,[],[f117]) ).

thf(f117,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) ) ),
    inference(superposition,[],[f111,f43]) ).

thf(f111,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X2) ) ),
    inference(trivial_inequality_removal,[],[f110]) ).

thf(f110,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X2) ) ),
    inference(superposition,[],[f39,f42]) ).

thf(f42,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f34,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
    inference(ennf_transformation,[],[f20]) ).

thf(f20,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) ) ),
    inference(fool_elimination,[],[f19]) ).

thf(f19,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).

thf(f39,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,X0),X1) ) ),
    inference(cnf_transformation,[],[f32]) ).

thf(f43,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) = $true,
    inference(cnf_transformation,[],[f22]) ).

thf(f22,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) = $true,
    inference(fool_elimination,[],[f21]) ).

thf(f21,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),less,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35  % Computer : n026.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Fri May  3 15:19:38 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.12/0.35  % (16176)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (16179)WARNING: value z3 for option sas not known
% 0.12/0.37  % (16180)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37  % (16181)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)
% 0.12/0.37  % (16179)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)
% 0.12/0.37  % (16183)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)
% 0.12/0.37  % Exception at run slice level% (16178)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37  
% 0.12/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37  % (16182)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)
% 0.12/0.37  % (16177)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37  % (16183)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37  % Exception at run slice level
% 0.12/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37  % Exception at run slice level
% 0.12/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37  % (16179)First to succeed.
% 0.12/0.37  % (16183)Also succeeded, but the first one will report.
% 0.12/0.37  % (16179)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16176"
% 0.12/0.37  % (16179)Refutation found. Thanks to Tanya!
% 0.12/0.37  % SZS status Theorem for theBenchmark
% 0.12/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37  % (16179)------------------------------
% 0.12/0.37  % (16179)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.37  % (16179)Termination reason: Refutation
% 0.12/0.37  
% 0.12/0.37  % (16179)Memory used [KB]: 774
% 0.12/0.37  % (16179)Time elapsed: 0.006 s
% 0.12/0.37  % (16179)Instructions burned: 10 (million)
% 0.12/0.37  % (16176)Success in time 0.018 s
%------------------------------------------------------------------------------