TSTP Solution File: NUM677^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM677^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n027.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 02:12:47 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   47 (  21 unt;  16 typ;   0 def)
%            Number of atoms       :  249 (  37 equ;   0 cnn)
%            Maximal formula atoms :    3 (   8 avg)
%            Number of connectives :   31 (  15   ~;  10   |;   0   &;   0   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   22 (  21   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   6 con; 0-6 aty)
%            Number of variables   :   40 (   0   ^  34   !;   0   ?;  40   :)
%                                         (   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,
    u: nat ).

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

thf(func_def_7,type,
    pl: nat > nat > nat ).

thf(func_def_10,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_11,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_12,type,
    vAND: $o > $o > $o ).

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

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

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

thf(func_def_16,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f84,plain,
    $false,
    inference(trivial_inequality_removal,[],[f81]) ).

thf(f81,plain,
    $true = $false,
    inference(superposition,[],[f56,f75]) ).

thf(f75,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),u)) ),
    inference(trivial_inequality_removal,[],[f71]) ).

thf(f71,plain,
    ! [X0: nat] :
      ( ( $true != $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),u)) ) ),
    inference(superposition,[],[f23,f22]) ).

thf(f22,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true,
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true,
    inference(fool_elimination,[],[f13]) ).

thf(f13,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(f23,plain,
    ! [X2: nat,X3: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) != $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ),
    inference(equality_resolution,[],[f21]) ).

thf(f21,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( 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),X3)) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) != $true )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f17]) ).

thf(f17,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( 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),X3)) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) != $true )
      | ( X0 != X1 ) ),
    inference(flattening,[],[f16]) ).

thf(f16,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( 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),X3)) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) != $true )
      | ( X0 != X1 ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( X0 = X1 )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) = $true )
       => ( vAPP(nat,$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),X3)) = $true ) ) ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( X0 = X1 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3)
       => 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),X3)) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( X0 = X1 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3)
       => 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),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19g) ).

thf(f56,plain,
    $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)),
    inference(forward_demodulation,[],[f55,f20]) ).

thf(f20,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X0) ),
    inference(cnf_transformation,[],[f4]) ).

thf(f4,axiom,
    ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).

thf(f55,plain,
    $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)),
    inference(forward_demodulation,[],[f54,f20]) ).

thf(f54,plain,
    $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),x)),
    inference(trivial_inequality_removal,[],[f53]) ).

thf(f53,plain,
    ( ( $true != $true )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),x)) ) ),
    inference(superposition,[],[f24,f8]) ).

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

thf(f24,plain,
    $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),x)),
    inference(forward_demodulation,[],[f18,f19]) ).

thf(f19,plain,
    x = y,
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    x = y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i) ).

thf(f18,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),y)) != $true,
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),y)) != $true,
    inference(flattening,[],[f10]) ).

thf(f10,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),y)) != $true,
    inference(fool_elimination,[],[f9]) ).

thf(f9,plain,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),y)),
    inference(rectify,[],[f6]) ).

thf(f6,negated_conjecture,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),y)),
    inference(negated_conjecture,[],[f5]) ).

thf(f5,conjecture,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,z),x)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,u),y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19h) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : NUM677^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n027.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 05:07:23 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (15859)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (15865)WARNING: value z3 for option sas not known
% 0.15/0.37  % (15866)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (15864)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (15868)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)
% 0.15/0.37  % (15869)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)
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  % (15867)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)
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % (15869)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37  % (15863)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (15865)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)
% 0.15/0.37  % Exception at run slice level
% 0.15/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37  % (15868)First to succeed.
% 0.15/0.37  % (15869)Also succeeded, but the first one will report.
% 0.15/0.38  % (15868)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15859"
% 0.15/0.38  % (15867)Also succeeded, but the first one will report.
% 0.15/0.38  % (15865)Also succeeded, but the first one will report.
% 0.15/0.38  % (15868)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (15868)------------------------------
% 0.15/0.38  % (15868)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (15868)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (15868)Memory used [KB]: 774
% 0.15/0.38  % (15868)Time elapsed: 0.006 s
% 0.15/0.38  % (15868)Instructions burned: 8 (million)
% 0.15/0.38  % (15859)Success in time 0.021 s
%------------------------------------------------------------------------------