TSTP Solution File: ALG280^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG280^5 : TPTP v8.1.2. Released v4.0.0.
% 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 04:29:34 EDT 2024

% Result   : Theorem 0.13s 0.39s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   33 (  11 unt;  14 typ;   0 def)
%            Number of atoms       :  189 (  40 equ;   0 cnn)
%            Maximal formula atoms :    4 (   9 avg)
%            Number of connectives :   32 (  10   ~;   0   |;  18   &;   0   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   21 (  20   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   3 con; 0-6 aty)
%            Number of variables   :   61 (   0   ^  51   !;   4   ?;  61   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

thf(func_def_1,type,
    cE: a ).

thf(func_def_2,type,
    cP: a > a > a ).

thf(func_def_3,type,
    cJ: a > a ).

thf(func_def_7,type,
    sK0: a ).

thf(func_def_8,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_9,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

thf(func_def_11,type,
    vOR: $o > $o > $o ).

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

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

thf(func_def_14,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f103,plain,
    $false,
    inference(trivial_inequality_removal,[],[f96]) ).

thf(f96,plain,
    sK0 != sK0,
    inference(superposition,[],[f14,f79]) ).

thf(f79,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),cE) = X0 ),
    inference(superposition,[],[f52,f50]) ).

thf(f50,plain,
    ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,vAPP(a,a,cJ,X0))),cE) = X0 ),
    inference(superposition,[],[f46,f13]) ).

thf(f13,plain,
    ! [X1: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X1)),X1) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( sK0 != vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),cE) )
    & ! [X1: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X1)),X1) )
    & ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X2) = X2 )
    & ! [X3: a,X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).

thf(f9,plain,
    ( ? [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),cE) != X0 )
   => ( sK0 != vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),cE) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ? [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),cE) != X0 )
    & ! [X1: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X1)),X1) )
    & ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X2) = X2 )
    & ! [X3: a,X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5)) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ? [X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),cE) != X5 )
    & ! [X0: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X0)),X0) )
    & ! [X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X1) = X1 )
    & ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( ? [X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),cE) != X5 )
    & ! [X0: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X0)),X0) )
    & ! [X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X1) = X1 )
    & ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ! [X0: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X0)),X0) )
        & ! [X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X1) = X1 )
        & ! [X2: a,X3: a,X4: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X3)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
     => ! [X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X5),cE) = X5 ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ! [X1: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X1)),X1) )
        & ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X0) = X0 )
        & ! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) )
     => ! [X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),cE) = X3 ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ! [X1: a] : ( cE = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X1)),X1) )
      & ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X0) = X0 )
      & ! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) )
   => ! [X3: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),cE) = X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM17_pme) ).

thf(f46,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) = X1 ),
    inference(forward_demodulation,[],[f44,f12]) ).

thf(f12,plain,
    ! [X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X2) = X2 ),
    inference(cnf_transformation,[],[f10]) ).

thf(f44,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,cE),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) ),
    inference(superposition,[],[f11,f13]) ).

thf(f11,plain,
    ! [X3: a,X4: a,X5: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),vAPP(a,a,vAPP(a,sTfun(a,a),cP,X4),X5)) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f52,plain,
    ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cJ,vAPP(a,a,cJ,X0))),X1) ),
    inference(superposition,[],[f46,f46]) ).

thf(f14,plain,
    sK0 != vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),cE),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : ALG280^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36  % Computer : n026.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Fri May  3 19:58:38 EDT 2024
% 0.13/0.37  % CPUTime    : 
% 0.13/0.37  % (18950)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38  % (18956)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)
% 0.13/0.38  % (18953)WARNING: value z3 for option sas not known
% 0.13/0.38  % (18953)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)
% 0.13/0.38  % (18957)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)
% 0.13/0.38  % (18957)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.38  % (18954)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38  % (18952)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38  % Exception at run slice level
% 0.13/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38  % (18955)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)
% 0.13/0.39  % Exception at run slice level
% 0.13/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39  % (18956)First to succeed.
% 0.13/0.39  % (18956)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18950"
% 0.13/0.39  % (18956)Refutation found. Thanks to Tanya!
% 0.13/0.39  % SZS status Theorem for theBenchmark
% 0.13/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39  % (18956)------------------------------
% 0.13/0.39  % (18956)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39  % (18956)Termination reason: Refutation
% 0.13/0.39  
% 0.13/0.39  % (18956)Memory used [KB]: 793
% 0.13/0.39  % (18956)Time elapsed: 0.006 s
% 0.13/0.39  % (18956)Instructions burned: 10 (million)
% 0.13/0.39  % (18950)Success in time 0.018 s
%------------------------------------------------------------------------------