TSTP Solution File: LCL839_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL839_5 : TPTP v8.1.2. Released v6.0.0.
% 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 : Sun May  5 07:55:27 EDT 2024

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  103 (  17 unt;  75 typ;   0 def)
%            Number of atoms       :   45 (   3 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   36 (  19   ~;   5   |;   4   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   92 (  44   >;  48   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   2 prp; 0-3 aty)
%            Number of functors    :   62 (  62 usr;  23 con; 0-5 aty)
%            Number of variables   :   83 (  55   !;   4   ?;  83   :)
%                                         (  24  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    bool: $tType ).

tff(type_def_6,type,
    dB: $tType ).

tff(type_def_7,type,
    list: $tType > $tType ).

tff(type_def_8,type,
    nat: $tType ).

tff(type_def_9,type,
    type: $tType ).

tff(type_def_10,type,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).

tff(func_def_1,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).

tff(func_def_2,type,
    combi: 
      !>[X0: $tType] : fun(X0,X0) ).

tff(func_def_3,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).

tff(func_def_4,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_5,type,
    it: fun(dB,bool) ).

tff(func_def_6,type,
    abs: dB > dB ).

tff(func_def_7,type,
    app: fun(dB,fun(dB,dB)) ).

tff(func_def_8,type,
    var: nat > dB ).

tff(func_def_9,type,
    lift: fun(dB,fun(nat,dB)) ).

tff(func_def_10,type,
    subst: fun(dB,fun(dB,fun(nat,dB))) ).

tff(func_def_11,type,
    foldl: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).

tff(func_def_12,type,
    foldr: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).

tff(func_def_13,type,
    map: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).

tff(func_def_14,type,
    suc: nat > nat ).

tff(func_def_15,type,
    shift: 
      !>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).

tff(func_def_16,type,
    fun1: fun(type,fun(type,type)) ).

tff(func_def_17,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_18,type,
    fFalse: bool ).

tff(func_def_19,type,
    fTrue: bool ).

tff(func_def_20,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_21,type,
    t1: type ).

tff(func_def_22,type,
    t_a: type ).

tff(func_def_23,type,
    t: type ).

tff(func_def_24,type,
    ua1: type ).

tff(func_def_25,type,
    a: dB ).

tff(func_def_26,type,
    as: list(dB) ).

tff(func_def_27,type,
    e: fun(nat,type) ).

tff(func_def_28,type,
    ea: fun(nat,type) ).

tff(func_def_29,type,
    i: nat ).

tff(func_def_30,type,
    ia: nat ).

tff(func_def_31,type,
    r: dB ).

tff(func_def_32,type,
    t2: dB ).

tff(func_def_33,type,
    u: dB ).

tff(func_def_34,type,
    ua: dB ).

tff(func_def_35,type,
    sK3: type ).

tff(func_def_36,type,
    sK4: nat > nat ).

tff(func_def_37,type,
    sK5: nat > nat ).

tff(func_def_38,type,
    sK6: dB > dB ).

tff(func_def_39,type,
    sK7: dB > list(dB) ).

tff(func_def_40,type,
    sK8: dB > nat ).

tff(func_def_41,type,
    sK9: dB > dB ).

tff(func_def_42,type,
    sK10: dB > dB ).

tff(func_def_43,type,
    sK11: dB > list(dB) ).

tff(func_def_44,type,
    sK12: ( dB * dB ) > dB ).

tff(func_def_45,type,
    sK13: fun(nat,bool) > nat ).

tff(func_def_46,type,
    sK14: fun(nat,bool) > nat ).

tff(func_def_47,type,
    sK15: ( dB * fun(nat,type) ) > type ).

tff(func_def_48,type,
    sK16: ( dB * fun(nat,type) ) > type ).

tff(func_def_49,type,
    sK17: ( type * dB * fun(nat,type) ) > type ).

tff(func_def_50,type,
    sK18: ( type * dB * fun(nat,type) ) > type ).

tff(func_def_51,type,
    sK19: ( dB * dB * dB ) > dB ).

tff(func_def_52,type,
    sK20: ( dB * dB * dB ) > dB ).

tff(func_def_53,type,
    sK21: ( dB * dB * dB ) > dB ).

tff(func_def_54,type,
    sK22: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).

tff(func_def_55,type,
    sK23: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).

tff(func_def_56,type,
    sK24: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).

tff(func_def_57,type,
    sK25: ( type * dB * dB * fun(nat,type) ) > type ).

tff(func_def_58,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_59,type,
    sK27: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).

tff(pred_def_1,type,
    zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    beta: ( dB * dB ) > $o ).

tff(pred_def_3,type,
    listsp: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_4,type,
    typing: ( fun(nat,type) * dB * type ) > $o ).

tff(pred_def_5,type,
    typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).

tff(pred_def_6,type,
    pp: bool > $o ).

tff(pred_def_8,type,
    sP0: dB > $o ).

tff(pred_def_9,type,
    sP1: dB > $o ).

tff(pred_def_10,type,
    sP2: ( dB * dB * dB ) > $o ).

tff(f753,plain,
    $false,
    inference(resolution,[],[f743,f656]) ).

tff(f656,plain,
    ! [X0: dB,X1: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),X0),X1),
    inference(forward_demodulation,[],[f651,f475]) ).

tff(f475,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(rectify,[],[f103]) ).

tff(f103,axiom,
    ! [X0: $tType,X2: $tType,X1: $tType,X82: X0,X83: X1,X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X84,X83),X82) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X82),X83) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

tff(f651,plain,
    ! [X0: dB,X1: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),a),X1),
    inference(resolution,[],[f450,f513]) ).

tff(f513,plain,
    ! [X0: type] : ~ typing(shift(type,e,i,t),a,X0),
    inference(resolution,[],[f335,f334]) ).

tff(f334,plain,
    ~ thesis,
    inference(cnf_transformation,[],[f112]) ).

tff(f112,plain,
    ~ thesis,
    inference(flattening,[],[f111]) ).

tff(f111,negated_conjecture,
    ~ thesis,
    inference(negated_conjecture,[],[f110]) ).

tff(f110,conjecture,
    thesis,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

tff(f335,plain,
    ! [X0: type] :
      ( thesis
      | ~ typing(shift(type,e,i,t),a,X0) ),
    inference(cnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: type] :
      ( thesis
      | ~ typing(shift(type,e,i,t),a,X0) ),
    inference(ennf_transformation,[],[f113]) ).

tff(f113,plain,
    ! [X0: type] :
      ( typing(shift(type,e,i,t),a,X0)
     => thesis ),
    inference(rectify,[],[f109]) ).

tff(f109,axiom,
    ! [X85: type] :
      ( typing(shift(type,e,i,t),a,X85)
     => thesis ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f450,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
      ( typing(X3,X1,sK25(X0,X1,X2,X3))
      | ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f319,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( ( typing(X3,X1,sK25(X0,X1,X2,X3))
        & typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK25(X0,X1,X2,X3)),X0)) )
      | ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f244,f318]) ).

tff(f318,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( ? [X4: type] :
          ( typing(X3,X1,X4)
          & typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
     => ( typing(X3,X1,sK25(X0,X1,X2,X3))
        & typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK25(X0,X1,X2,X3)),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f244,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( ? [X4: type] :
          ( typing(X3,X1,X4)
          & typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
      | ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
    inference(ennf_transformation,[],[f181]) ).

tff(f181,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
     => ~ ! [X4: type] :
            ( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0))
           => ~ typing(X3,X1,X4) ) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X4: type,X10: dB,X9: dB,X5: fun(nat,type)] :
      ( typing(X5,aa(dB,dB,aa(dB,fun(dB,dB),app,X9),X10),X4)
     => ~ ! [X25: type] :
            ( typing(X5,X9,aa(type,type,aa(type,fun(type,type),fun1,X25),X4))
           => ~ typing(X5,X10,X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_typing__elims_I2_J) ).

tff(f743,plain,
    typing(shift(type,e,i,t),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),sK3),
    inference(superposition,[],[f353,f475]) ).

tff(f353,plain,
    typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK3),
    inference(cnf_transformation,[],[f273]) ).

tff(f273,plain,
    typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f206,f272]) ).

tff(f272,plain,
    ( ? [X0: type] : typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
   => typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK3) ),
    introduced(choice_axiom,[]) ).

tff(f206,plain,
    ? [X0: type] : typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
    inference(ennf_transformation,[],[f114]) ).

tff(f114,plain,
    ~ ! [X0: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ~ ! [X3: type] : ~ typing(shift(type,e,i,t),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : LCL839_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n027.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 14:22:36 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (31220)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (31223)WARNING: value z3 for option sas not known
% 0.15/0.39  % (31224)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (31221)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (31225)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)
% 0.15/0.39  % (31226)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)
% 0.15/0.39  % (31222)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (31227)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)
% 0.15/0.39  % (31223)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)
% 0.15/0.40  % (31227)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40  % Exception at run slice level% Exception at run slice level
% 0.15/0.40  
% 0.15/0.40  User error: % Exception at run slice levelFinite model buillding is currently not compatible with polymorphism or higher-order constructsUser error: 
% 0.15/0.40  Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40  
% 0.15/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41  % (31228)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41  % (31230)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.42  % (31229)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.42  % (31228)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42  % Exception at run slice level
% 0.22/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42  % (31229)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42  % (31226)First to succeed.
% 0.22/0.43  % (31226)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31220"
% 0.22/0.43  % (31226)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for theBenchmark
% 0.22/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43  % (31226)------------------------------
% 0.22/0.43  % (31226)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43  % (31226)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (31226)Memory used [KB]: 1468
% 0.22/0.43  % (31226)Time elapsed: 0.036 s
% 0.22/0.43  % (31226)Instructions burned: 58 (million)
% 0.22/0.43  % (31220)Success in time 0.06 s
%------------------------------------------------------------------------------