TSTP Solution File: LCL800_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL800_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 : n020.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 Apr 30 13:49:29 EDT 2024

% Result   : Theorem 0.22s 0.48s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   66
% Syntax   : Number of formulae    :   88 (  29 unt;  59 typ;   0 def)
%            Number of atoms       :   29 (  17 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   69 (  38   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-3 aty)
%            Number of functors    :   41 (  41 usr;  10 con; 0-5 aty)
%            Number of variables   :   70 (  39   !;   0   ?;  70   :)
%                                         (  31  !>;   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,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    plus_plus: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_1,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_2,type,
    app: ( dB * dB ) > dB ).

tff(func_def_3,type,
    var: nat > dB ).

tff(func_def_4,type,
    dB_case: 
      !>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).

tff(func_def_5,type,
    dB_rec: 
      !>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,fun(X0,fun(X0,X0)))) * fun(dB,fun(X0,X0)) * dB ) > X0 ) ).

tff(func_def_6,type,
    dB_size: dB > nat ).

tff(func_def_7,type,
    lift: ( dB * nat ) > dB ).

tff(func_def_8,type,
    liftn: ( nat * dB * nat ) > dB ).

tff(func_def_9,type,
    subst: ( dB * dB * nat ) > dB ).

tff(func_def_10,type,
    substn: ( dB * dB * nat ) > dB ).

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

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

tff(func_def_13,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_14,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_15,type,
    list_rec: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).

tff(func_def_16,type,
    splice: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_17,type,
    sublist: 
      !>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).

tff(func_def_18,type,
    suc: nat > nat ).

tff(func_def_19,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

tff(func_def_20,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_21,type,
    fFalse: bool ).

tff(func_def_22,type,
    fTrue: bool ).

tff(func_def_23,type,
    a: dB ).

tff(func_def_24,type,
    as: list(dB) ).

tff(func_def_25,type,
    i: nat ).

tff(func_def_26,type,
    n: nat ).

tff(func_def_27,type,
    rs: list(dB) ).

tff(func_def_28,type,
    t: dB ).

tff(func_def_29,type,
    u: dB ).

tff(func_def_30,type,
    ua: dB ).

tff(func_def_31,type,
    sK2: nat > nat ).

tff(func_def_32,type,
    sK3: nat > nat ).

tff(func_def_33,type,
    sK4: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_34,type,
    sK5: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_35,type,
    sK6: fun(nat,bool) > nat ).

tff(func_def_36,type,
    sK7: fun(nat,bool) > nat ).

tff(func_def_37,type,
    sK8: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_38,type,
    sK9: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

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

tff(pred_def_2,type,
    comm_monoid_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    ab_semigroup_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    cancel_semigroup_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_5,type,
    cancel146912293up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    equal_equal: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

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

tff(pred_def_9,type,
    listMem: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).

tff(pred_def_10,type,
    member1: 
      !>[X0: $tType] : ( ( list(X0) * X0 ) > $o ) ).

tff(pred_def_11,type,
    null: 
      !>[X0: $tType] : ( list(X0) > $o ) ).

tff(pred_def_12,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_13,type,
    pp: bool > $o ).

tff(pred_def_14,type,
    sP0: ( nat * nat ) > $o ).

tff(pred_def_15,type,
    sP1: ( nat * nat ) > $o ).

tff(f2041,plain,
    $false,
    inference(subsumption_resolution,[],[f2040,f438]) ).

tff(f438,plain,
    ~ it(app(u,subst(a,u,n))),
    inference(backward_demodulation,[],[f268,f279]) ).

tff(f279,plain,
    n = i,
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    n = i,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_True) ).

tff(f268,plain,
    ~ it(app(u,subst(a,u,i))),
    inference(cnf_transformation,[],[f108]) ).

tff(f108,plain,
    ~ it(app(u,subst(a,u,i))),
    inference(flattening,[],[f107]) ).

tff(f107,negated_conjecture,
    ~ it(app(u,subst(a,u,i))),
    inference(negated_conjecture,[],[f106]) ).

tff(f106,conjecture,
    it(app(u,subst(a,u,i))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f2040,plain,
    it(app(u,subst(a,u,n))),
    inference(forward_demodulation,[],[f2039,f507]) ).

tff(f507,plain,
    ! [X0: dB] : ( substn(var(zero_zero(nat)),X0,zero_zero(nat)) = X0 ),
    inference(superposition,[],[f317,f311]) ).

tff(f311,plain,
    ! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
    inference(cnf_transformation,[],[f136]) ).

tff(f136,plain,
    ! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X7: dB,X5: nat] : ( subst(var(X5),X7,X5) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__eq) ).

tff(f317,plain,
    ! [X0: dB,X1: dB] : ( substn(X1,X0,zero_zero(nat)) = subst(X1,X0,zero_zero(nat)) ),
    inference(cnf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: dB,X1: dB] : ( substn(X1,X0,zero_zero(nat)) = subst(X1,X0,zero_zero(nat)) ),
    inference(rectify,[],[f22]) ).

tff(f22,axiom,
    ! [X6: dB,X4: dB] : ( substn(X4,X6,zero_zero(nat)) = subst(X4,X6,zero_zero(nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_substn__subst__0) ).

tff(f2039,plain,
    it(app(u,substn(var(zero_zero(nat)),subst(a,u,n),zero_zero(nat)))),
    inference(backward_demodulation,[],[f440,f2022]) ).

tff(f2022,plain,
    ! [X2: dB,X0: dB,X1: dB] : ( substn(app(lift(X0,zero_zero(nat)),X2),X1,zero_zero(nat)) = app(X0,substn(X2,X1,zero_zero(nat))) ),
    inference(superposition,[],[f391,f508]) ).

tff(f508,plain,
    ! [X0: dB,X1: dB] : ( substn(lift(X0,zero_zero(nat)),X1,zero_zero(nat)) = X0 ),
    inference(superposition,[],[f317,f371]) ).

tff(f371,plain,
    ! [X2: dB,X0: dB,X1: nat] : ( subst(lift(X2,X1),X0,X1) = X2 ),
    inference(cnf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: dB,X1: nat,X2: dB] : ( subst(lift(X2,X1),X0,X1) = X2 ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X6: dB,X5: nat,X4: dB] : ( subst(lift(X4,X5),X6,X5) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__lift) ).

tff(f391,plain,
    ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( substn(app(X3,X2),X1,X0) = app(substn(X3,X1,X0),substn(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f187]) ).

tff(f187,plain,
    ! [X0: nat,X1: dB,X2: dB,X3: dB] : ( substn(app(X3,X2),X1,X0) = app(substn(X3,X1,X0),substn(X2,X1,X0)) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X5: nat,X6: dB,X7: dB,X4: dB] : ( substn(app(X4,X7),X6,X5) = app(substn(X4,X6,X5),substn(X7,X6,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_substn_Osimps_I2_J) ).

tff(f440,plain,
    it(substn(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,n),zero_zero(nat))),
    inference(backward_demodulation,[],[f439,f317]) ).

tff(f439,plain,
    it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,n),zero_zero(nat))),
    inference(forward_demodulation,[],[f281,f279]) ).

tff(f281,plain,
    it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,i),zero_zero(nat))),
    inference(cnf_transformation,[],[f5]) ).

tff(f5,axiom,
    it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,i),zero_zero(nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : LCL800_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
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon Apr 29 22:42:32 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.37  % (28935)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39  % (28939)WARNING: value z3 for option sas not known
% 0.22/0.39  % (28937)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (28938)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (28940)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (28941)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)
% 0.22/0.39  % (28942)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)
% 0.22/0.39  % (28939)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)
% 0.22/0.39  % (28943)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)
% 0.22/0.39  % (28943)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.39  % Exception at run slice level
% 0.22/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39  % Exception at run slice level
% 0.22/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39  % Exception at run slice level
% 0.22/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41  % (28954)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41  % (28955)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)
% 0.22/0.41  % (28956)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)
% 0.22/0.41  % (28954)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41  % (28955)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41  % Exception at run slice level
% 0.22/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43  % (28963)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.47  % (28956)First to succeed.
% 0.22/0.48  % (28956)Refutation found. Thanks to Tanya!
% 0.22/0.48  % SZS status Theorem for theBenchmark
% 0.22/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.48  % (28956)------------------------------
% 0.22/0.48  % (28956)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.48  % (28956)Termination reason: Refutation
% 0.22/0.48  
% 0.22/0.48  % (28956)Memory used [KB]: 1460
% 0.22/0.48  % (28956)Time elapsed: 0.069 s
% 0.22/0.48  % (28956)Instructions burned: 130 (million)
% 0.22/0.48  % (28956)------------------------------
% 0.22/0.48  % (28956)------------------------------
% 0.22/0.48  % (28935)Success in time 0.108 s
%------------------------------------------------------------------------------