TSTP Solution File: SWW503_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW503_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 : n023.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 11:41:12 EDT 2024

% Result   : Theorem 19.94s 3.22s
% Output   : Refutation 19.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   71
% Syntax   : Number of formulae    :   86 (  16 unt;  66 typ;   0 def)
%            Number of atoms       :   24 (  17 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   6   ~;   2   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   28 (  16   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   46 (  44 usr;   1 prp; 0-4 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-3 aty)
%            Number of variables   :   76 (  26   !;   0   ?;  76   :)
%                                         (  50  !>;   0  ?*;   0  @-;   0  @+)

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

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

tff(type_def_7,type,
    nat: $tType ).

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

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

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

tff(func_def_2,type,
    plus_plus: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_3,type,
    times_times: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

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

tff(func_def_5,type,
    root: ( nat * real ) > real ).

tff(func_def_6,type,
    power_power: 
      !>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).

tff(func_def_7,type,
    norm_norm: 
      !>[X0: $tType] : ( X0 > real ) ).

tff(func_def_8,type,
    of_real: 
      !>[X0: $tType] : ( real > X0 ) ).

tff(func_def_9,type,
    fFalse: bool ).

tff(func_def_10,type,
    fTrue: bool ).

tff(func_def_11,type,
    b: complex ).

tff(func_def_12,type,
    n: nat ).

tff(func_def_13,type,
    na: nat ).

tff(func_def_14,type,
    v: complex ).

tff(func_def_15,type,
    sK9: complex ).

tff(func_def_16,type,
    sK10: nat > complex ).

tff(func_def_17,type,
    sK11: complex ).

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

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

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

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

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

tff(pred_def_6,type,
    semiring_0: 
      !>[X0: $tType] : $o ).

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

tff(pred_def_8,type,
    monoid_mult: 
      !>[X0: $tType] : $o ).

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

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

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

tff(pred_def_12,type,
    linordered_idom: 
      !>[X0: $tType] : $o ).

tff(pred_def_13,type,
    comm_monoid_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_14,type,
    no_zero_divisors: 
      !>[X0: $tType] : $o ).

tff(pred_def_15,type,
    linordered_field: 
      !>[X0: $tType] : $o ).

tff(pred_def_16,type,
    ab_semigroup_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_17,type,
    linordered_semidom: 
      !>[X0: $tType] : $o ).

tff(pred_def_18,type,
    field_inverse_zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_19,type,
    real_algebra_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_20,type,
    cancel_semigroup_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_21,type,
    real_normed_field: 
      !>[X0: $tType] : $o ).

tff(pred_def_22,type,
    real_normed_vector: 
      !>[X0: $tType] : $o ).

tff(pred_def_23,type,
    ring_11004092258visors: 
      !>[X0: $tType] : $o ).

tff(pred_def_24,type,
    cancel146912293up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_25,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_26,type,
    ordere216010020id_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_27,type,
    real_n2089651433ebra_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_28,type,
    divisi14063676e_zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_29,type,
    real_n1866405975lgebra: 
      !>[X0: $tType] : $o ).

tff(pred_def_30,type,
    linord1117847801e_zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_31,type,
    ordere236663937imp_le: 
      !>[X0: $tType] : $o ).

tff(pred_def_32,type,
    ordere223160158up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_33,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_34,type,
    even_odd_even: 
      !>[X0: $tType] : ( X0 > $o ) ).

tff(pred_def_35,type,
    pp: bool > $o ).

tff(pred_def_36,type,
    sP0: 
      !>[X0: $tType] : ( ( X0 * nat ) > $o ) ).

tff(pred_def_37,type,
    sP1: 
      !>[X0: $tType] : $o ).

tff(pred_def_38,type,
    sP2: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_39,type,
    sP3: 
      !>[X0: $tType] : $o ).

tff(pred_def_40,type,
    sP4: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_41,type,
    sP5: 
      !>[X0: $tType] : $o ).

tff(pred_def_42,type,
    sP6: 
      !>[X0: $tType] : ( ( X0 * X0 * X0 ) > $o ) ).

tff(pred_def_43,type,
    sP7: 
      !>[X0: $tType] : $o ).

tff(pred_def_44,type,
    sP8: ( nat * nat ) > $o ).

tff(f64410,plain,
    $false,
    inference(trivial_inequality_removal,[],[f64379]) ).

tff(f64379,plain,
    inverse_divide(complex,power_power(complex,v,na),of_real(complex,norm_norm(complex,b))) != inverse_divide(complex,power_power(complex,v,na),of_real(complex,norm_norm(complex,b))),
    inference(superposition,[],[f424,f8838]) ).

tff(f8838,plain,
    ! [X0: complex] : ( power_power(complex,inverse_divide(complex,X0,of_real(complex,root(na,norm_norm(complex,b)))),na) = inverse_divide(complex,power_power(complex,X0,na),of_real(complex,norm_norm(complex,b))) ),
    inference(superposition,[],[f4970,f945]) ).

tff(f945,plain,
    of_real(complex,norm_norm(complex,b)) = power_power(complex,of_real(complex,root(na,norm_norm(complex,b))),na),
    inference(superposition,[],[f645,f506]) ).

tff(f506,plain,
    norm_norm(complex,b) = power_power(real,root(na,norm_norm(complex,b)),na),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    norm_norm(complex,b) = power_power(real,root(na,norm_norm(complex,b)),na),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096root_An_A_Icmod_Ab_J_A_094_An_A_061_Acmod_Ab_096) ).

tff(f645,plain,
    ! [X0: nat,X1: real] : ( power_power(complex,of_real(complex,X1),X0) = of_real(complex,power_power(real,X1,X0)) ),
    inference(cnf_transformation,[],[f247]) ).

tff(f247,plain,
    ! [X0: nat,X1: real] : ( power_power(complex,of_real(complex,X1),X0) = of_real(complex,power_power(real,X1,X0)) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X3: nat,X2: real] : ( power_power(complex,of_real(complex,X2),X3) = of_real(complex,power_power(real,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_complex__of__real__power) ).

tff(f4970,plain,
    ! [X2: nat,X0: complex,X1: complex] : ( power_power(complex,inverse_divide(complex,X0,X1),X2) = inverse_divide(complex,power_power(complex,X0,X2),power_power(complex,X1,X2)) ),
    inference(resolution,[],[f580,f450]) ).

tff(f450,plain,
    field_inverse_zero(complex),
    inference(cnf_transformation,[],[f157]) ).

tff(f157,axiom,
    field_inverse_zero(complex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield__inverse__zero) ).

tff(f580,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: nat] :
      ( ~ field_inverse_zero(X0)
      | ( power_power(X0,inverse_divide(X0,X3,X2),X1) = inverse_divide(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) ) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f296,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0,X3: X0] : ( power_power(X0,inverse_divide(X0,X3,X2),X1) = inverse_divide(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) )
      | ~ field_inverse_zero(X0) ),
    inference(ennf_transformation,[],[f203]) ).

tff(f203,plain,
    ! [X0: $tType] :
      ( field_inverse_zero(X0)
     => ! [X1: nat,X2: X0,X3: X0] : ( power_power(X0,inverse_divide(X0,X3,X2),X1) = inverse_divide(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X0: $tType] :
      ( field_inverse_zero(X0)
     => ! [X3: nat,X6: X0,X7: X0] : ( power_power(X0,inverse_divide(X0,X7,X6),X3) = inverse_divide(X0,power_power(X0,X7,X3),power_power(X0,X6,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power__divide) ).

tff(f424,plain,
    power_power(complex,inverse_divide(complex,v,of_real(complex,root(na,norm_norm(complex,b)))),na) != inverse_divide(complex,power_power(complex,v,na),of_real(complex,norm_norm(complex,b))),
    inference(cnf_transformation,[],[f176]) ).

tff(f176,plain,
    power_power(complex,inverse_divide(complex,v,of_real(complex,root(na,norm_norm(complex,b)))),na) != inverse_divide(complex,power_power(complex,v,na),of_real(complex,norm_norm(complex,b))),
    inference(flattening,[],[f175]) ).

tff(f175,negated_conjecture,
    ( ~ power_power(complex,inverse_divide(complex,v,of_real(complex,root(na,norm_norm(complex,b)))),na) = inverse_divide(complex,power_power(complex,v,na),of_real(complex,norm_norm(complex,b))) ),
    inference(negated_conjecture,[],[f174]) ).

tff(f174,conjecture,
    power_power(complex,inverse_divide(complex,v,of_real(complex,root(na,norm_norm(complex,b)))),na) = inverse_divide(complex,power_power(complex,v,na),of_real(complex,norm_norm(complex,b))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWW503_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n023.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   : Fri May  3 19:24:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.22/0.36  % (3422)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37  % (3423)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.37  % Exception at run slice level
% 0.22/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.38  % (3425)WARNING: value z3 for option sas not known
% 0.22/0.38  % (3426)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38  % (3424)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38  % (3425)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)
% 0.22/0.38  % (3427)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)
% 0.22/0.38  % (3428)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)
% 0.22/0.38  % (3429)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)
% 0.22/0.38  % (3429)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.38  % (3430)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.38  % Exception at run slice level% Exception at run slice level
% 0.22/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.38  
% 0.22/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39  % (3430)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
% 0.22/0.40  % (3434)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)
% 0.22/0.40  % (3433)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)
% 0.22/0.40  % (3432)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  % (3432)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 19.94/3.21  % (3428)First to succeed.
% 19.94/3.22  % (3428)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3422"
% 19.94/3.22  % (3428)Refutation found. Thanks to Tanya!
% 19.94/3.22  % SZS status Theorem for theBenchmark
% 19.94/3.22  % SZS output start Proof for theBenchmark
% See solution above
% 19.94/3.22  % (3428)------------------------------
% 19.94/3.22  % (3428)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 19.94/3.22  % (3428)Termination reason: Refutation
% 19.94/3.22  
% 19.94/3.22  % (3428)Memory used [KB]: 19812
% 19.94/3.22  % (3428)Time elapsed: 2.840 s
% 19.94/3.22  % (3428)Instructions burned: 6323 (million)
% 19.94/3.22  % (3422)Success in time 2.853 s
%------------------------------------------------------------------------------