TSTP Solution File: NUM926_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM926_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 14:39:04 EDT 2024

% Result   : Theorem 0.16s 0.48s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   63 (  13 unt;  29 typ;   0 def)
%            Number of atoms       :   60 (  27 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   52 (  26   ~;  19   |;   1   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    7 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   26 (  16   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  11 con; 0-2 aty)
%            Number of variables   :   45 (  29   !;  16   ?;  45   :)

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

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

tff(func_def_0,type,
    one_one_int: int ).

tff(func_def_1,type,
    one_one_nat: nat ).

tff(func_def_2,type,
    plus_plus_int: ( int * int ) > int ).

tff(func_def_3,type,
    plus_plus_nat: ( nat * nat ) > nat ).

tff(func_def_4,type,
    times_times_int: ( int * int ) > int ).

tff(func_def_5,type,
    times_times_nat: ( nat * nat ) > nat ).

tff(func_def_6,type,
    bit0: int > int ).

tff(func_def_7,type,
    bit1: int > int ).

tff(func_def_8,type,
    pls: int ).

tff(func_def_9,type,
    number_number_of_int: int > int ).

tff(func_def_10,type,
    number_number_of_nat: int > nat ).

tff(func_def_11,type,
    power_power_int: ( int * nat ) > int ).

tff(func_def_12,type,
    power_power_nat: ( nat * nat ) > nat ).

tff(func_def_13,type,
    m: int ).

tff(func_def_14,type,
    s: int ).

tff(func_def_15,type,
    t: int ).

tff(func_def_16,type,
    sK0: int ).

tff(func_def_17,type,
    sK1: int ).

tff(func_def_18,type,
    sK2: int ).

tff(func_def_19,type,
    sK3: int ).

tff(func_def_20,type,
    sK4: int ).

tff(pred_def_1,type,
    zprime: int > $o ).

tff(pred_def_2,type,
    ord_less_int: ( int * int ) > $o ).

tff(pred_def_3,type,
    ord_less_nat: ( nat * nat ) > $o ).

tff(pred_def_4,type,
    ord_less_eq_int: ( int * int ) > $o ).

tff(pred_def_5,type,
    ord_less_eq_nat: ( nat * nat ) > $o ).

tff(pred_def_6,type,
    twoSqu1431725154sum2sq: int > $o ).

tff(f9824,plain,
    $false,
    inference(unit_resulting_resolution,[],[f464,f527,f465,f352]) ).

tff(f352,plain,
    ! [X0: int,X1: int] :
      ( ord_less_int(X1,X0)
      | ord_less_int(X0,X1)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f161]) ).

tff(f161,plain,
    ! [X0: int,X1: int] :
      ( ord_less_int(X1,X0)
      | ( X0 = X1 )
      | ord_less_int(X0,X1) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ! [X18: int,X19: int] :
      ( ord_less_int(X19,X18)
      | ( X18 = X19 )
      | ord_less_int(X18,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zless__linear) ).

tff(f465,plain,
    ~ ord_less_int(one_one_int,t),
    inference(subsumption_resolution,[],[f308,f294]) ).

tff(f294,plain,
    ! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    inference(cnf_transformation,[],[f235]) ).

tff(f235,plain,
    ! [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    inference(ennf_transformation,[],[f125]) ).

tff(f125,negated_conjecture,
    ~ ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    inference(negated_conjecture,[],[f124]) ).

tff(f124,conjecture,
    ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f308,plain,
    ( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))) )
    | ~ ord_less_int(one_one_int,t) ),
    inference(cnf_transformation,[],[f254]) ).

tff(f254,plain,
    ( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))) )
    | ~ ord_less_int(one_one_int,t) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f237,f253]) ).

tff(f253,plain,
    ( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
   => ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK3,number_number_of_nat(bit0(bit1(pls))))) ) ),
    introduced(choice_axiom,[]) ).

tff(f237,plain,
    ( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
    | ~ ord_less_int(one_one_int,t) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,axiom,
    ( ord_less_int(one_one_int,t)
   => ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

tff(f527,plain,
    ~ ord_less_int(t,one_one_int),
    inference(unit_resulting_resolution,[],[f296,f513]) ).

tff(f513,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less_eq_int(X0,X1)
      | ~ ord_less_int(X1,X0) ),
    inference(forward_demodulation,[],[f512,f311]) ).

tff(f311,plain,
    ! [X0: int] : ( number_number_of_int(X0) = X0 ),
    inference(cnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: int] : ( number_number_of_int(X0) = X0 ),
    inference(rectify,[],[f112]) ).

tff(f112,axiom,
    ! [X20: int] : ( number_number_of_int(X20) = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_number__of__is__id) ).

tff(f512,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less_eq_int(number_number_of_int(X0),X1)
      | ~ ord_less_int(X1,X0) ),
    inference(forward_demodulation,[],[f511,f311]) ).

tff(f511,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less_int(X1,X0)
      | ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
    inference(forward_demodulation,[],[f510,f311]) ).

tff(f510,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less_int(number_number_of_int(X1),X0)
      | ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
    inference(forward_demodulation,[],[f398,f311]) ).

tff(f398,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0))
      | ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
    inference(cnf_transformation,[],[f284]) ).

tff(f284,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
        | ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) )
      & ( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0))
        | ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ) ),
    inference(nnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
    <=> ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X27: int,X17: int] :
      ( ord_less_eq_int(number_number_of_int(X27),number_number_of_int(X17))
    <=> ~ ord_less_int(number_number_of_int(X17),number_number_of_int(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_le__number__of__eq__not__less) ).

tff(f296,plain,
    ord_less_eq_int(one_one_int,t),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ord_less_eq_int(one_one_int,t),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos) ).

tff(f464,plain,
    one_one_int != t,
    inference(subsumption_resolution,[],[f307,f294]) ).

tff(f307,plain,
    ( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))) )
    | ( one_one_int != t ) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,plain,
    ( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))) )
    | ( one_one_int != t ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f236,f251]) ).

tff(f251,plain,
    ( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
   => ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(sK0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK1,number_number_of_nat(bit0(bit1(pls))))) ) ),
    introduced(choice_axiom,[]) ).

tff(f236,plain,
    ( ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) )
    | ( one_one_int != t ) ),
    inference(ennf_transformation,[],[f2]) ).

tff(f2,axiom,
    ( ( one_one_int = t )
   => ? [X0: int,X1: int] : ( plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM926_1 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n017.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon Apr 29 22:51:03 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.31  % (10934)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (10941)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)
% 0.16/0.34  % (10937)WARNING: value z3 for option sas not known
% 0.16/0.35  % (10937)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)
% 0.16/0.35  % (10939)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)
% 0.16/0.37  % (10940)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)
% 0.16/0.37  % (10938)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38  % (10936)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.40  % (10935)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.46  TRYING [1,1]
% 0.16/0.47  TRYING [2,1]
% 0.16/0.48  % (10941)First to succeed.
% 0.16/0.48  % (10941)Refutation found. Thanks to Tanya!
% 0.16/0.48  % SZS status Theorem for theBenchmark
% 0.16/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48  % (10941)------------------------------
% 0.16/0.48  % (10941)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.48  % (10941)Termination reason: Refutation
% 0.16/0.48  
% 0.16/0.48  % (10941)Memory used [KB]: 2867
% 0.16/0.48  % (10941)Time elapsed: 0.147 s
% 0.16/0.48  % (10941)Instructions burned: 317 (million)
% 0.16/0.48  % (10941)------------------------------
% 0.16/0.48  % (10941)------------------------------
% 0.16/0.48  % (10934)Success in time 0.166 s
%------------------------------------------------------------------------------