TSTP Solution File: SWW498_5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW498_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n022.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 : Mon Jun 24 18:33:17 EDT 2024

% Result   : Theorem 0.24s 0.51s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   36 (  24 unt;   0 typ;   0 def)
%            Number of atoms       :   48 (  18 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   23 (  11   ~;   6   |;   0   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :   35 (  35   !;   0   ?;  35   :)

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

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

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

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

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

tff(func_def_0,type,
    fundam1563812824_csqrt: complex > complex ).

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

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

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

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

tff(func_def_5,type,
    bit0: int > int ).

tff(func_def_6,type,
    bit1: int > int ).

tff(func_def_7,type,
    min: int ).

tff(func_def_8,type,
    pls: int ).

tff(func_def_9,type,
    number_number_of: 
      !>[X0: $tType] : ( int > X0 ) ).

tff(func_def_10,type,
    power_power: 
      !>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).

tff(func_def_11,type,
    fFalse: bool ).

tff(func_def_12,type,
    fTrue: bool ).

tff(func_def_13,type,
    x: real ).

tff(func_def_14,type,
    y: real ).

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

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

tff(pred_def_3,type,
    ring_char_0: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_7,type,
    comm_semiring_1: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_10,type,
    pp: bool > $o ).

tff(f1662,plain,
    $false,
    inference(subsumption_resolution,[],[f1650,f886]) ).

tff(f886,plain,
    ~ ord_less_eq(real,power_power(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real)),
    inference(forward_demodulation,[],[f883,f567]) ).

tff(f567,plain,
    ! [X0: real,X1: real] : ( times_times(real,X0,X1) = times_times(real,X1,X0) ),
    inference(resolution,[],[f367,f311]) ).

tff(f311,plain,
    comm_semiring_1(real),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,axiom,
    comm_semiring_1(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f367,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ~ comm_semiring_1(X0)
      | ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
    inference(cnf_transformation,[],[f226]) ).

tff(f226,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
      | ~ comm_semiring_1(X0) ),
    inference(ennf_transformation,[],[f158]) ).

tff(f158,plain,
    ! [X0: $tType] :
      ( comm_semiring_1(X0)
     => ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
    inference(rectify,[],[f81]) ).

tff(f81,axiom,
    ! [X0: $tType] :
      ( comm_semiring_1(X0)
     => ! [X29: X0,X7: X0] : ( times_times(X0,X7,X29) = times_times(X0,X29,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f883,plain,
    ~ ord_less_eq(real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),number_number_of(nat,bit0(bit1(pls)))),one_one(real)),
    inference(superposition,[],[f282,f341]) ).

tff(f341,plain,
    ! [X0: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X0),number_number_of(nat,bit0(bit1(pls)))) ),
    inference(cnf_transformation,[],[f138]) ).

tff(f138,plain,
    ! [X0: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X0),number_number_of(nat,bit0(bit1(pls)))) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X5: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X5,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X5),number_number_of(nat,bit0(bit1(pls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f282,plain,
    ~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
    inference(cnf_transformation,[],[f130]) ).

tff(f130,plain,
    ~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
    inference(flattening,[],[f129]) ).

tff(f129,negated_conjecture,
    ~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
    inference(negated_conjecture,[],[f128]) ).

tff(f128,conjecture,
    ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f1650,plain,
    ord_less_eq(real,power_power(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real)),
    inference(superposition,[],[f875,f836]) ).

tff(f836,plain,
    ! [X0: real] : ( power_power(real,X0,number_number_of(nat,bit0(bit1(pls)))) = power_power(real,abs_abs(real,X0),number_number_of(nat,bit0(bit1(pls)))) ),
    inference(resolution,[],[f345,f285]) ).

tff(f285,plain,
    linordered_idom(real),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    linordered_idom(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f345,plain,
    ! [X0: $tType,X1: X0] :
      ( ~ linordered_idom(X0)
      | ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) ) ),
    inference(cnf_transformation,[],[f204]) ).

tff(f204,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) )
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) ) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X7: X0] : ( power_power(X0,X7,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X7),number_number_of(nat,bit0(bit1(pls)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f875,plain,
    ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,x,number_number_of(real,bit0(bit1(pls))))),number_number_of(nat,bit0(bit1(pls)))),one_one(real)),
    inference(forward_demodulation,[],[f874,f567]) ).

tff(f874,plain,
    ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),one_one(real)),
    inference(forward_demodulation,[],[f333,f513]) ).

tff(f513,plain,
    ! [X0: nat] : ( one_one(real) = power_power(real,one_one(real),X0) ),
    inference(resolution,[],[f359,f307]) ).

tff(f307,plain,
    monoid_mult(real),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,axiom,
    monoid_mult(real),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f359,plain,
    ! [X0: $tType,X1: nat] :
      ( ~ monoid_mult(X0)
      | ( one_one(X0) = power_power(X0,one_one(X0),X1) ) ),
    inference(cnf_transformation,[],[f218]) ).

tff(f218,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] : ( one_one(X0) = power_power(X0,one_one(X0),X1) )
      | ~ monoid_mult(X0) ),
    inference(ennf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: $tType] :
      ( monoid_mult(X0)
     => ! [X1: nat] : ( one_one(X0) = power_power(X0,one_one(X0),X1) ) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X0: $tType] :
      ( monoid_mult(X0)
     => ! [X6: nat] : ( one_one(X0) = power_power(X0,one_one(X0),X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f333,plain,
    ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWW498_5 : TPTP v8.2.0. Released v6.0.0.
% 0.12/0.13  % Command    : run_vampire %s %d THM
% 0.14/0.37  % Computer : n022.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Wed Jun 19 04:20:24 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.39  This is a TF1_THM_EQU_NAR problem
% 0.14/0.39  Running first-order theorem proving
% 0.14/0.39  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3396)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3395)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3397)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3393)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3398)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3399)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.24/0.46  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46  % (3394)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.24/0.50  % (3394)First to succeed.
% 0.24/0.50  % (3394)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3392"
% 0.24/0.51  % (3392)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.51  % (3394)Refutation found. Thanks to Tanya!
% 0.24/0.51  % SZS status Theorem for theBenchmark
% 0.24/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.51  % (3394)------------------------------
% 0.24/0.51  % (3394)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.51  % (3394)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.51  % (3394)Termination reason: Refutation
% 0.24/0.51  
% 0.24/0.51  % (3394)Memory used [KB]: 1738
% 0.24/0.51  % (3394)Time elapsed: 0.047 s
% 0.24/0.51  % (3394)Instructions burned: 80 (million)
% 0.24/0.51  % (3394)------------------------------
% 0.24/0.51  % (3394)------------------------------
% 0.24/0.51  % (3392)Success in time 0.1 s
%------------------------------------------------------------------------------