TSTP Solution File: ANA109^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA109^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n009.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 04:31:12 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   25 (  12 unt;  12 typ;   0 def)
%            Number of atoms       :   32 (  13 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   86 (   7   ~;   0   |;   0   &;  78   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   2 con; 0-4 aty)
%            Number of variables   :   23 (   0   ^  14   !;   4   ?;  23   :)
%                                         (   5  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_6,type,
    'type/realax/real': $tType ).

thf(type_def_7,type,
    'type/nums/num': $tType ).

thf(func_def_0,type,
    'type/realax/real': $tType ).

thf(func_def_1,type,
    'type/nums/num': $tType ).

thf(func_def_2,type,
    'const/sets/INSERT': 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).

thf(func_def_3,type,
    'const/sets/EMPTY': 
      !>[X0: $tType] : ( X0 > $o ) ).

thf(func_def_4,type,
    'const/iterate/sum': 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).

thf(func_def_5,type,
    'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).

thf(func_def_7,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_10,type,
    sK0: 'type/nums/num' > 'type/realax/real' ).

thf(func_def_11,type,
    sK1: 'type/nums/num' ).

thf(func_def_13,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(f22,plain,
    $false,
    inference(trivial_inequality_removal,[],[f21]) ).

thf(f21,plain,
    ( ( sK0 @ sK1 )
   != ( sK0 @ sK1 ) ),
    inference(superposition,[],[f10,f15]) ).

thf(f15,plain,
    ! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
      ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X0 ) @ X1 )
      = ( X1 @ X0 ) ),
    inference(superposition,[],[f9,f11]) ).

thf(f11,plain,
    ! [X0: 'type/nums/num'] :
      ( ( 'const/iterate/..' @ X0 @ X0 )
      = ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
    inference(cnf_transformation,[],[f2]) ).

thf(f2,axiom,
    ! [X0: 'type/nums/num'] :
      ( ( 'const/iterate/..' @ X0 @ X0 )
      = ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WDqHkzytiT/Vampire---4.8_12896','thm/iterate/NUMSEG_SING_') ).

thf(f9,plain,
    ! [X0: $tType,X2: X0,X1: X0 > 'type/realax/real'] :
      ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
      = ( X1 @ X2 ) ),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0] :
      ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
      = ( X1 @ X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WDqHkzytiT/Vampire---4.8_12896','thm/iterate/SUM_SING_') ).

thf(f10,plain,
    ( ( sK0 @ sK1 )
   != ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( sK0 @ sK1 )
   != ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
        ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
       != ( X0 @ X1 ) )
   => ( ( sK0 @ sK1 )
     != ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
      ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
     != ( X0 @ X1 ) ),
    inference(ennf_transformation,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
        ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
        = ( X0 @ X1 ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
      ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
      = ( X0 @ X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.WDqHkzytiT/Vampire---4.8_12896','thm/iterate/SUM_SING_NUMSEG_') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : ANA109^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n009.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 15:29:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH1_THM_EQU_NAR problem
% 0.15/0.36  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.WDqHkzytiT/Vampire---4.8_12896
% 0.15/0.38  % (13121)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.15/0.38  % (13121)First to succeed.
% 0.15/0.38  % (13118)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.38  % (13122)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38  % (13123)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38  % (13120)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.38  % (13123)Instruction limit reached!
% 0.15/0.38  % (13123)------------------------------
% 0.15/0.38  % (13123)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (13123)Termination reason: Unknown
% 0.15/0.38  % (13123)Termination phase: Preprocessing 3
% 0.15/0.38  
% 0.15/0.38  % (13123)Memory used [KB]: 895
% 0.15/0.38  % (13123)Time elapsed: 0.003 s
% 0.15/0.38  % (13123)Instructions burned: 2 (million)
% 0.15/0.38  % (13123)------------------------------
% 0.15/0.38  % (13123)------------------------------
% 0.15/0.38  % (13121)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for Vampire---4
% 0.15/0.38  % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.38  % (13121)------------------------------
% 0.15/0.38  % (13121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (13121)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (13121)Memory used [KB]: 5500
% 0.15/0.38  % (13121)Time elapsed: 0.005 s
% 0.15/0.38  % (13121)Instructions burned: 5 (million)
% 0.15/0.38  % (13121)------------------------------
% 0.15/0.38  % (13121)------------------------------
% 0.15/0.38  % (13116)Success in time 0.005 s
% 0.15/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------