TSTP Solution File: PUZ140^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : PUZ140^1 : TPTP v8.1.2. Released v6.1.0.
% 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 : n002.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 08:49:27 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   28 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   47 (  21 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   82 (  17   ~;   6   |;   4   &;  54   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (   4   ^  22   !;  10   ?;  37   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    beverage: $tType ).

thf(type_def_7,type,
    syrup: $tType ).

thf(func_def_0,type,
    syrup: $tType ).

thf(func_def_1,type,
    beverage: $tType ).

thf(func_def_2,type,
    coffee: beverage ).

thf(func_def_3,type,
    heat: beverage > beverage ).

thf(func_def_4,type,
    hot: beverage > $o ).

thf(func_def_5,type,
    mix: beverage > syrup > beverage ).

thf(func_def_6,type,
    hot_mixture: beverage > syrup > beverage ).

thf(func_def_7,type,
    cold_mixture: beverage > syrup > beverage ).

thf(func_def_14,type,
    sK0: ( beverage > syrup > beverage ) > syrup ).

thf(func_def_16,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(f23,plain,
    $false,
    inference(flex-flex_simplify,[],[f22]) ).

thf(f22,plain,
    ! [X0: beverage > syrup > beverage,X1: beverage] :
      ( ( X0 @ coffee
        @ ( sK0
          @ ^ [Y0: beverage,Y1: syrup] : ( heat @ ( X0 @ Y0 @ Y1 ) ) ) )
     != X1 ),
    inference(trivial_inequality_removal,[],[f21]) ).

thf(f21,plain,
    ! [X0: beverage > syrup > beverage,X1: beverage] :
      ( ( ( X0 @ coffee
          @ ( sK0
            @ ^ [Y0: beverage,Y1: syrup] : ( heat @ ( X0 @ Y0 @ Y1 ) ) ) )
       != X1 )
      | ( $true != $true ) ),
    inference(constrained_superposition,[],[f20,f18]) ).

thf(f18,plain,
    ! [X0: beverage] :
      ( ( hot @ ( heat @ X0 ) )
      = $true ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ! [X0: beverage] :
      ( ( hot @ ( heat @ X0 ) )
      = $true ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ! [X0: beverage] : ( hot @ ( heat @ X0 ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: beverage] : ( hot @ ( heat @ X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.k7UH2TrYbe/Vampire---4.8_21210',its_hot) ).

thf(f20,plain,
    ! [X0: beverage > syrup > beverage] :
      ( ( hot @ ( X0 @ coffee @ ( sK0 @ X0 ) ) )
     != $true ),
    inference(equality_resolution,[],[f17]) ).

thf(f17,plain,
    ! [X2: beverage,X0: beverage > syrup > beverage] :
      ( ( ( X0 @ coffee @ ( sK0 @ X0 ) )
       != X2 )
      | ( ( hot @ X2 )
       != $true ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ! [X0: beverage > syrup > beverage,X2: beverage] :
      ( ( ( X0 @ coffee @ ( sK0 @ X0 ) )
       != X2 )
      | ( ( hot @ X2 )
       != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).

thf(f14,plain,
    ! [X0: beverage > syrup > beverage] :
      ( ? [X1: syrup] :
        ! [X2: beverage] :
          ( ( ( X0 @ coffee @ X1 )
           != X2 )
          | ( ( hot @ X2 )
           != $true ) )
     => ! [X2: beverage] :
          ( ( ( X0 @ coffee @ ( sK0 @ X0 ) )
           != X2 )
          | ( ( hot @ X2 )
           != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ! [X0: beverage > syrup > beverage] :
    ? [X1: syrup] :
    ! [X2: beverage] :
      ( ( ( X0 @ coffee @ X1 )
       != X2 )
      | ( ( hot @ X2 )
       != $true ) ),
    inference(ennf_transformation,[],[f9]) ).

thf(f9,plain,
    ~ ? [X0: beverage > syrup > beverage] :
      ! [X1: syrup] :
      ? [X2: beverage] :
        ( ( ( X0 @ coffee @ X1 )
          = X2 )
        & ( ( hot @ X2 )
          = $true ) ),
    inference(fool_elimination,[],[f8]) ).

thf(f8,plain,
    ~ ? [X0: beverage > syrup > beverage] :
      ! [X1: syrup] :
      ? [X2: beverage] :
        ( ( hot @ X2 )
        & ( ( X0 @ coffee @ X1 )
          = X2 ) ),
    inference(rectify,[],[f5]) ).

thf(f5,negated_conjecture,
    ~ ? [X2: beverage > syrup > beverage] :
      ! [X1: syrup] :
      ? [X0: beverage] :
        ( ( hot @ X0 )
        & ( ( X2 @ coffee @ X1 )
          = X0 ) ),
    inference(negated_conjecture,[],[f4]) ).

thf(f4,conjecture,
    ? [X2: beverage > syrup > beverage] :
    ! [X1: syrup] :
    ? [X0: beverage] :
      ( ( hot @ X0 )
      & ( ( X2 @ coffee @ X1 )
        = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.k7UH2TrYbe/Vampire---4.8_21210',hot_coffee) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : PUZ140^1 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.15  % 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
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 18:04:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TH0_THM_EQU_NAR problem
% 0.14/0.36  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.k7UH2TrYbe/Vampire---4.8_21210
% 0.14/0.38  % (21405)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)
% 0.14/0.38  % (21406)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)
% 0.14/0.38  % (21408)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.38  % (21407)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)
% 0.14/0.38  % (21409)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)
% 0.14/0.38  % (21411)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.14/0.38  % (21410)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.14/0.38  % (21412)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.14/0.38  % (21408)Instruction limit reached!
% 0.14/0.38  % (21408)------------------------------
% 0.14/0.38  % (21408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (21408)Termination reason: Unknown
% 0.14/0.38  % (21409)Instruction limit reached!
% 0.14/0.38  % (21409)------------------------------
% 0.14/0.38  % (21409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (21408)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (21408)Memory used [KB]: 5500
% 0.14/0.38  % (21408)Time elapsed: 0.004 s
% 0.14/0.38  % (21408)Instructions burned: 2 (million)
% 0.14/0.38  % (21408)------------------------------
% 0.14/0.38  % (21408)------------------------------
% 0.14/0.38  % (21409)Termination reason: Unknown
% 0.14/0.38  % (21409)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (21410)Refutation not found, incomplete strategy
% 0.14/0.38  % (21410)------------------------------
% 0.14/0.38  % (21410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (21410)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38  
% 0.14/0.38  
% 0.14/0.38  % (21410)Memory used [KB]: 5500
% 0.14/0.38  % (21410)Time elapsed: 0.003 s
% 0.14/0.38  % (21410)Instructions burned: 1 (million)
% 0.14/0.38  % (21410)------------------------------
% 0.14/0.38  % (21410)------------------------------
% 0.14/0.38  % (21409)Memory used [KB]: 5500
% 0.14/0.38  % (21407)Refutation not found, incomplete strategy
% 0.14/0.38  % (21407)------------------------------
% 0.14/0.38  % (21407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (21407)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38  
% 0.14/0.38  
% 0.14/0.38  % (21407)Memory used [KB]: 5500
% 0.14/0.38  % (21407)Time elapsed: 0.004 s
% 0.14/0.38  % (21407)Instructions burned: 2 (million)
% 0.14/0.38  % (21407)------------------------------
% 0.14/0.38  % (21407)------------------------------
% 0.14/0.38  % (21405)First to succeed.
% 0.14/0.38  % (21409)Time elapsed: 0.004 s
% 0.14/0.38  % (21409)Instructions burned: 2 (million)
% 0.14/0.38  % (21409)------------------------------
% 0.14/0.38  % (21409)------------------------------
% 0.14/0.38  % (21411)Also succeeded, but the first one will report.
% 0.14/0.39  % (21405)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for Vampire---4
% 0.14/0.39  % SZS output start Proof for Vampire---4
% See solution above
% 0.14/0.39  % (21405)------------------------------
% 0.14/0.39  % (21405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (21405)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (21405)Memory used [KB]: 5500
% 0.14/0.39  % (21405)Time elapsed: 0.004 s
% 0.14/0.39  % (21405)Instructions burned: 2 (million)
% 0.14/0.39  % (21405)------------------------------
% 0.14/0.39  % (21405)------------------------------
% 0.14/0.39  % (21404)Success in time 0.006 s
% 0.14/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------