TSTP Solution File: ANA100^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA100^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n008.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 04:31:10 EDT 2024

% Result   : Theorem 0.23s 0.39s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   30 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :   43 (  26 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  246 (  20   ~;   7   |;   0   &; 218   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   39 (  39   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   2 con; 0-5 aty)
%            Number of variables   :   64 (  16   ^  37   !;   8   ?;  64   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    'type/realax/real': $tType ).

thf(type_def_7,type,
    sK0: $tType ).

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

thf(func_def_1,type,
    'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).

thf(func_def_2,type,
    'const/iterate/sum': 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).

thf(func_def_8,type,
    sK1: sK0 > 'type/realax/real' ).

thf(func_def_9,type,
    sK2: 'type/realax/real' ).

thf(func_def_10,type,
    sK3: sK0 > $o ).

thf(func_def_12,type,
    ph5: 
      !>[X0: $tType] : X0 ).

thf(func_def_13,type,
    sK6: 
      !>[X0: $tType] : ( 'type/realax/real' > ( X0 > 'type/realax/real' ) > 'type/realax/real' > ( X0 > 'type/realax/real' ) > X0 ) ).

thf(func_def_14,type,
    sK7: 'type/realax/real' > ( sK0 > 'type/realax/real' ) > sK0 ).

thf(f27,plain,
    $false,
    inference(subsumption_resolution,[],[f26,f12]) ).

thf(f12,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( 'const/realax/real_mul' @ X0 @ X1 )
      = ( 'const/realax/real_mul' @ X1 @ X0 ) ),
    inference(cnf_transformation,[],[f2]) ).

thf(f2,axiom,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( 'const/realax/real_mul' @ X0 @ X1 )
      = ( 'const/realax/real_mul' @ X1 @ X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.SaCJ1eLvBi/Vampire---4.8_31544','thm/realax/REAL_MUL_SYM_') ).

thf(f26,plain,
    ( ( 'const/realax/real_mul' @ sK2 @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) )
   != ( 'const/realax/real_mul' @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) @ sK2 ) ),
    inference(trivial_inequality_removal,[],[f24]) ).

thf(f24,plain,
    ( ( ( 'const/realax/real_mul' @ sK2 @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) )
     != ( 'const/realax/real_mul' @ ( sK1 @ ( sK7 @ sK2 @ sK1 ) ) @ sK2 ) )
    | ( sK3 != sK3 ) ),
    inference(equality_resolution,[],[f20]) ).

thf(f20,plain,
    ! [X2: sK0 > 'type/realax/real',X0: sK0 > $o,X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ sK0 @ X0 @ X2 ) )
       != ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) )
      | ( ( 'const/realax/real_mul' @ ( sK1 @ ( sK7 @ X1 @ X2 ) ) @ sK2 )
       != ( 'const/realax/real_mul' @ X1 @ ( X2 @ ( sK7 @ X1 @ X2 ) ) ) )
      | ( sK3 != X0 ) ),
    inference(beta_eta_normalization,[],[f19]) ).

thf(f19,plain,
    ! [X2: sK0 > 'type/realax/real',X0: sK0 > $o,X1: 'type/realax/real'] :
      ( ( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 )
          @ ( sK7 @ X1 @ X2 ) )
       != ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ X1 @ ( X2 @ Y0 ) )
          @ ( sK7 @ X1 @ X2 ) ) )
      | ( ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ sK0 @ X0 @ X2 ) )
       != ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) )
      | ( sK3 != X0 ) ),
    inference(negative_extensionality,[],[f16]) ).

thf(f16,plain,
    ! [X2: sK0 > 'type/realax/real',X0: sK0 > $o,X1: 'type/realax/real'] :
      ( ( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
       != ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ X1 @ ( X2 @ Y0 ) ) ) )
      | ( sK3 != X0 )
      | ( ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ sK0 @ X0 @ X2 ) )
       != ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ) ),
    inference(constrained_superposition,[],[f14,f13]) ).

thf(f13,plain,
    ! [X0: $tType,X2: 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
      ( ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
      = ( 'const/iterate/sum' @ X0 @ X3
        @ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ Y0 ) ) ) ),
    inference(cnf_transformation,[],[f6]) ).

thf(f6,plain,
    ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
      ( ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
      = ( 'const/iterate/sum' @ X0 @ X3
        @ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ Y0 ) ) ) ),
    inference(fool_elimination,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
      ( ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
      = ( 'const/iterate/sum' @ X0 @ X3
        @ ^ [X4: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SaCJ1eLvBi/Vampire---4.8_31544','thm/iterate/SUM_LMUL_') ).

thf(f14,plain,
    ( ( 'const/iterate/sum' @ sK0 @ sK3
      @ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
   != ( 'const/realax/real_mul' @ sK2 @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ),
    inference(backward_demodulation,[],[f11,f12]) ).

thf(f11,plain,
    ( ( 'const/iterate/sum' @ sK0 @ sK3
      @ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
   != ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ sK2 ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( 'const/iterate/sum' @ sK0 @ sK3
      @ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
   != ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ sK2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9]) ).

thf(f9,plain,
    ( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
        ( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
       != ( 'const/iterate/sum' @ X0 @ X3
          @ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X2 ) ) )
   => ( ( 'const/iterate/sum' @ sK0 @ sK3
        @ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK2 ) )
     != ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ sK2 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
      ( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
     != ( 'const/iterate/sum' @ X0 @ X3
        @ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X2 ) ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
        ( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
        = ( 'const/iterate/sum' @ X0 @ X3
          @ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X2 ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,negated_conjecture,
    ~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
        ( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
        = ( 'const/iterate/sum' @ X0 @ X3
          @ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ X2 ) ) ),
    inference(negated_conjecture,[],[f3]) ).

thf(f3,conjecture,
    ! [X0: $tType,X1: X0 > 'type/realax/real',X2: 'type/realax/real',X3: X0 > $o] :
      ( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
      = ( 'const/iterate/sum' @ X0 @ X3
        @ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SaCJ1eLvBi/Vampire---4.8_31544','thm/iterate/SUM_RMUL_') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : ANA100^1 : TPTP v8.1.2. Released v7.0.0.
% 0.15/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n008.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 15:29:53 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a TH1_THM_EQU_NAR problem
% 0.16/0.37  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/sandbox/tmp/tmp.SaCJ1eLvBi/Vampire---4.8_31544
% 0.23/0.39  % (31798)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.23/0.39  % (31796)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)
% 0.23/0.39  % (31797)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)
% 0.23/0.39  % (31795)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)
% 0.23/0.39  % (31799)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)
% 0.23/0.39  % (31800)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)
% 0.23/0.39  % (31801)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.23/0.39  % (31802)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)
% 0.23/0.39  % (31798)Instruction limit reached!
% 0.23/0.39  % (31798)------------------------------
% 0.23/0.39  % (31798)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (31798)Termination reason: Unknown
% 0.23/0.39  % (31798)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (31798)Memory used [KB]: 5500
% 0.23/0.39  % (31798)Time elapsed: 0.004 s
% 0.23/0.39  % (31798)Instructions burned: 2 (million)
% 0.23/0.39  % Exception at run slice level% (31798)------------------------------
% 0.23/0.39  % (31798)------------------------------
% 0.23/0.39  
% 0.23/0.39  User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.23/0.39  % (31800)Refutation not found, incomplete strategy
% 0.23/0.39  % (31800)------------------------------
% 0.23/0.39  % (31800)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (31800)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.39  
% 0.23/0.39  
% 0.23/0.39  % (31800)Memory used [KB]: 5500
% 0.23/0.39  % (31800)Time elapsed: 0.004 s
% 0.23/0.39  % (31800)Instructions burned: 2 (million)
% 0.23/0.39  % (31800)------------------------------
% 0.23/0.39  % (31800)------------------------------
% 0.23/0.39  % (31796)Instruction limit reached!
% 0.23/0.39  % (31796)------------------------------
% 0.23/0.39  % (31796)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (31796)Termination reason: Unknown
% 0.23/0.39  % (31796)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (31796)Memory used [KB]: 5500
% 0.23/0.39  % (31796)Time elapsed: 0.005 s
% 0.23/0.39  % (31796)Instructions burned: 4 (million)
% 0.23/0.39  % (31796)------------------------------
% 0.23/0.39  % (31796)------------------------------
% 0.23/0.39  % (31797)Refutation not found, incomplete strategy
% 0.23/0.39  % (31797)------------------------------
% 0.23/0.39  % (31797)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (31797)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.39  
% 0.23/0.39  
% 0.23/0.39  % (31797)Memory used [KB]: 5500
% 0.23/0.39  % (31797)Time elapsed: 0.004 s
% 0.23/0.39  % (31797)Instructions burned: 3 (million)
% 0.23/0.39  % (31797)------------------------------
% 0.23/0.39  % (31797)------------------------------
% 0.23/0.39  % (31802)Instruction limit reached!
% 0.23/0.39  % (31802)------------------------------
% 0.23/0.39  % (31802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (31802)Termination reason: Unknown
% 0.23/0.39  % (31802)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (31802)Memory used [KB]: 5500
% 0.23/0.39  % (31802)Time elapsed: 0.005 s
% 0.23/0.39  % (31802)Instructions burned: 3 (million)
% 0.23/0.39  % (31802)------------------------------
% 0.23/0.39  % (31802)------------------------------
% 0.23/0.39  % (31801)First to succeed.
% 0.23/0.39  % (31801)Refutation found. Thanks to Tanya!
% 0.23/0.39  % SZS status Theorem for Vampire---4
% 0.23/0.39  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.40  % (31801)------------------------------
% 0.23/0.40  % (31801)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (31801)Termination reason: Refutation
% 0.23/0.40  
% 0.23/0.40  % (31801)Memory used [KB]: 5500
% 0.23/0.40  % (31801)Time elapsed: 0.009 s
% 0.23/0.40  % (31801)Instructions burned: 8 (million)
% 0.23/0.40  % (31801)------------------------------
% 0.23/0.40  % (31801)------------------------------
% 0.23/0.40  % (31794)Success in time 0.01 s
% 0.23/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------