TSTP Solution File: SEU844^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU844^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : n026.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 May 21 03:51:54 EDT 2024

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   47 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :  200 (  59 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  160 (  33   ~;  32   |;  17   &;  60   @)
%                                         (   4 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   42 (   0   ^  34   !;   6   ?;  42   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    cS: a > $o ).

thf(func_def_2,type,
    cT: a > $o ).

thf(func_def_4,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_7,type,
    sK0: a ).

thf(func_def_8,type,
    sK1: a ).

thf(func_def_10,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(f61,plain,
    $false,
    inference(avatar_sat_refutation,[],[f24,f33,f34,f35,f50,f58]) ).

thf(f58,plain,
    ( spl2_1
    | ~ spl2_4 ),
    inference(avatar_contradiction_clause,[],[f57]) ).

thf(f57,plain,
    ( $false
    | spl2_1
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f54]) ).

thf(f54,plain,
    ( ( $false = $true )
    | spl2_1
    | ~ spl2_4 ),
    inference(backward_demodulation,[],[f32,f43]) ).

thf(f43,plain,
    ( ! [X0: a > $o] :
        ( $false
        = ( X0 @ sK1 ) )
    | spl2_1 ),
    inference(trivial_inequality_removal,[],[f39]) ).

thf(f39,plain,
    ( ! [X0: a > $o] :
        ( ( $true != $true )
        | ( $false
          = ( X0 @ sK1 ) ) )
    | spl2_1 ),
    inference(superposition,[],[f19,f37]) ).

thf(f37,plain,
    ! [X2: a,X0: a > $o,X1: a > $o] :
      ( ( $true
        = ( X0 @ X2 ) )
      | ( $false
        = ( X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ! [X2: a,X0: a > $o,X1: a > $o] :
      ( ( X0 @ X2 )
      = ( X1 @ X2 ) ),
    inference(argument_congruence,[],[f15]) ).

thf(f15,plain,
    ! [X0: a > $o,X1: a > $o] : ( X0 = X1 ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ! [X0: a > $o,X1: a > $o] : ( X0 = X1 )
    & ( ( ( $true
          = ( cT @ sK0 ) )
        & ( ( cS @ sK0 )
         != $true ) )
      | ( ( $true
         != ( cT @ sK1 ) )
        & ( $true
          = ( cS @ sK1 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).

thf(f8,plain,
    ( ? [X2: a] :
        ( ( ( cT @ X2 )
          = $true )
        & ( ( cS @ X2 )
         != $true ) )
   => ( ( $true
        = ( cT @ sK0 ) )
      & ( ( cS @ sK0 )
       != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ( ? [X3: a] :
        ( ( $true
         != ( cT @ X3 ) )
        & ( $true
          = ( cS @ X3 ) ) )
   => ( ( $true
       != ( cT @ sK1 ) )
      & ( $true
        = ( cS @ sK1 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f7,plain,
    ( ! [X0: a > $o,X1: a > $o] : ( X0 = X1 )
    & ( ? [X2: a] :
          ( ( ( cT @ X2 )
            = $true )
          & ( ( cS @ X2 )
           != $true ) )
      | ? [X3: a] :
          ( ( $true
           != ( cT @ X3 ) )
          & ( $true
            = ( cS @ X3 ) ) ) ) ),
    inference(rectify,[],[f6]) ).

thf(f6,plain,
    ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
    & ( ? [X2: a] :
          ( ( ( cT @ X2 )
            = $true )
          & ( ( cS @ X2 )
           != $true ) )
      | ? [X3: a] :
          ( ( $true
           != ( cT @ X3 ) )
          & ( $true
            = ( cS @ X3 ) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
     => ( ! [X2: a] :
            ( ( ( cT @ X2 )
              = $true )
           => ( ( cS @ X2 )
              = $true ) )
        & ! [X3: a] :
            ( ( $true
              = ( cS @ X3 ) )
           => ( $true
              = ( cT @ X3 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ! [X0: a > $o,X1: a > $o] : ( X0 = X1 )
     => ( ! [X2: a] :
            ( ( cT @ X2 )
           => ( cS @ X2 ) )
        & ! [X3: a] :
            ( ( cS @ X3 )
           => ( cT @ X3 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
     => ( ! [X2: a] :
            ( ( cT @ X2 )
           => ( cS @ X2 ) )
        & ! [X2: a] :
            ( ( cS @ X2 )
           => ( cT @ X2 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
   => ( ! [X2: a] :
          ( ( cT @ X2 )
         => ( cS @ X2 ) )
      & ! [X2: a] :
          ( ( cS @ X2 )
         => ( cT @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM8_pme) ).

thf(f19,plain,
    ( ( $true
     != ( cT @ sK1 ) )
    | spl2_1 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f17,plain,
    ( spl2_1
  <=> ( $true
      = ( cT @ sK1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f32,plain,
    ( ( $true
      = ( cS @ sK1 ) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f30]) ).

thf(f30,plain,
    ( spl2_4
  <=> ( $true
      = ( cS @ sK1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f50,plain,
    ( spl2_2
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f49]) ).

thf(f49,plain,
    ( $false
    | spl2_2
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f45]) ).

thf(f45,plain,
    ( ( $false = $true )
    | spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f28,f42]) ).

thf(f42,plain,
    ( ! [X0: a > $o] :
        ( $false
        = ( X0 @ sK0 ) )
    | spl2_2 ),
    inference(trivial_inequality_removal,[],[f40]) ).

thf(f40,plain,
    ( ! [X0: a > $o] :
        ( ( $true != $true )
        | ( $false
          = ( X0 @ sK0 ) ) )
    | spl2_2 ),
    inference(superposition,[],[f23,f37]) ).

thf(f23,plain,
    ( ( ( cS @ sK0 )
     != $true )
    | spl2_2 ),
    inference(avatar_component_clause,[],[f21]) ).

thf(f21,plain,
    ( spl2_2
  <=> ( ( cS @ sK0 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f28,plain,
    ( ( $true
      = ( cT @ sK0 ) )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f26]) ).

thf(f26,plain,
    ( spl2_3
  <=> ( $true
      = ( cT @ sK0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f35,plain,
    ( ~ spl2_2
    | spl2_4 ),
    inference(avatar_split_clause,[],[f11,f30,f21]) ).

thf(f11,plain,
    ( ( $true
      = ( cS @ sK1 ) )
    | ( ( cS @ sK0 )
     != $true ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f34,plain,
    ( spl2_3
    | ~ spl2_1 ),
    inference(avatar_split_clause,[],[f14,f17,f26]) ).

thf(f14,plain,
    ( ( $true
     != ( cT @ sK1 ) )
    | ( $true
      = ( cT @ sK0 ) ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f33,plain,
    ( spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f13,f30,f26]) ).

thf(f13,plain,
    ( ( $true
      = ( cS @ sK1 ) )
    | ( $true
      = ( cT @ sK0 ) ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f24,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f12,f21,f17]) ).

thf(f12,plain,
    ( ( ( cS @ sK0 )
     != $true )
    | ( $true
     != ( cT @ sK1 ) ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU844^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14  % 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
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 17:35:22 EDT 2024
% 0.20/0.35  % CPUTime    : 
% 0.20/0.35  This is a TH0_THM_EQU_NAR problem
% 0.20/0.35  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/benchmark/theBenchmark.p
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% 0.20/0.53  % (5182)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.20/0.53  % (5175)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2998ds/183Mi)
% 0.20/0.53  % (5177)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 theBenchmark for (2998ds/27Mi)
% 0.20/0.53  % (5178)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2998ds/2Mi)
% 0.20/0.53  % (5179)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2998ds/2Mi)
% 0.20/0.53  % (5181)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2998ds/18Mi)
% 0.20/0.53  % (5179)Instruction limit reached!
% 0.20/0.53  % (5179)------------------------------
% 0.20/0.53  % (5179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.53  % (5179)Termination reason: Unknown
% 0.20/0.53  % (5179)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (5179)Memory used [KB]: 5373
% 0.20/0.53  % (5179)Time elapsed: 0.003 s
% 0.20/0.53  % (5179)Instructions burned: 2 (million)
% 0.20/0.53  % (5179)------------------------------
% 0.20/0.53  % (5179)------------------------------
% 0.20/0.53  % (5182)Instruction limit reached!
% 0.20/0.53  % (5182)------------------------------
% 0.20/0.53  % (5182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.53  % (5182)Termination reason: Unknown
% 0.20/0.53  % (5182)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (5182)Memory used [KB]: 5500
% 0.20/0.53  % (5182)Time elapsed: 0.004 s
% 0.20/0.53  % (5182)Instructions burned: 3 (million)
% 0.20/0.53  % (5182)------------------------------
% 0.20/0.53  % (5182)------------------------------
% 0.20/0.53  % (5178)Instruction limit reached!
% 0.20/0.53  % (5178)------------------------------
% 0.20/0.53  % (5178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.53  % (5178)Termination reason: Unknown
% 0.20/0.53  % (5178)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (5178)Memory used [KB]: 5500
% 0.20/0.53  % (5178)Time elapsed: 0.004 s
% 0.20/0.53  % (5178)Instructions burned: 3 (million)
% 0.20/0.53  % (5178)------------------------------
% 0.20/0.53  % (5178)------------------------------
% 0.20/0.53  % (5177)First to succeed.
% 0.20/0.53  % (5175)Also succeeded, but the first one will report.
% 0.20/0.53  % (5177)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (5177)------------------------------
% 0.20/0.54  % (5177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.54  % (5177)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (5177)Memory used [KB]: 5500
% 0.20/0.54  % (5177)Time elapsed: 0.005 s
% 0.20/0.54  % (5177)Instructions burned: 2 (million)
% 0.20/0.54  % (5177)------------------------------
% 0.20/0.54  % (5177)------------------------------
% 0.20/0.54  % (5040)Success in time 0.181 s
% 0.20/0.54  % Vampire---4.8 exiting
%------------------------------------------------------------------------------