TSTP Solution File: SEV273^5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV273^5 : TPTP v8.2.0. Released v4.0.0.
% 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 16:02:35 EDT 2024

% Result   : Theorem 0.13s 0.39s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (   4 unt;   0 typ;   0 def)
%            Number of atoms       :  202 (  92 equ;   1 cnn)
%            Maximal formula atoms :   14 (   9 avg)
%            Number of connectives :  285 (  47   ~;  33   |;  36   &; 146   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   82 (   0   ^  60   !;  22   ?;  82   :)

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

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

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

thf(func_def_5,type,
    sK0: a ).

thf(func_def_6,type,
    sK1: ( a > $o ) > a ).

thf(func_def_7,type,
    sK2: a > ( a > $o ) > a ).

thf(func_def_10,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(f48,plain,
    $false,
    inference(equality_resolution,[],[f33]) ).

thf(f33,plain,
    ! [X0: a] : ( sK0 != X0 ),
    inference(trivial_inequality_removal,[],[f32]) ).

thf(f32,plain,
    ! [X0: a] :
      ( ( $true != $true )
      | ( sK0 != X0 )
      | ( sK0 != sK0 ) ),
    inference(superposition,[],[f17,f31]) ).

thf(f31,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( $true
        = ( cR @ X0 @ X1 ) )
      | ( X0 != X1 )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f30]) ).

thf(f30,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( $true
       != ( X0 = X2 ) )
      | ( X0 != X1 )
      | ( $true
        = ( cR @ X0 @ X1 ) ) ),
    inference(equality_proxy_clausification,[],[f29]) ).

thf(f29,plain,
    ! [X2: a,X0: a,X1: a] :
      ( ( ( X0 = X1 )
       != $true )
      | ( $true
       != ( X0 = X2 ) )
      | ( $true
        = ( cR @ X0 @ X1 ) ) ),
    inference(superposition,[],[f16,f18]) ).

thf(f18,plain,
    ! [X0: a] :
      ( ( sK1 @ ( (=) @ X0 ) )
      = X0 ),
    inference(leibniz_equality_elimination,[],[f15]) ).

thf(f15,plain,
    ! [X1: a > $o,X6: a] :
      ( ( ( X1 @ ( sK1 @ X1 ) )
        = $true )
      | ( $true
       != ( X1 @ X6 ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ( ( cR @ sK0 @ sK0 )
     != $true )
    & ! [X1: a > $o] :
        ( ( ! [X3: a] :
              ( ( $true
               != ( X1 @ X3 ) )
              | ( ( cR @ ( sK1 @ X1 ) @ X3 )
                = $true ) )
          & ( ( X1 @ ( sK1 @ X1 ) )
            = $true )
          & ! [X4: a] :
              ( ( ( ( X1 @ ( sK2 @ X4 @ X1 ) )
                  = $true )
                & ( ( cR @ X4 @ ( sK2 @ X4 @ X1 ) )
                 != $true ) )
              | ( $true
               != ( X1 @ X4 ) )
              | ( ( sK1 @ X1 )
                = X4 ) ) )
        | ! [X6: a] :
            ( $true
           != ( X1 @ X6 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: a] :
        ( $true
       != ( cR @ X0 @ X0 ) )
   => ( ( cR @ sK0 @ sK0 )
     != $true ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ! [X1: a > $o] :
      ( ? [X2: a] :
          ( ! [X3: a] :
              ( ( $true
               != ( X1 @ X3 ) )
              | ( ( cR @ X2 @ X3 )
                = $true ) )
          & ( ( X1 @ X2 )
            = $true )
          & ! [X4: a] :
              ( ? [X5: a] :
                  ( ( $true
                    = ( X1 @ X5 ) )
                  & ( ( cR @ X4 @ X5 )
                   != $true ) )
              | ( $true
               != ( X1 @ X4 ) )
              | ( X2 = X4 ) ) )
     => ( ! [X3: a] :
            ( ( $true
             != ( X1 @ X3 ) )
            | ( ( cR @ ( sK1 @ X1 ) @ X3 )
              = $true ) )
        & ( ( X1 @ ( sK1 @ X1 ) )
          = $true )
        & ! [X4: a] :
            ( ? [X5: a] :
                ( ( $true
                  = ( X1 @ X5 ) )
                & ( ( cR @ X4 @ X5 )
                 != $true ) )
            | ( $true
             != ( X1 @ X4 ) )
            | ( ( sK1 @ X1 )
              = X4 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X1: a > $o,X4: a] :
      ( ? [X5: a] :
          ( ( $true
            = ( X1 @ X5 ) )
          & ( ( cR @ X4 @ X5 )
           != $true ) )
     => ( ( ( X1 @ ( sK2 @ X4 @ X1 ) )
          = $true )
        & ( ( cR @ X4 @ ( sK2 @ X4 @ X1 ) )
         != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ? [X0: a] :
        ( $true
       != ( cR @ X0 @ X0 ) )
    & ! [X1: a > $o] :
        ( ? [X2: a] :
            ( ! [X3: a] :
                ( ( $true
                 != ( X1 @ X3 ) )
                | ( ( cR @ X2 @ X3 )
                  = $true ) )
            & ( ( X1 @ X2 )
              = $true )
            & ! [X4: a] :
                ( ? [X5: a] :
                    ( ( $true
                      = ( X1 @ X5 ) )
                    & ( ( cR @ X4 @ X5 )
                     != $true ) )
                | ( $true
                 != ( X1 @ X4 ) )
                | ( X2 = X4 ) ) )
        | ! [X6: a] :
            ( $true
           != ( X1 @ X6 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ? [X6: a] :
        ( $true
       != ( cR @ X6 @ X6 ) )
    & ! [X0: a > $o] :
        ( ? [X2: a] :
            ( ! [X5: a] :
                ( ( ( X0 @ X5 )
                 != $true )
                | ( $true
                  = ( cR @ X2 @ X5 ) ) )
            & ( ( X0 @ X2 )
              = $true )
            & ! [X3: a] :
                ( ? [X4: a] :
                    ( ( ( X0 @ X4 )
                      = $true )
                    & ( ( cR @ X3 @ X4 )
                     != $true ) )
                | ( ( X0 @ X3 )
                 != $true )
                | ( X2 = X3 ) ) )
        | ! [X1: a] :
            ( ( X0 @ X1 )
           != $true ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( ? [X6: a] :
        ( $true
       != ( cR @ X6 @ X6 ) )
    & ! [X0: a > $o] :
        ( ? [X2: a] :
            ( ! [X5: a] :
                ( ( ( X0 @ X5 )
                 != $true )
                | ( $true
                  = ( cR @ X2 @ X5 ) ) )
            & ( ( X0 @ X2 )
              = $true )
            & ! [X3: a] :
                ( ( X2 = X3 )
                | ? [X4: a] :
                    ( ( ( X0 @ X4 )
                      = $true )
                    & ( ( cR @ X3 @ X4 )
                     != $true ) )
                | ( ( X0 @ X3 )
                 != $true ) ) )
        | ! [X1: a] :
            ( ( X0 @ X1 )
           != $true ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X0: a > $o] :
          ( ? [X1: a] :
              ( ( X0 @ X1 )
              = $true )
         => ? [X2: a] :
              ( ! [X5: a] :
                  ( ( ( X0 @ X5 )
                    = $true )
                 => ( $true
                    = ( cR @ X2 @ X5 ) ) )
              & ( ( X0 @ X2 )
                = $true )
              & ! [X3: a] :
                  ( ( ! [X4: a] :
                        ( ( ( X0 @ X4 )
                          = $true )
                       => ( ( cR @ X3 @ X4 )
                          = $true ) )
                    & ( ( X0 @ X3 )
                      = $true ) )
                 => ( X2 = X3 ) ) ) )
     => ! [X6: a] :
          ( $true
          = ( cR @ X6 @ X6 ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ! [X0: a > $o] :
          ( ? [X1: a] : ( X0 @ X1 )
         => ? [X2: a] :
              ( ! [X3: a] :
                  ( ( ! [X4: a] :
                        ( ( X0 @ X4 )
                       => ( cR @ X3 @ X4 ) )
                    & ( X0 @ X3 ) )
                 => ( X2 = X3 ) )
              & ! [X5: a] :
                  ( ( X0 @ X5 )
                 => ( cR @ X2 @ X5 ) )
              & ( X0 @ X2 ) ) )
     => ! [X6: a] : ( cR @ X6 @ X6 ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ! [X0: a > $o] :
          ( ? [X1: a] : ( X0 @ X1 )
         => ? [X1: a] :
              ( ! [X3: a] :
                  ( ( ! [X2: a] :
                        ( ( X0 @ X2 )
                       => ( cR @ X3 @ X2 ) )
                    & ( X0 @ X3 ) )
                 => ( X1 = X3 ) )
              & ! [X2: a] :
                  ( ( X0 @ X2 )
                 => ( cR @ X1 @ X2 ) )
              & ( X0 @ X1 ) ) )
     => ! [X2: a] : ( cR @ X2 @ X2 ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ! [X0: a > $o] :
        ( ? [X1: a] : ( X0 @ X1 )
       => ? [X1: a] :
            ( ! [X3: a] :
                ( ( ! [X2: a] :
                      ( ( X0 @ X2 )
                     => ( cR @ X3 @ X2 ) )
                  & ( X0 @ X3 ) )
               => ( X1 = X3 ) )
            & ! [X2: a] :
                ( ( X0 @ X2 )
               => ( cR @ X1 @ X2 ) )
            & ( X0 @ X1 ) ) )
   => ! [X2: a] : ( cR @ X2 @ X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM542_pme) ).

thf(f16,plain,
    ! [X3: a,X1: a > $o,X6: a] :
      ( ( ( cR @ ( sK1 @ X1 ) @ X3 )
        = $true )
      | ( $true
       != ( X1 @ X6 ) )
      | ( $true
       != ( X1 @ X3 ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f17,plain,
    ( ( cR @ sK0 @ sK0 )
   != $true ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV273^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Fri Jun 21 19:44:09 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.36  This is a TH0_THM_EQU_NAR problem
% 0.13/0.36  Running higher-order theorem proving
% 0.13/0.36  Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.13/0.38  % (21444)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38  % (21445)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 theBenchmark for (2999ds/4Mi)
% 0.13/0.38  % (21447)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38  % (21449)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.38  % (21446)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 (2999ds/27Mi)
% 0.13/0.38  % (21448)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 (2999ds/2Mi)
% 0.13/0.38  % (21451)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38  % (21447)Instruction limit reached!
% 0.13/0.38  % (21447)------------------------------
% 0.13/0.38  % (21447)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38  % (21447)Termination reason: Unknown
% 0.13/0.38  % (21447)Termination phase: Saturation
% 0.13/0.38  
% 0.13/0.38  % (21447)Memory used [KB]: 5500
% 0.13/0.38  % (21447)Time elapsed: 0.004 s
% 0.13/0.38  % (21447)Instructions burned: 2 (million)
% 0.13/0.38  % (21447)------------------------------
% 0.13/0.38  % (21447)------------------------------
% 0.13/0.38  % (21448)Instruction limit reached!
% 0.13/0.38  % (21448)------------------------------
% 0.13/0.38  % (21448)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38  % (21448)Termination reason: Unknown
% 0.13/0.38  % (21448)Termination phase: Saturation
% 0.13/0.38  
% 0.13/0.38  % (21448)Memory used [KB]: 5500
% 0.13/0.38  % (21448)Time elapsed: 0.004 s
% 0.13/0.38  % (21448)Instructions burned: 2 (million)
% 0.13/0.38  % (21448)------------------------------
% 0.13/0.38  % (21448)------------------------------
% 0.13/0.38  % (21446)Refutation not found, incomplete strategy
% 0.13/0.38  % (21446)------------------------------
% 0.13/0.38  % (21446)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38  % (21446)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.38  
% 0.13/0.38  
% 0.13/0.38  % (21446)Memory used [KB]: 5500
% 0.13/0.38  % (21446)Time elapsed: 0.004 s
% 0.13/0.38  % (21446)Instructions burned: 2 (million)
% 0.13/0.38  % (21446)------------------------------
% 0.13/0.38  % (21446)------------------------------
% 0.13/0.38  % (21445)Instruction limit reached!
% 0.13/0.38  % (21445)------------------------------
% 0.13/0.38  % (21445)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38  % (21445)Termination reason: Unknown
% 0.13/0.38  % (21445)Termination phase: Saturation
% 0.13/0.38  
% 0.13/0.38  % (21445)Memory used [KB]: 5500
% 0.13/0.38  % (21445)Time elapsed: 0.007 s
% 0.13/0.38  % (21445)Instructions burned: 4 (million)
% 0.13/0.38  % (21445)------------------------------
% 0.13/0.38  % (21445)------------------------------
% 0.13/0.38  % (21449)First to succeed.
% 0.13/0.39  % (21449)Refutation found. Thanks to Tanya!
% 0.13/0.39  % SZS status Theorem for theBenchmark
% 0.13/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39  % (21449)------------------------------
% 0.13/0.39  % (21449)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39  % (21449)Termination reason: Refutation
% 0.13/0.39  
% 0.13/0.39  % (21449)Memory used [KB]: 5500
% 0.13/0.39  % (21449)Time elapsed: 0.007 s
% 0.13/0.39  % (21449)Instructions burned: 5 (million)
% 0.13/0.39  % (21449)------------------------------
% 0.13/0.39  % (21449)------------------------------
% 0.13/0.39  % (21442)Success in time 0.021 s
%------------------------------------------------------------------------------