TSTP Solution File: SYO024^1 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SYO024^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% 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 : Mon Jun 24 21:00:08 EDT 2024

% Result   : Theorem 0.12s 0.38s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   44 (  23 unt;   0 typ;   0 def)
%            Number of atoms       :  227 (  66 equ;  15 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  212 (  84   ~;  48   |;  23   &;  45   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   53 (  53   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   5 usr;   6 con; 0-2 aty)
%                                         (   4  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   47 (  45   ^   2   !;   0   ?;  47   :)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_0,type,
    leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).

thf(func_def_14,type,
    sK1: ( $o > $o > $o ) > $o ).

thf(func_def_15,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(f54,plain,
    $false,
    inference(trivial_inequality_removal,[],[f53]) ).

thf(f53,plain,
    $true = $false,
    inference(backward_demodulation,[],[f46,f52]) ).

thf(f52,plain,
    sK4 = $false,
    inference(trivial_inequality_removal,[],[f51]) ).

thf(f51,plain,
    ( ( $true = $false )
    | ( sK4 = $false ) ),
    inference(forward_demodulation,[],[f34,f41]) ).

thf(f41,plain,
    $true = sK3,
    inference(duplicate_literal_removal,[],[f40]) ).

thf(f40,plain,
    ( ( $true = sK3 )
    | ( $true = sK3 ) ),
    inference(not_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ( ( ~ sK3 = $false )
    | ( $true = sK3 ) ),
    inference(binary_proxy_clausification,[],[f37]) ).

thf(f37,plain,
    ( ( ( sK3
        & sK4 )
      = $true )
    | ( ~ sK3 = $false ) ),
    inference(binary_proxy_clausification,[],[f35]) ).

thf(f35,plain,
    ( ( ( ~ sK3
        | ~ sK4 )
      = $false )
    | ( ( sK3
        & sK4 )
      = $true ) ),
    inference(not_proxy_clausification,[],[f26]) ).

thf(f26,plain,
    ( ( $true
      = ( ~ ( ~ sK3
            | ~ sK4 ) ) )
    | ( ( sK3
        & sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( sK3
      & sK4 )
   != ( ~ ( ~ sK3
          | ~ sK4 ) ) ),
    inference(beta_eta_normalization,[],[f24]) ).

thf(f24,plain,
    ( ( sK3
      & sK4 )
   != ( ^ [Y0: $o] :
          ~ ( ~ sK3
            | ~ Y0 )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f23]) ).

thf(f23,plain,
    ( ( ^ [Y0: $o] :
          ~ ( ~ sK3
            | ~ Y0 ) )
   != ( (&) @ sK3 ) ),
    inference(beta_eta_normalization,[],[f22]) ).

thf(f22,plain,
    ( ( (&) @ sK3 )
   != ( ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 )
      @ sK3 ) ),
    inference(negative_extensionality,[],[f21]) ).

thf(f21,plain,
    ( (&)
   != ( ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 ) ) ),
    inference(trivial_inequality_removal,[],[f19]) ).

thf(f19,plain,
    ( ( $true = $false )
    | ( (&)
     != ( ^ [Y0: $o,Y1: $o] :
            ~ ( ~ Y0
              | ~ Y1 ) ) ) ),
    inference(constrained_superposition,[],[f17,f16]) ).

thf(f16,plain,
    ( ( sK1
      @ ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( ( sK1 @ (&) )
     => ( sK1
        @ ^ [Y0: $o,Y1: $o] :
            ~ ( ~ Y0
              | ~ Y1 ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f14]) ).

thf(f14,plain,
    ( $false
    = ( ^ [Y0: ( $o > $o > $o ) > $o] :
          ( ( Y0 @ (&) )
         => ( Y0
            @ ^ [Y1: $o,Y2: $o] :
                ~ ( ~ Y1
                  | ~ Y2 ) ) )
      @ sK1 ) ),
    inference(sigma_clausification,[],[f13]) ).

thf(f13,plain,
    ( $true
   != ( !! @ ( ( $o > $o > $o ) > $o )
      @ ^ [Y0: ( $o > $o > $o ) > $o] :
          ( ( Y0 @ (&) )
         => ( Y0
            @ ^ [Y1: $o,Y2: $o] :
                ~ ( ~ Y1
                  | ~ Y2 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f12]) ).

thf(f12,plain,
    ( $true
   != ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
          ( !! @ ( ( $o > $o > $o ) > $o )
          @ ^ [Y2: ( $o > $o > $o ) > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) )
      @ (&)
      @ ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 ) ) ),
    inference(definition_unfolding,[],[f10,f11]) ).

thf(f11,plain,
    ( leibeq
    = ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
          ( !! @ ( ( $o > $o > $o ) > $o )
          @ ^ [Y2: ( $o > $o > $o ) > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( leibeq
    = ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
          ( !! @ ( ( $o > $o > $o ) > $o )
          @ ^ [Y2: ( $o > $o > $o ) > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) ) ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ( leibeq
    = ( ^ [X0: $o > $o > $o,X1: $o > $o > $o] :
        ! [X2: ( $o > $o > $o ) > $o] :
          ( ( X2 @ X0 )
         => ( X2 @ X1 ) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( leibeq
    = ( ^ [X0: $o > $o > $o,X1: $o > $o > $o] :
        ! [X2: ( $o > $o > $o ) > $o] :
          ( ( X2 @ X0 )
         => ( X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq) ).

thf(f10,plain,
    ( $true
   != ( leibeq @ (&)
      @ ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 ) ) ),
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ( $true
   != ( leibeq @ (&)
      @ ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( $true
   != ( leibeq @ (&)
      @ ^ [Y0: $o,Y1: $o] :
          ~ ( ~ Y0
            | ~ Y1 ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ( leibeq @ (&)
      @ ^ [X0: $o,X1: $o] :
          ~ ( ~ X1
            | ~ X0 ) ),
    inference(rectify,[],[f3]) ).

thf(f3,negated_conjecture,
    ~ ( leibeq @ (&)
      @ ^ [X0: $o,X1: $o] :
          ~ ( ~ X1
            | ~ X0 ) ),
    inference(negated_conjecture,[],[f2]) ).

thf(f2,conjecture,
    ( leibeq @ (&)
    @ ^ [X0: $o,X1: $o] :
        ~ ( ~ X1
          | ~ X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(f17,plain,
    ( $true
    = ( sK1 @ (&) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f34,plain,
    ( ( sK3 = $false )
    | ( sK4 = $false ) ),
    inference(duplicate_literal_removal,[],[f33]) ).

thf(f33,plain,
    ( ( sK4 = $false )
    | ( sK3 = $false )
    | ( sK4 = $false ) ),
    inference(not_proxy_clausification,[],[f32]) ).

thf(f32,plain,
    ( ( sK4 = $false )
    | ( ~ sK4 = $true )
    | ( sK3 = $false ) ),
    inference(duplicate_literal_removal,[],[f31]) ).

thf(f31,plain,
    ( ( sK3 = $false )
    | ( sK3 = $false )
    | ( ~ sK4 = $true )
    | ( sK4 = $false ) ),
    inference(not_proxy_clausification,[],[f30]) ).

thf(f30,plain,
    ( ( sK3 = $false )
    | ( sK4 = $false )
    | ( $true = ~ sK3 )
    | ( ~ sK4 = $true ) ),
    inference(binary_proxy_clausification,[],[f29]) ).

thf(f29,plain,
    ( ( sK4 = $false )
    | ( $true
      = ( ~ sK3
        | ~ sK4 ) )
    | ( sK3 = $false ) ),
    inference(not_proxy_clausification,[],[f28]) ).

thf(f28,plain,
    ( ( sK3 = $false )
    | ( ( ~ ( ~ sK3
            | ~ sK4 ) )
      = $false )
    | ( sK4 = $false ) ),
    inference(binary_proxy_clausification,[],[f27]) ).

thf(f27,plain,
    ( ( ( sK3
        & sK4 )
      = $false )
    | ( ( ~ ( ~ sK3
            | ~ sK4 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

thf(f46,plain,
    sK4 = $true,
    inference(duplicate_literal_removal,[],[f44]) ).

thf(f44,plain,
    ( ( sK4 = $true )
    | ( sK4 = $true ) ),
    inference(binary_proxy_clausification,[],[f43]) ).

thf(f43,plain,
    ( ( sK4 = $true )
    | ( ( sK3
        & sK4 )
      = $true ) ),
    inference(not_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ( ( ~ sK4 = $false )
    | ( ( sK3
        & sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO024^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun Jun 23 09:15:24 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a TH0_THM_EQU_NAR problem
% 0.12/0.36  Running higher-order theorem proving
% 0.12/0.36  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
% 0.12/0.38  % (10998)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)
% 0.12/0.38  % (10996)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)
% 0.12/0.38  % (10995)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)
% 0.12/0.38  % (10997)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.38  % (10994)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38  % (10999)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)
% 0.12/0.38  % (11000)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38  % (10997)Instruction limit reached!
% 0.12/0.38  % (10997)------------------------------
% 0.12/0.38  % (10997)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (10997)Termination reason: Unknown
% 0.12/0.38  % (10997)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (10997)Memory used [KB]: 5373
% 0.12/0.38  % (10997)Time elapsed: 0.004 s
% 0.12/0.38  % (10997)Instructions burned: 2 (million)
% 0.12/0.38  % (10997)------------------------------
% 0.12/0.38  % (10997)------------------------------
% 0.12/0.38  % (10998)Instruction limit reached!
% 0.12/0.38  % (10998)------------------------------
% 0.12/0.38  % (10998)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (10998)Termination reason: Unknown
% 0.12/0.38  % (10998)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (10998)Memory used [KB]: 5373
% 0.12/0.38  % (10998)Time elapsed: 0.004 s
% 0.12/0.38  % (10998)Instructions burned: 2 (million)
% 0.12/0.38  % (10998)------------------------------
% 0.12/0.38  % (10998)------------------------------
% 0.12/0.38  % (10999)Refutation not found, incomplete strategy
% 0.12/0.38  % (10999)------------------------------
% 0.12/0.38  % (10999)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (10999)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38  
% 0.12/0.38  
% 0.12/0.38  % (10999)Memory used [KB]: 5373
% 0.12/0.38  % (10999)Time elapsed: 0.004 s
% 0.12/0.38  % (10999)Instructions burned: 1 (million)
% 0.12/0.38  % (10999)------------------------------
% 0.12/0.38  % (10999)------------------------------
% 0.12/0.38  % (10996)Refutation not found, incomplete strategy
% 0.12/0.38  % (10996)------------------------------
% 0.12/0.38  % (10996)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (10996)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38  
% 0.12/0.38  
% 0.12/0.38  % (10996)Memory used [KB]: 5500
% 0.12/0.38  % (10996)Time elapsed: 0.004 s
% 0.12/0.38  % (10996)Instructions burned: 1 (million)
% 0.12/0.38  % (10996)------------------------------
% 0.12/0.38  % (10996)------------------------------
% 0.12/0.38  % (10995)Refutation not found, incomplete strategy
% 0.12/0.38  % (10995)------------------------------
% 0.12/0.38  % (10995)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (10995)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38  
% 0.12/0.38  
% 0.12/0.38  % (10995)Memory used [KB]: 5500
% 0.12/0.38  % (10995)Time elapsed: 0.003 s
% 0.12/0.38  % (10995)Instructions burned: 1 (million)
% 0.12/0.38  % (10995)------------------------------
% 0.12/0.38  % (10995)------------------------------
% 0.12/0.38  % (11000)First to succeed.
% 0.12/0.38  % (10994)Also succeeded, but the first one will report.
% 0.12/0.38  % (11000)Refutation found. Thanks to Tanya!
% 0.12/0.38  % SZS status Theorem for theBenchmark
% 0.12/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38  % (11000)------------------------------
% 0.12/0.38  % (11000)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (11000)Termination reason: Refutation
% 0.12/0.38  
% 0.12/0.38  % (11000)Memory used [KB]: 5500
% 0.12/0.38  % (11000)Time elapsed: 0.006 s
% 0.12/0.38  % (11000)Instructions burned: 3 (million)
% 0.12/0.38  % (11000)------------------------------
% 0.12/0.38  % (11000)------------------------------
% 0.12/0.38  % (10993)Success in time 0.02 s
%------------------------------------------------------------------------------