TSTP Solution File: SEV116^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV116^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n021.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 16:01:52 EDT 2024

% Result   : Theorem 0.22s 0.40s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   26 (  23 unt;   0 typ;   0 def)
%            Number of atoms       :  229 (  22 equ;   0 cnn)
%            Maximal formula atoms :   11 (   8 avg)
%            Number of connectives :  366 (   6   ~;   0   |;  41   &; 253   @)
%                                         (   0 <=>;  41  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  131 ( 131   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   6 usr;   5 con; 0-3 aty)
%                                         (  25  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   65 (  61   ^   4   !;   0   ?;  65   :)

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

thf(func_def_3,type,
    cSTRANGE_HO_ABBR: ( ( $i > $i > $o ) > $o ) > $i > $i > $o ).

thf(func_def_17,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_18,type,
    sK2: $i > $i > $o ).

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

thf(f53,plain,
    $false = $true,
    inference(forward_demodulation,[],[f52,f16]) ).

thf(f16,plain,
    ( $false
    = ( !! @ ( $i > $i > $o )
      @ ^ [Y0: $i > $i > $o] :
          ( ( ( cS @ Y0 )
            & ( Y0 @ y @ x ) )
         => ( Y0 @ x @ y ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( $false
    = ( ( ( cS
          @ ^ [Y0: $i,Y1: $i] :
              ( !! @ ( $i > $i > $o )
              @ ^ [Y2: $i > $i > $o] :
                  ( ( ( cS @ Y2 )
                    & ( Y2 @ Y0 @ Y1 ) )
                 => ( Y2 @ Y1 @ Y0 ) ) ) )
        & ( !! @ ( $i > $i > $o )
          @ ^ [Y0: $i > $i > $o] :
              ( ( ( cS @ Y0 )
                & ( Y0 @ x @ y ) )
             => ( Y0 @ y @ x ) ) ) )
     => ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ y @ x ) )
           => ( Y0 @ x @ y ) ) ) ) ),
    inference(not_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( ~ ( ( ( cS
              @ ^ [Y0: $i,Y1: $i] :
                  ( !! @ ( $i > $i > $o )
                  @ ^ [Y2: $i > $i > $o] :
                      ( ( ( cS @ Y2 )
                        & ( Y2 @ Y0 @ Y1 ) )
                     => ( Y2 @ Y1 @ Y0 ) ) ) )
            & ( !! @ ( $i > $i > $o )
              @ ^ [Y0: $i > $i > $o] :
                  ( ( ( cS @ Y0 )
                    & ( Y0 @ x @ y ) )
                 => ( Y0 @ y @ x ) ) ) )
         => ( !! @ ( $i > $i > $o )
            @ ^ [Y0: $i > $i > $o] :
                ( ( ( cS @ Y0 )
                  & ( Y0 @ y @ x ) )
               => ( Y0 @ x @ y ) ) ) ) )
    = $true ),
    inference(beta_eta_normalization,[],[f11]) ).

thf(f11,plain,
    ( ( ~ ( ( ( cS
              @ ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
                    ( !! @ ( $i > $i > $o )
                    @ ^ [Y3: $i > $i > $o] :
                        ( ( ( Y0 @ Y3 )
                          & ( Y3 @ Y1 @ Y2 ) )
                       => ( Y3 @ Y2 @ Y1 ) ) )
                @ cS ) )
            & ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
                  ( !! @ ( $i > $i > $o )
                  @ ^ [Y3: $i > $i > $o] :
                      ( ( ( Y0 @ Y3 )
                        & ( Y3 @ Y1 @ Y2 ) )
                     => ( Y3 @ Y2 @ Y1 ) ) )
              @ cS
              @ x
              @ y ) )
         => ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
                ( !! @ ( $i > $i > $o )
                @ ^ [Y3: $i > $i > $o] :
                    ( ( ( Y0 @ Y3 )
                      & ( Y3 @ Y1 @ Y2 ) )
                   => ( Y3 @ Y2 @ Y1 ) ) )
            @ cS
            @ y
            @ x ) ) )
    = $true ),
    inference(definition_unfolding,[],[f9,f10,f10,f10]) ).

thf(f10,plain,
    ( cSTRANGE_HO_ABBR
    = ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y3: $i > $i > $o] :
              ( ( ( Y0 @ Y3 )
                & ( Y3 @ Y1 @ Y2 ) )
             => ( Y3 @ Y2 @ Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f6]) ).

thf(f6,plain,
    ( cSTRANGE_HO_ABBR
    = ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y3: $i > $i > $o] :
              ( ( ( Y0 @ Y3 )
                & ( Y3 @ Y1 @ Y2 ) )
             => ( Y3 @ Y2 @ Y1 ) ) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ( cSTRANGE_HO_ABBR
    = ( ^ [X0: ( $i > $i > $o ) > $o,X1: $i,X2: $i] :
        ! [X3: $i > $i > $o] :
          ( ( ( X3 @ X1 @ X2 )
            & ( X0 @ X3 ) )
         => ( X3 @ X2 @ X1 ) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( cSTRANGE_HO_ABBR
    = ( ^ [X0: ( $i > $i > $o ) > $o,X1: $i,X2: $i] :
        ! [X3: $i > $i > $o] :
          ( ( ( X3 @ X1 @ X2 )
            & ( X0 @ X3 ) )
         => ( X3 @ X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSTRANGE_HO_ABBR_def) ).

thf(f9,plain,
    ( ( ~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
            & ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
         => ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ) )
    = $true ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
            & ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
         => ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ) )
    = $true ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ~ ( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
        & ( cS @ ( cSTRANGE_HO_ABBR @ cS ) ) )
     => ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
    inference(rectify,[],[f3]) ).

thf(f3,negated_conjecture,
    ~ ( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
        & ( cS @ ( cSTRANGE_HO_ABBR @ cS ) ) )
     => ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
    inference(negated_conjecture,[],[f2]) ).

thf(f2,conjecture,
    ( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
      & ( cS @ ( cSTRANGE_HO_ABBR @ cS ) ) )
   => ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSTRANGE_HO_EXAMPLE) ).

thf(f52,plain,
    ( $true
    = ( !! @ ( $i > $i > $o )
      @ ^ [Y0: $i > $i > $o] :
          ( ( ( cS @ Y0 )
            & ( Y0 @ y @ x ) )
         => ( Y0 @ x @ y ) ) ) ),
    inference(boolean_simplification,[],[f51]) ).

thf(f51,plain,
    ( ( $true
     => ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ y @ x ) )
           => ( Y0 @ x @ y ) ) ) )
    = $true ),
    inference(forward_demodulation,[],[f47,f32]) ).

thf(f32,plain,
    ( ( !! @ ( $i > $i > $o )
      @ ^ [Y0: $i > $i > $o] :
          ( ( ( cS @ Y0 )
            & ( Y0 @ x @ y ) )
         => ( Y0 @ y @ x ) ) )
    = $true ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( ( ( cS
        @ ^ [Y0: $i,Y1: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y2: $i > $i > $o] :
                ( ( ( cS @ Y2 )
                  & ( Y2 @ Y0 @ Y1 ) )
               => ( Y2 @ Y1 @ Y0 ) ) ) )
      & ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ x @ y ) )
           => ( Y0 @ y @ x ) ) ) )
    = $true ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f47,plain,
    ( $true
    = ( ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ x @ y ) )
           => ( Y0 @ y @ x ) ) )
     => ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ y @ x ) )
           => ( Y0 @ x @ y ) ) ) ) ),
    inference(boolean_simplification,[],[f46]) ).

thf(f46,plain,
    ( $true
    = ( ( $true
        & ( !! @ ( $i > $i > $o )
          @ ^ [Y0: $i > $i > $o] :
              ( ( ( cS @ Y0 )
                & ( Y0 @ x @ y ) )
             => ( Y0 @ y @ x ) ) ) )
     => ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ y @ x ) )
           => ( Y0 @ x @ y ) ) ) ) ),
    inference(beta_eta_normalization,[],[f41]) ).

thf(f41,plain,
    ( $true
    = ( ( $true
        & ( ^ [Y0: $i,Y1: $i] :
              ( !! @ ( $i > $i > $o )
              @ ^ [Y2: $i > $i > $o] :
                  ( ( ( cS @ Y2 )
                    & ( Y2 @ Y0 @ Y1 ) )
                 => ( Y2 @ Y1 @ Y0 ) ) )
          @ x
          @ y ) )
     => ( ^ [Y0: $i,Y1: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y2: $i > $i > $o] :
                ( ( ( cS @ Y2 )
                  & ( Y2 @ Y0 @ Y1 ) )
               => ( Y2 @ Y1 @ Y0 ) ) )
        @ y
        @ x ) ) ),
    inference(superposition,[],[f37,f35]) ).

thf(f35,plain,
    ( ( cS
      @ ^ [Y0: $i,Y1: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y2: $i > $i > $o] :
              ( ( ( cS @ Y2 )
                & ( Y2 @ Y0 @ Y1 ) )
             => ( Y2 @ Y1 @ Y0 ) ) ) )
    = $true ),
    inference(boolean_simplification,[],[f34]) ).

thf(f34,plain,
    ( ( ( cS
        @ ^ [Y0: $i,Y1: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y2: $i > $i > $o] :
                ( ( ( cS @ Y2 )
                  & ( Y2 @ Y0 @ Y1 ) )
               => ( Y2 @ Y1 @ Y0 ) ) ) )
      & $true )
    = $true ),
    inference(backward_demodulation,[],[f17,f32]) ).

thf(f37,plain,
    ! [X1: $i > $i > $o] :
      ( $true
      = ( ( ( cS @ X1 )
          & ( X1 @ x @ y ) )
       => ( X1 @ y @ x ) ) ),
    inference(beta_eta_normalization,[],[f36]) ).

thf(f36,plain,
    ! [X1: $i > $i > $o] :
      ( ( ^ [Y0: $i > $i > $o] :
            ( ( ( cS @ Y0 )
              & ( Y0 @ x @ y ) )
           => ( Y0 @ y @ x ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14  % Problem    : SEV116^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.14/0.14  % Command    : run_vampire %s %d THM
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Jun 21 19:12:09 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.36  This is a TH0_THM_EQU_NAR problem
% 0.14/0.36  Running higher-order theorem proving
% 0.14/0.36  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.37  % (10839)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38  % (10841)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)
% 0.22/0.38  % (10843)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)
% 0.22/0.38  % (10844)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)
% 0.22/0.38  % (10842)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38  % (10840)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)
% 0.22/0.38  % (10845)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38  % (10842)Instruction limit reached!
% 0.22/0.38  % (10842)------------------------------
% 0.22/0.38  % (10842)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38  % (10842)Termination reason: Unknown
% 0.22/0.38  % (10842)Termination phase: Saturation
% 0.22/0.38  % (10844)Refutation not found, incomplete strategy
% 0.22/0.38  % (10844)------------------------------
% 0.22/0.38  % (10844)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38  % (10844)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38  
% 0.22/0.38  
% 0.22/0.38  % (10844)Memory used [KB]: 5500
% 0.22/0.38  % (10844)Time elapsed: 0.003 s
% 0.22/0.38  % (10844)Instructions burned: 1 (million)
% 0.22/0.38  % (10844)------------------------------
% 0.22/0.38  % (10844)------------------------------
% 0.22/0.38  % (10843)Instruction limit reached!
% 0.22/0.38  % (10843)------------------------------
% 0.22/0.38  % (10843)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38  % (10843)Termination reason: Unknown
% 0.22/0.38  % (10843)Termination phase: Saturation
% 0.22/0.38  
% 0.22/0.38  % (10843)Memory used [KB]: 5500
% 0.22/0.38  % (10843)Time elapsed: 0.003 s
% 0.22/0.38  % (10843)Instructions burned: 2 (million)
% 0.22/0.38  % (10843)------------------------------
% 0.22/0.38  % (10843)------------------------------
% 0.22/0.38  
% 0.22/0.38  % (10842)Memory used [KB]: 5500
% 0.22/0.38  % (10842)Time elapsed: 0.003 s
% 0.22/0.38  % (10842)Instructions burned: 2 (million)
% 0.22/0.38  % (10842)------------------------------
% 0.22/0.38  % (10842)------------------------------
% 0.22/0.38  % (10841)Refutation not found, incomplete strategy
% 0.22/0.38  % (10841)------------------------------
% 0.22/0.38  % (10841)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38  % (10841)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.38  
% 0.22/0.38  
% 0.22/0.38  % (10841)Memory used [KB]: 5500
% 0.22/0.38  % (10841)Time elapsed: 0.004 s
% 0.22/0.38  % (10841)Instructions burned: 3 (million)
% 0.22/0.38  % (10841)------------------------------
% 0.22/0.38  % (10841)------------------------------
% 0.22/0.38  % (10840)Instruction limit reached!
% 0.22/0.38  % (10840)------------------------------
% 0.22/0.38  % (10840)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38  % (10840)Termination reason: Unknown
% 0.22/0.38  % (10840)Termination phase: Saturation
% 0.22/0.38  
% 0.22/0.38  % (10840)Memory used [KB]: 5500
% 0.22/0.38  % (10840)Time elapsed: 0.004 s
% 0.22/0.38  % (10840)Instructions burned: 5 (million)
% 0.22/0.38  % (10840)------------------------------
% 0.22/0.38  % (10840)------------------------------
% 0.22/0.39  % (10845)Instruction limit reached!
% 0.22/0.39  % (10845)------------------------------
% 0.22/0.39  % (10845)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39  % (10845)Termination reason: Unknown
% 0.22/0.39  % (10845)Termination phase: Saturation
% 0.22/0.39  
% 0.22/0.39  % (10845)Memory used [KB]: 5628
% 0.22/0.39  % (10845)Time elapsed: 0.012 s
% 0.22/0.39  % (10845)Instructions burned: 18 (million)
% 0.22/0.39  % (10845)------------------------------
% 0.22/0.39  % (10845)------------------------------
% 0.22/0.39  % (10850)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.22/0.39  % (10848)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.39  % (10847)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.22/0.39  % (10850)First to succeed.
% 0.22/0.40  % (10846)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40  % (10849)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40  % (10850)Refutation found. Thanks to Tanya!
% 0.22/0.40  % SZS status Theorem for theBenchmark
% 0.22/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40  % (10850)------------------------------
% 0.22/0.40  % (10850)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40  % (10850)Termination reason: Refutation
% 0.22/0.40  
% 0.22/0.40  % (10850)Memory used [KB]: 5500
% 0.22/0.40  % (10850)Time elapsed: 0.006 s
% 0.22/0.40  % (10850)Instructions burned: 7 (million)
% 0.22/0.40  % (10850)------------------------------
% 0.22/0.40  % (10850)------------------------------
% 0.22/0.40  % (10838)Success in time 0.026 s
%------------------------------------------------------------------------------