TSTP Solution File: ARI091_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ARI091_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n003.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 04:35:20 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   72 (  25 unt;   1 typ;   0 def)
%            Number of atoms       :  144 (  44 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  126 (  53   ~;  47   |;   4   &)
%                                         (  18 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  248 (  34 atm;  85 fun;  62 num;  67 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  18 usr;  19 prp; 0-2 aty)
%            Number of functors    :   10 (   1 usr;   7 con; 0-2 aty)
%            Number of variables   :   67 (  65   !;   2   ?;  67   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_8,type,
    sK0: $int ).

tff(f187,plain,
    $false,
    inference(avatar_sat_refutation,[],[f26,f31,f35,f39,f43,f47,f51,f60,f64,f68,f78,f82,f94,f98,f127,f151,f155,f171,f186]) ).

tff(f186,plain,
    ( spl1_1
    | ~ spl1_6
    | ~ spl1_18 ),
    inference(avatar_split_clause,[],[f179,f169,f45,f23]) ).

tff(f23,plain,
    ( spl1_1
  <=> ( 5 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

tff(f45,plain,
    ( spl1_6
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).

tff(f169,plain,
    ( spl1_18
  <=> ! [X0: $int] : ( $sum(sK0,$sum(-2,X0)) = $sum(3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).

tff(f179,plain,
    ( ( 5 = sK0 )
    | ~ spl1_6
    | ~ spl1_18 ),
    inference(evaluation,[],[f173]) ).

tff(f173,plain,
    ( ( $sum(3,$uminus(-2)) = $sum(sK0,0) )
    | ~ spl1_6
    | ~ spl1_18 ),
    inference(superposition,[],[f170,f46]) ).

tff(f46,plain,
    ( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
    | ~ spl1_6 ),
    inference(avatar_component_clause,[],[f45]) ).

tff(f170,plain,
    ( ! [X0: $int] : ( $sum(sK0,$sum(-2,X0)) = $sum(3,X0) )
    | ~ spl1_18 ),
    inference(avatar_component_clause,[],[f169]) ).

tff(f171,plain,
    ( spl1_18
    | ~ spl1_2
    | ~ spl1_15 ),
    inference(avatar_split_clause,[],[f133,f125,f28,f169]) ).

tff(f28,plain,
    ( spl1_2
  <=> ( 3 = $sum(sK0,-2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

tff(f125,plain,
    ( spl1_15
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).

tff(f133,plain,
    ( ! [X0: $int] : ( $sum(sK0,$sum(-2,X0)) = $sum(3,X0) )
    | ~ spl1_2
    | ~ spl1_15 ),
    inference(superposition,[],[f126,f30]) ).

tff(f30,plain,
    ( ( 3 = $sum(sK0,-2) )
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f28]) ).

tff(f126,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
    | ~ spl1_15 ),
    inference(avatar_component_clause,[],[f125]) ).

tff(f155,plain,
    ( spl1_17
    | ~ spl1_2
    | ~ spl1_14 ),
    inference(avatar_split_clause,[],[f122,f96,f28,f153]) ).

tff(f153,plain,
    ( spl1_17
  <=> ! [X0: $int] :
        ( $less($sum(X0,-2),3)
        | ~ $less(X0,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).

tff(f96,plain,
    ( spl1_14
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).

tff(f122,plain,
    ( ! [X0: $int] :
        ( $less($sum(X0,-2),3)
        | ~ $less(X0,sK0) )
    | ~ spl1_2
    | ~ spl1_14 ),
    inference(superposition,[],[f97,f30]) ).

tff(f97,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X0,X2),$sum(X1,X2))
        | ~ $less(X0,X1) )
    | ~ spl1_14 ),
    inference(avatar_component_clause,[],[f96]) ).

tff(f151,plain,
    ( spl1_16
    | ~ spl1_2
    | ~ spl1_14 ),
    inference(avatar_split_clause,[],[f116,f96,f28,f149]) ).

tff(f149,plain,
    ( spl1_16
  <=> ! [X0: $int] :
        ( $less(3,$sum(X0,-2))
        | ~ $less(sK0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).

tff(f116,plain,
    ( ! [X0: $int] :
        ( $less(3,$sum(X0,-2))
        | ~ $less(sK0,X0) )
    | ~ spl1_2
    | ~ spl1_14 ),
    inference(superposition,[],[f97,f30]) ).

tff(f127,plain,
    spl1_15,
    inference(avatar_split_clause,[],[f5,f125]) ).

tff(f5,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f98,plain,
    spl1_14,
    inference(avatar_split_clause,[],[f12,f96]) ).

tff(f12,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f94,plain,
    spl1_13,
    inference(avatar_split_clause,[],[f7,f92]) ).

tff(f92,plain,
    ( spl1_13
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).

tff(f7,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f82,plain,
    spl1_12,
    inference(avatar_split_clause,[],[f11,f80]) ).

tff(f80,plain,
    ( spl1_12
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).

tff(f11,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f78,plain,
    spl1_11,
    inference(avatar_split_clause,[],[f10,f76]) ).

tff(f76,plain,
    ( spl1_11
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).

tff(f10,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f68,plain,
    spl1_10,
    inference(avatar_split_clause,[],[f15,f66]) ).

tff(f66,plain,
    ( spl1_10
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).

tff(f15,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f64,plain,
    spl1_9,
    inference(avatar_split_clause,[],[f13,f62]) ).

tff(f62,plain,
    ( spl1_9
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).

tff(f13,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f60,plain,
    ( spl1_8
    | ~ spl1_2
    | ~ spl1_7 ),
    inference(avatar_split_clause,[],[f52,f49,f28,f57]) ).

tff(f57,plain,
    ( spl1_8
  <=> ( 3 = $sum(-2,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).

tff(f49,plain,
    ( spl1_7
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).

tff(f52,plain,
    ( ( 3 = $sum(-2,sK0) )
    | ~ spl1_2
    | ~ spl1_7 ),
    inference(superposition,[],[f50,f30]) ).

tff(f50,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
    | ~ spl1_7 ),
    inference(avatar_component_clause,[],[f49]) ).

tff(f51,plain,
    spl1_7,
    inference(avatar_split_clause,[],[f4,f49]) ).

tff(f4,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f47,plain,
    spl1_6,
    inference(avatar_split_clause,[],[f8,f45]) ).

tff(f8,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f43,plain,
    spl1_5,
    inference(avatar_split_clause,[],[f14,f41]) ).

tff(f41,plain,
    ( spl1_5
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

tff(f14,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f39,plain,
    spl1_4,
    inference(avatar_split_clause,[],[f6,f37]) ).

tff(f37,plain,
    ( spl1_4
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

tff(f6,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f35,plain,
    spl1_3,
    inference(avatar_split_clause,[],[f9,f33]) ).

tff(f33,plain,
    ( spl1_3
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f9,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f31,plain,
    spl1_2,
    inference(avatar_split_clause,[],[f21,f28]) ).

tff(f21,plain,
    3 = $sum(sK0,-2),
    inference(evaluation,[],[f19]) ).

tff(f19,plain,
    3 = $sum(sK0,$uminus(2)),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,plain,
    ( ( 5 != sK0 )
    & ( 3 = $sum(sK0,$uminus(2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).

tff(f17,plain,
    ( ? [X0: $int] :
        ( ( 5 != X0 )
        & ( 3 = $sum(X0,$uminus(2)) ) )
   => ( ( 5 != sK0 )
      & ( 3 = $sum(sK0,$uminus(2)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ? [X0: $int] :
      ( ( 5 != X0 )
      & ( 3 = $sum(X0,$uminus(2)) ) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,plain,
    ~ ! [X0: $int] :
        ( ( 3 = $sum(X0,$uminus(2)) )
       => ( 5 = X0 ) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X0: $int] :
        ( ( $difference(X0,2) = 3 )
       => ( 5 = X0 ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X0: $int] :
      ( ( $difference(X0,2) = 3 )
     => ( 5 = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_only_5_2_3) ).

tff(f26,plain,
    ~ spl1_1,
    inference(avatar_split_clause,[],[f20,f23]) ).

tff(f20,plain,
    5 != sK0,
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ARI091_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 21:46:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (19907)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (19910)WARNING: value z3 for option sas not known
% 0.14/0.37  % (19911)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (19911)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37  % (19911)Terminated due to inappropriate strategy.
% 0.14/0.37  % (19911)------------------------------
% 0.14/0.37  % (19911)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (19911)Termination reason: Inappropriate
% 0.14/0.37  
% 0.14/0.37  % (19911)Memory used [KB]: 723
% 0.14/0.37  % (19911)Time elapsed: 0.002 s
% 0.14/0.37  % (19911)Instructions burned: 2 (million)
% 0.14/0.37  % (19908)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (19911)------------------------------
% 0.14/0.37  % (19911)------------------------------
% 0.14/0.37  % (19910)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (19913)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37  % (19912)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37  % (19914)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37  % (19908)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37  % (19908)Terminated due to inappropriate strategy.
% 0.14/0.37  % (19908)------------------------------
% 0.14/0.37  % (19908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (19908)Termination reason: Inappropriate
% 0.14/0.37  
% 0.14/0.37  % (19908)Memory used [KB]: 723
% 0.14/0.37  % (19908)Time elapsed: 0.002 s
% 0.14/0.37  % (19908)Instructions burned: 2 (million)
% 0.14/0.37  % (19909)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (19908)------------------------------
% 0.14/0.37  % (19908)------------------------------
% 0.14/0.37  % (19909)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37  % (19909)Terminated due to inappropriate strategy.
% 0.14/0.37  % (19909)------------------------------
% 0.14/0.37  % (19909)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (19909)Termination reason: Inappropriate
% 0.14/0.37  
% 0.14/0.37  % (19909)Memory used [KB]: 724
% 0.14/0.37  % (19909)Time elapsed: 0.002 s
% 0.14/0.37  % (19909)Instructions burned: 2 (million)
% 0.14/0.37  % (19909)------------------------------
% 0.14/0.37  % (19909)------------------------------
% 0.14/0.38  % (19912)First to succeed.
% 0.14/0.38  % (19912)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19907"
% 0.14/0.38  % (19912)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (19912)------------------------------
% 0.14/0.38  % (19912)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (19912)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (19912)Memory used [KB]: 868
% 0.14/0.38  % (19912)Time elapsed: 0.009 s
% 0.14/0.38  % (19912)Instructions burned: 10 (million)
% 0.14/0.38  % (19907)Success in time 0.022 s
%------------------------------------------------------------------------------