TSTP Solution File: SYN417+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 Apr 30 18:03:14 EDT 2024

% Result   : Theorem 0.15s 0.33s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   78 (   2 unt;   0 def)
%            Number of atoms       :  278 ( 165 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  350 ( 150   ~; 146   |;  36   &)
%                                         (   6 <=>;  10  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-1 aty)
%            Number of variables   :   69 (  47   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f108,plain,
    $false,
    inference(avatar_sat_refutation,[],[f33,f54,f91,f94,f98,f106]) ).

fof(f106,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f105]) ).

fof(f105,plain,
    ( $false
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f104,f60]) ).

fof(f60,plain,
    ( g(sK2) != sK3(g(sK2))
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f57]) ).

fof(f57,plain,
    ( g(sK2) != g(sK2)
    | g(sK2) != sK3(g(sK2))
    | ~ spl5_1 ),
    inference(superposition,[],[f56,f55]) ).

fof(f55,plain,
    ( sK2 = f(g(sK2))
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f17,f28]) ).

fof(f28,plain,
    ( sP0
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f26]) ).

fof(f26,plain,
    ( spl5_1
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f17,plain,
    ( sK2 = f(g(sK2))
    | ~ sP0 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ( ( sP0
      | ! [X0] :
          ( ( sK1(X0) != X0
            & sK1(X0) = f(g(sK1(X0))) )
          | f(g(X0)) != X0 ) )
    & ( ( ! [X3] :
            ( sK2 = X3
            | f(g(X3)) != X3 )
        & sK2 = f(g(sK2)) )
      | ~ sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f8,f10,f9]) ).

fof(f9,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & f(g(X1)) = X1 )
     => ( sK1(X0) != X0
        & sK1(X0) = f(g(sK1(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ( ? [X2] :
        ( ! [X3] :
            ( X2 = X3
            | f(g(X3)) != X3 )
        & f(g(X2)) = X2 )
   => ( ! [X3] :
          ( sK2 = X3
          | f(g(X3)) != X3 )
      & sK2 = f(g(sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ( sP0
      | ! [X0] :
          ( ? [X1] :
              ( X0 != X1
              & f(g(X1)) = X1 )
          | f(g(X0)) != X0 ) )
    & ( ? [X2] :
          ( ! [X3] :
              ( X2 = X3
              | f(g(X3)) != X3 )
          & f(g(X2)) = X2 )
      | ~ sP0 ) ),
    inference(rectify,[],[f7]) ).

fof(f7,plain,
    ( ( sP0
      | ! [X0] :
          ( ? [X1] :
              ( X0 != X1
              & f(g(X1)) = X1 )
          | f(g(X0)) != X0 ) )
    & ( ? [X0] :
          ( ! [X1] :
              ( X0 = X1
              | f(g(X1)) != X1 )
          & f(g(X0)) = X0 )
      | ~ sP0 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,plain,
    ( sP0
  <=> ? [X0] :
        ( ! [X1] :
            ( X0 = X1
            | f(g(X1)) != X1 )
        & f(g(X0)) = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f56,plain,
    ( ! [X0] :
        ( g(f(X0)) != X0
        | sK3(X0) != X0 )
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f24,f28]) ).

fof(f24,plain,
    ! [X0] :
      ( sK3(X0) != X0
      | g(f(X0)) != X0
      | ~ sP0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ( ! [X0] :
          ( ( sK3(X0) != X0
            & sK3(X0) = g(f(sK3(X0))) )
          | g(f(X0)) != X0 )
      | ~ sP0 )
    & ( ( ! [X3] :
            ( sK4 = X3
            | g(f(X3)) != X3 )
        & sK4 = g(f(sK4)) )
      | sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f15,f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & g(f(X1)) = X1 )
     => ( sK3(X0) != X0
        & sK3(X0) = g(f(sK3(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ? [X2] :
        ( ! [X3] :
            ( X2 = X3
            | g(f(X3)) != X3 )
        & g(f(X2)) = X2 )
   => ( ! [X3] :
          ( sK4 = X3
          | g(f(X3)) != X3 )
      & sK4 = g(f(sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ( ( ! [X0] :
          ( ? [X1] :
              ( X0 != X1
              & g(f(X1)) = X1 )
          | g(f(X0)) != X0 )
      | ~ sP0 )
    & ( ? [X2] :
          ( ! [X3] :
              ( X2 = X3
              | g(f(X3)) != X3 )
          & g(f(X2)) = X2 )
      | sP0 ) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ( ( ! [X2] :
          ( ? [X3] :
              ( X2 != X3
              & g(f(X3)) = X3 )
          | g(f(X2)) != X2 )
      | ~ sP0 )
    & ( ? [X2] :
          ( ! [X3] :
              ( X2 = X3
              | g(f(X3)) != X3 )
          & g(f(X2)) = X2 )
      | sP0 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,plain,
    ( sP0
  <~> ? [X2] :
        ( ! [X3] :
            ( X2 = X3
            | g(f(X3)) != X3 )
        & g(f(X2)) = X2 ) ),
    inference(definition_folding,[],[f4,f5]) ).

fof(f4,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( X0 = X1
            | f(g(X1)) != X1 )
        & f(g(X0)) = X0 )
  <~> ? [X2] :
        ( ! [X3] :
            ( X2 = X3
            | g(f(X3)) != X3 )
        & g(f(X2)) = X2 ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ( ? [X0] :
          ( ! [X1] :
              ( f(g(X1)) = X1
             => X0 = X1 )
          & f(g(X0)) = X0 )
    <=> ? [X2] :
          ( ! [X3] :
              ( g(f(X3)) = X3
             => X2 = X3 )
          & g(f(X2)) = X2 ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ? [X0] :
          ( ! [X1] :
              ( f(g(X1)) = X1
             => X0 = X1 )
          & f(g(X0)) = X0 )
    <=> ? [X0] :
          ( ! [X1] :
              ( g(f(X1)) = X1
             => X0 = X1 )
          & g(f(X0)) = X0 ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ? [X0] :
        ( ! [X1] :
            ( f(g(X1)) = X1
           => X0 = X1 )
        & f(g(X0)) = X0 )
  <=> ? [X0] :
        ( ! [X1] :
            ( g(f(X1)) = X1
           => X0 = X1 )
        & g(f(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cute) ).

fof(f104,plain,
    ( g(sK2) = sK3(g(sK2))
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f100]) ).

fof(f100,plain,
    ( g(sK2) != g(sK2)
    | g(sK2) = sK3(g(sK2))
    | ~ spl5_1 ),
    inference(superposition,[],[f77,f55]) ).

fof(f77,plain,
    ( ! [X0] :
        ( g(f(X0)) != X0
        | g(sK2) = sK3(X0) )
    | ~ spl5_1 ),
    inference(duplicate_literal_removal,[],[f75]) ).

fof(f75,plain,
    ( ! [X0] :
        ( g(sK2) = sK3(X0)
        | g(f(X0)) != X0
        | g(f(X0)) != X0 )
    | ~ spl5_1 ),
    inference(superposition,[],[f70,f73]) ).

fof(f73,plain,
    ( ! [X0] :
        ( sK2 = f(sK3(X0))
        | g(f(X0)) != X0 )
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f72]) ).

fof(f72,plain,
    ( ! [X0] :
        ( f(sK3(X0)) != f(sK3(X0))
        | sK2 = f(sK3(X0))
        | g(f(X0)) != X0 )
    | ~ spl5_1 ),
    inference(superposition,[],[f61,f70]) ).

fof(f61,plain,
    ( ! [X3] :
        ( f(g(X3)) != X3
        | sK2 = X3 )
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f18,f28]) ).

fof(f18,plain,
    ! [X3] :
      ( sK2 = X3
      | f(g(X3)) != X3
      | ~ sP0 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f70,plain,
    ( ! [X0] :
        ( sK3(X0) = g(f(sK3(X0)))
        | g(f(X0)) != X0 )
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f23,f28]) ).

fof(f23,plain,
    ! [X0] :
      ( sK3(X0) = g(f(sK3(X0)))
      | g(f(X0)) != X0
      | ~ sP0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f98,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f97]) ).

fof(f97,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f87,f59]) ).

fof(f59,plain,
    ( sK4 != sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f58]) ).

fof(f58,plain,
    ( sK4 != sK4
    | sK4 != sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f56,f32]) ).

fof(f32,plain,
    ( sK4 = g(f(sK4))
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f30]) ).

fof(f30,plain,
    ( spl5_2
  <=> sK4 = g(f(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f87,plain,
    ( sK4 = sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f84]) ).

fof(f84,plain,
    ( sK4 != sK4
    | sK4 = sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f78,f32]) ).

fof(f78,plain,
    ( ! [X0] :
        ( g(f(X0)) != X0
        | sK3(X0) = sK4 )
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f77,f65]) ).

fof(f65,plain,
    ( g(sK2) = sK4
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f32,f64]) ).

fof(f64,plain,
    ( sK2 = f(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f62]) ).

fof(f62,plain,
    ( f(sK4) != f(sK4)
    | sK2 = f(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f61,f32]) ).

fof(f94,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f93]) ).

fof(f93,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f92,f59]) ).

fof(f92,plain,
    ( sK4 = sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f82,f65]) ).

fof(f82,plain,
    ( g(sK2) != sK4
    | sK4 = sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f78,f64]) ).

fof(f91,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f90]) ).

fof(f90,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f89,f59]) ).

fof(f89,plain,
    ( sK4 = sK3(sK4)
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f88,f65]) ).

fof(f88,plain,
    ( sK4 = sK3(g(sK2))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f81]) ).

fof(f81,plain,
    ( g(sK2) != g(sK2)
    | sK4 = sK3(g(sK2))
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f78,f55]) ).

fof(f54,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f53]) ).

fof(f53,plain,
    ( $false
    | spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f52]) ).

fof(f52,plain,
    ( f(sK4) != f(sK4)
    | spl5_1
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f51,f32]) ).

fof(f51,plain,
    ( f(sK4) != f(g(f(sK4)))
    | spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f48,f38]) ).

fof(f38,plain,
    ( f(sK4) != sK1(f(sK4))
    | spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f37]) ).

fof(f37,plain,
    ( f(sK4) != f(sK4)
    | f(sK4) != sK1(f(sK4))
    | spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f36,f32]) ).

fof(f36,plain,
    ( ! [X0] :
        ( f(g(X0)) != X0
        | sK1(X0) != X0 )
    | spl5_1 ),
    inference(subsumption_resolution,[],[f20,f27]) ).

fof(f27,plain,
    ( ~ sP0
    | spl5_1 ),
    inference(avatar_component_clause,[],[f26]) ).

fof(f20,plain,
    ! [X0] :
      ( sP0
      | sK1(X0) != X0
      | f(g(X0)) != X0 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f48,plain,
    ( f(sK4) = sK1(f(sK4))
    | f(sK4) != f(g(f(sK4)))
    | spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f39,f47]) ).

fof(f47,plain,
    ( sK4 = g(sK1(f(sK4)))
    | spl5_1
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f44]) ).

fof(f44,plain,
    ( f(sK4) != f(sK4)
    | sK4 = g(sK1(f(sK4)))
    | spl5_1
    | ~ spl5_2 ),
    inference(superposition,[],[f42,f32]) ).

fof(f42,plain,
    ( ! [X0] :
        ( f(g(X0)) != X0
        | g(sK1(X0)) = sK4 )
    | spl5_1 ),
    inference(trivial_inequality_removal,[],[f41]) ).

fof(f41,plain,
    ( ! [X0] :
        ( g(sK1(X0)) != g(sK1(X0))
        | g(sK1(X0)) = sK4
        | f(g(X0)) != X0 )
    | spl5_1 ),
    inference(superposition,[],[f34,f39]) ).

fof(f34,plain,
    ( ! [X3] :
        ( g(f(X3)) != X3
        | sK4 = X3 )
    | spl5_1 ),
    inference(subsumption_resolution,[],[f22,f27]) ).

fof(f22,plain,
    ! [X3] :
      ( sK4 = X3
      | g(f(X3)) != X3
      | sP0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f39,plain,
    ( ! [X0] :
        ( sK1(X0) = f(g(sK1(X0)))
        | f(g(X0)) != X0 )
    | spl5_1 ),
    inference(subsumption_resolution,[],[f19,f27]) ).

fof(f19,plain,
    ! [X0] :
      ( sP0
      | sK1(X0) = f(g(sK1(X0)))
      | f(g(X0)) != X0 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f33,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f21,f30,f26]) ).

fof(f21,plain,
    ( sK4 = g(f(sK4))
    | sP0 ),
    inference(cnf_transformation,[],[f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem    : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n025.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Apr 30 02:09:26 EDT 2024
% 0.15/0.31  % CPUTime    : 
% 0.15/0.31  % (3512)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33  % (3515)WARNING: value z3 for option sas not known
% 0.15/0.33  % (3516)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33  % (3517)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)
% 0.15/0.33  % (3513)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33  % (3514)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33  % (3518)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)
% 0.15/0.33  % (3515)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)
% 0.15/0.33  % (3519)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)
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [3]
% 0.15/0.33  TRYING [3]
% 0.15/0.33  % (3515)First to succeed.
% 0.15/0.33  TRYING [4]
% 0.15/0.33  TRYING [4]
% 0.15/0.33  % (3515)Refutation found. Thanks to Tanya!
% 0.15/0.33  % SZS status Theorem for theBenchmark
% 0.15/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.34  % (3515)------------------------------
% 0.15/0.34  % (3515)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.34  % (3515)Termination reason: Refutation
% 0.15/0.34  
% 0.15/0.34  % (3515)Memory used [KB]: 779
% 0.15/0.34  % (3515)Time elapsed: 0.006 s
% 0.15/0.34  % (3515)Instructions burned: 8 (million)
% 0.15/0.34  % (3515)------------------------------
% 0.15/0.34  % (3515)------------------------------
% 0.15/0.34  % (3512)Success in time 0.021 s
%------------------------------------------------------------------------------