TSTP Solution File: SYN415+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN415+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 : n019.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 18:03:13 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   71 (   2 unt;   0 def)
%            Number of atoms       :  263 (  48 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  311 ( 119   ~; 122   |;  48   &)
%                                         (   9 <=>;  10  =>;   0  <=;   3 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   92 (  62   !;  30   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f97,plain,
    $false,
    inference(avatar_sat_refutation,[],[f36,f47,f71,f87,f90,f91,f96]) ).

fof(f96,plain,
    ( spl6_3
    | spl6_1
    | ~ spl6_4
    | ~ spl6_5 ),
    inference(avatar_split_clause,[],[f95,f84,f44,f29,f41]) ).

fof(f41,plain,
    ( spl6_3
  <=> ! [X2] : ~ f(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

fof(f29,plain,
    ( spl6_1
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f44,plain,
    ( spl6_4
  <=> f(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

fof(f84,plain,
    ( spl6_5
  <=> f(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

fof(f95,plain,
    ( ! [X2] : ~ f(X2)
    | spl6_1
    | ~ spl6_4
    | ~ spl6_5 ),
    inference(subsumption_resolution,[],[f73,f93]) ).

fof(f93,plain,
    ( sK1 = sK2
    | spl6_1
    | ~ spl6_4
    | ~ spl6_5 ),
    inference(forward_demodulation,[],[f92,f81]) ).

fof(f81,plain,
    ( sK1 = sK5
    | spl6_1
    | ~ spl6_4 ),
    inference(resolution,[],[f78,f46]) ).

fof(f46,plain,
    ( f(sK1)
    | ~ spl6_4 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f78,plain,
    ( ! [X3] :
        ( ~ f(X3)
        | sK5 = X3 )
    | spl6_1 ),
    inference(global_subsumption,[],[f24,f30,f37,f39,f19,f20,f72,f23,f73,f27,f74,f22,f75,f21,f76,f26,f77,f25]) ).

fof(f25,plain,
    ! [X3] :
      ( sK5 = X3
      | ~ f(X3)
      | sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( ! [X0] :
          ( ( sK4(X0) != X0
            & f(sK4(X0)) )
          | ~ f(X0) )
      | ~ sP0 )
    & ( ( ! [X3] :
            ( sK5 = X3
            | ~ f(X3) )
        & f(sK5) )
      | sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f15,f17,f16]) ).

fof(f16,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & f(X1) )
     => ( sK4(X0) != X0
        & f(sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ? [X2] :
        ( ! [X3] :
            ( X2 = X3
            | ~ f(X3) )
        & f(X2) )
   => ( ! [X3] :
          ( sK5 = X3
          | ~ f(X3) )
      & f(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ( ! [X0] :
          ( ? [X1] :
              ( X0 != X1
              & f(X1) )
          | ~ f(X0) )
      | ~ sP0 )
    & ( ? [X2] :
          ( ! [X3] :
              ( X2 = X3
              | ~ f(X3) )
          & f(X2) )
      | sP0 ) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ( ( ! [X3] :
          ( ? [X4] :
              ( X3 != X4
              & f(X4) )
          | ~ f(X3) )
      | ~ sP0 )
    & ( ? [X3] :
          ( ! [X4] :
              ( X3 = X4
              | ~ f(X4) )
          & f(X3) )
      | sP0 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,plain,
    ( sP0
  <~> ? [X3] :
        ( ! [X4] :
            ( X3 = X4
            | ~ f(X4) )
        & f(X3) ) ),
    inference(definition_folding,[],[f5,f6]) ).

fof(f6,plain,
    ( sP0
  <=> ( ! [X0,X1] :
          ( X0 = X1
          | ~ f(X1)
          | ~ f(X0) )
      & ? [X2] : f(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f5,plain,
    ( ( ! [X0,X1] :
          ( X0 = X1
          | ~ f(X1)
          | ~ f(X0) )
      & ? [X2] : f(X2) )
  <~> ? [X3] :
        ( ! [X4] :
            ( X3 = X4
            | ~ f(X4) )
        & f(X3) ) ),
    inference(flattening,[],[f4]) ).

fof(f4,plain,
    ( ( ! [X0,X1] :
          ( X0 = X1
          | ~ f(X1)
          | ~ f(X0) )
      & ? [X2] : f(X2) )
  <~> ? [X3] :
        ( ! [X4] :
            ( X3 = X4
            | ~ f(X4) )
        & f(X3) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ( ( ! [X0,X1] :
            ( ( f(X1)
              & f(X0) )
           => X0 = X1 )
        & ? [X2] : f(X2) )
    <=> ? [X3] :
          ( ! [X4] :
              ( f(X4)
             => X3 = X4 )
          & f(X3) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ( ! [X1,X2] :
            ( ( f(X2)
              & f(X1) )
           => X1 = X2 )
        & ? [X0] : f(X0) )
    <=> ? [X3] :
          ( ! [X4] :
              ( f(X4)
             => X3 = X4 )
          & f(X3) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ( ! [X1,X2] :
          ( ( f(X2)
            & f(X1) )
         => X1 = X2 )
      & ? [X0] : f(X0) )
  <=> ? [X3] :
        ( ! [X4] :
            ( f(X4)
           => X3 = X4 )
        & f(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish317) ).

fof(f77,plain,
    ( ~ sP0
    | spl6_1 ),
    inference(global_subsumption,[],[f24,f30,f37,f39,f25,f19,f20,f72,f23,f73,f27,f74,f22,f75,f21,f76,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( f(sK4(X0))
      | ~ f(X0)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f76,plain,
    ( ! [X2] :
        ( f(sK1)
        | ~ f(X2) )
    | spl6_1 ),
    inference(global_subsumption,[],[f24,f30,f37,f39,f26,f25,f19,f20,f72,f23,f73,f27,f74,f22,f75,f21]) ).

fof(f21,plain,
    ! [X2] :
      ( sP0
      | f(sK1)
      | ~ f(X2) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ( sP0
      | ( sK1 != sK2
        & f(sK2)
        & f(sK1) )
      | ! [X2] : ~ f(X2) )
    & ( ( ! [X3,X4] :
            ( X3 = X4
            | ~ f(X4)
            | ~ f(X3) )
        & f(sK3) )
      | ~ sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f10,f12,f11]) ).

fof(f11,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & f(X1)
        & f(X0) )
   => ( sK1 != sK2
      & f(sK2)
      & f(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ( ? [X5] : f(X5)
   => f(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ( ( sP0
      | ? [X0,X1] :
          ( X0 != X1
          & f(X1)
          & f(X0) )
      | ! [X2] : ~ f(X2) )
    & ( ( ! [X3,X4] :
            ( X3 = X4
            | ~ f(X4)
            | ~ f(X3) )
        & ? [X5] : f(X5) )
      | ~ sP0 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ( ( sP0
      | ? [X0,X1] :
          ( X0 != X1
          & f(X1)
          & f(X0) )
      | ! [X2] : ~ f(X2) )
    & ( ( ! [X0,X1] :
            ( X0 = X1
            | ~ f(X1)
            | ~ f(X0) )
        & ? [X2] : f(X2) )
      | ~ sP0 ) ),
    inference(flattening,[],[f8]) ).

fof(f8,plain,
    ( ( sP0
      | ? [X0,X1] :
          ( X0 != X1
          & f(X1)
          & f(X0) )
      | ! [X2] : ~ f(X2) )
    & ( ( ! [X0,X1] :
            ( X0 = X1
            | ~ f(X1)
            | ~ f(X0) )
        & ? [X2] : f(X2) )
      | ~ sP0 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f75,plain,
    ( ! [X2] :
        ( f(sK2)
        | ~ f(X2) )
    | spl6_1 ),
    inference(global_subsumption,[],[f24,f30,f37,f39,f21,f26,f25,f19,f20,f72,f23,f73,f27,f74,f22]) ).

fof(f22,plain,
    ! [X2] :
      ( sP0
      | f(sK2)
      | ~ f(X2) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f74,plain,
    ( ~ sP0
    | spl6_1 ),
    inference(global_subsumption,[],[f22,f24,f30,f37,f39,f21,f26,f25,f19,f20,f72,f23,f73,f27]) ).

fof(f27,plain,
    ! [X0] :
      ( sK4(X0) != X0
      | ~ f(X0)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f23,plain,
    ! [X2] :
      ( sP0
      | sK1 != sK2
      | ~ f(X2) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f72,plain,
    ( ~ sP0
    | spl6_1 ),
    inference(global_subsumption,[],[f23,f22,f27,f24,f30,f37,f39,f21,f26,f25,f19,f20]) ).

fof(f20,plain,
    ! [X3,X4] :
      ( X3 = X4
      | ~ f(X4)
      | ~ f(X3)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f19,plain,
    ( f(sK3)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f39,plain,
    ( ! [X2] :
        ( f(sK1)
        | ~ f(X2) )
    | spl6_1 ),
    inference(subsumption_resolution,[],[f21,f30]) ).

fof(f37,plain,
    ( ! [X3] :
        ( ~ f(X3)
        | sK5 = X3 )
    | spl6_1 ),
    inference(subsumption_resolution,[],[f25,f30]) ).

fof(f30,plain,
    ( ~ sP0
    | spl6_1 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f24,plain,
    ( f(sK5)
    | sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f92,plain,
    ( sK2 = sK5
    | spl6_1
    | ~ spl6_5 ),
    inference(resolution,[],[f86,f78]) ).

fof(f86,plain,
    ( f(sK2)
    | ~ spl6_5 ),
    inference(avatar_component_clause,[],[f84]) ).

fof(f73,plain,
    ( ! [X2] :
        ( sK1 != sK2
        | ~ f(X2) )
    | spl6_1 ),
    inference(global_subsumption,[],[f22,f27,f24,f30,f37,f39,f21,f26,f25,f19,f20,f72,f23]) ).

fof(f91,plain,
    ( ~ spl6_2
    | ~ spl6_3 ),
    inference(avatar_contradiction_clause,[],[f88]) ).

fof(f88,plain,
    ( $false
    | ~ spl6_2
    | ~ spl6_3 ),
    inference(resolution,[],[f42,f35]) ).

fof(f35,plain,
    ( f(sK5)
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f33]) ).

fof(f33,plain,
    ( spl6_2
  <=> f(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f42,plain,
    ( ! [X2] : ~ f(X2)
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f41]) ).

fof(f90,plain,
    ( ~ spl6_3
    | ~ spl6_4 ),
    inference(avatar_contradiction_clause,[],[f89]) ).

fof(f89,plain,
    ( $false
    | ~ spl6_3
    | ~ spl6_4 ),
    inference(resolution,[],[f42,f46]) ).

fof(f87,plain,
    ( spl6_3
    | spl6_5
    | spl6_1 ),
    inference(avatar_split_clause,[],[f75,f29,f84,f41]) ).

fof(f71,plain,
    ~ spl6_1,
    inference(avatar_contradiction_clause,[],[f70]) ).

fof(f70,plain,
    ( $false
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f69,f48]) ).

fof(f48,plain,
    ( f(sK3)
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f19,f31]) ).

fof(f31,plain,
    ( sP0
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f69,plain,
    ( ~ f(sK3)
    | ~ spl6_1 ),
    inference(trivial_inequality_removal,[],[f67]) ).

fof(f67,plain,
    ( sK3 != sK3
    | ~ f(sK3)
    | ~ spl6_1 ),
    inference(superposition,[],[f50,f64]) ).

fof(f64,plain,
    ( sK3 = sK4(sK3)
    | ~ spl6_1 ),
    inference(resolution,[],[f61,f48]) ).

fof(f61,plain,
    ( ! [X0] :
        ( ~ f(X0)
        | sK3 = sK4(X0) )
    | ~ spl6_1 ),
    inference(resolution,[],[f53,f49]) ).

fof(f49,plain,
    ( ! [X0] :
        ( f(sK4(X0))
        | ~ f(X0) )
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f26,f31]) ).

fof(f53,plain,
    ( ! [X0] :
        ( ~ f(X0)
        | sK3 = X0 )
    | ~ spl6_1 ),
    inference(resolution,[],[f51,f48]) ).

fof(f51,plain,
    ( ! [X3,X4] :
        ( ~ f(X4)
        | X3 = X4
        | ~ f(X3) )
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f20,f31]) ).

fof(f50,plain,
    ( ! [X0] :
        ( sK4(X0) != X0
        | ~ f(X0) )
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f27,f31]) ).

fof(f47,plain,
    ( spl6_3
    | spl6_4
    | spl6_1 ),
    inference(avatar_split_clause,[],[f39,f29,f44,f41]) ).

fof(f36,plain,
    ( spl6_1
    | spl6_2 ),
    inference(avatar_split_clause,[],[f24,f33,f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYN415+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n019.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   : Tue Apr 30 01:54:59 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (13059)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (13063)WARNING: value z3 for option sas not known
% 0.14/0.37  % (13061)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (13062)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  % (13064)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (13063)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  % (13066)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  % (13065)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)
% 0.14/0.38  % (13067)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  TRYING [6]
% 0.14/0.38  % (13063)First to succeed.
% 0.14/0.38  TRYING [6]
% 0.14/0.38  % (13067)Also succeeded, but the first one will report.
% 0.14/0.38  TRYING [7]
% 0.14/0.38  TRYING [7]
% 0.14/0.38  % (13063)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  % (13063)------------------------------
% 0.14/0.38  % (13063)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (13063)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (13063)Memory used [KB]: 784
% 0.14/0.38  % (13063)Time elapsed: 0.007 s
% 0.14/0.38  % (13063)Instructions burned: 6 (million)
% 0.14/0.38  % (13063)------------------------------
% 0.14/0.38  % (13063)------------------------------
% 0.14/0.38  % (13059)Success in time 0.022 s
%------------------------------------------------------------------------------