TSTP Solution File: ALG203+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ALG203+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n027.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 : Wed Aug 31 15:43:36 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   63 (  11 unt;   0 def)
%            Number of atoms       :  223 (  67 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  261 ( 101   ~;  81   |;  43   &)
%                                         (   5 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   82 (  74   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f163,plain,
    $false,
    inference(avatar_sat_refutation,[],[f41,f45,f101,f135,f162]) ).

fof(f162,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f161]) ).

fof(f161,plain,
    ( $false
    | ~ spl3_3 ),
    inference(resolution,[],[f160,f20]) ).

fof(f20,plain,
    sorti1(sK1),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( sorti1(sK0)
    & sK0 != op1(sK0,sK0)
    & op1(sK1,sK1) = sK1
    & sorti1(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f15,f14]) ).

fof(f14,plain,
    ( ? [X0] :
        ( sorti1(X0)
        & op1(X0,X0) != X0 )
   => ( sorti1(sK0)
      & sK0 != op1(sK0,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ? [X1] :
        ( op1(X1,X1) = X1
        & sorti1(X1) )
   => ( op1(sK1,sK1) = sK1
      & sorti1(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ? [X0] :
        ( sorti1(X0)
        & op1(X0,X0) != X0 )
    & ? [X1] :
        ( op1(X1,X1) = X1
        & sorti1(X1) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ( ? [X1] :
        ( op1(X1,X1) != X1
        & sorti1(X1) )
    & ? [X0] :
        ( sorti1(X0)
        & op1(X0,X0) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(f160,plain,
    ( ~ sorti1(sK1)
    | ~ spl3_3 ),
    inference(resolution,[],[f153,f27]) ).

fof(f27,plain,
    ! [X4] :
      ( sorti2(h(X4))
      | ~ sorti1(X4) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ! [X0] :
        ( ~ sorti2(X0)
        | h(j(X0)) = X0 )
    & ! [X1] :
        ( ~ sorti2(X1)
        | ! [X2] :
            ( ~ sorti2(X2)
            | op1(j(X1),j(X2)) = j(op2(X1,X2)) ) )
    & ! [X3] :
        ( j(h(X3)) = X3
        | ~ sorti1(X3) )
    & ! [X4] :
        ( ~ sorti1(X4)
        | sorti2(h(X4)) )
    & ! [X5] :
        ( ~ sorti1(X5)
        | ! [X6] :
            ( ~ sorti1(X6)
            | h(op1(X5,X6)) = op2(h(X5),h(X6)) ) )
    & ! [X7] :
        ( sorti1(j(X7))
        | ~ sorti2(X7) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ( ! [X5] :
        ( ~ sorti2(X5)
        | h(j(X5)) = X5 )
    & ! [X2] :
        ( ~ sorti2(X2)
        | ! [X3] :
            ( ~ sorti2(X3)
            | j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
    & ! [X4] :
        ( j(h(X4)) = X4
        | ~ sorti1(X4) )
    & ! [X1] :
        ( ~ sorti1(X1)
        | sorti2(h(X1)) )
    & ! [X6] :
        ( ~ sorti1(X6)
        | ! [X7] :
            ( ~ sorti1(X7)
            | op2(h(X6),h(X7)) = h(op1(X6,X7)) ) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(X0) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ( ! [X2] :
        ( ~ sorti2(X2)
        | ! [X3] :
            ( ~ sorti2(X3)
            | j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
    & ! [X4] :
        ( j(h(X4)) = X4
        | ~ sorti1(X4) )
    & ! [X6] :
        ( ~ sorti1(X6)
        | ! [X7] :
            ( ~ sorti1(X7)
            | op2(h(X6),h(X7)) = h(op1(X6,X7)) ) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | h(j(X5)) = X5 )
    & ! [X1] :
        ( ~ sorti1(X1)
        | sorti2(h(X1)) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ~ ( ( ! [X1] :
            ( sorti1(X1)
           => sorti2(h(X1)) )
        & ! [X0] :
            ( sorti2(X0)
           => sorti1(j(X0)) ) )
     => ~ ( ! [X2] :
              ( sorti2(X2)
             => ! [X3] :
                  ( sorti2(X3)
                 => j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
          & ! [X4] :
              ( sorti1(X4)
             => j(h(X4)) = X4 )
          & ! [X6] :
              ( sorti1(X6)
             => ! [X7] :
                  ( sorti1(X7)
                 => op2(h(X6),h(X7)) = h(op1(X6,X7)) ) )
          & ! [X5] :
              ( sorti2(X5)
             => h(j(X5)) = X5 ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti2(X1)
           => sorti1(j(X1)) )
        & ! [X0] :
            ( sorti1(X0)
           => sorti2(h(X0)) ) )
     => ~ ( ! [X4] :
              ( sorti2(X4)
             => ! [X5] :
                  ( sorti2(X5)
                 => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
          & ! [X7] :
              ( sorti1(X7)
             => j(h(X7)) = X7 )
          & ! [X6] :
              ( sorti2(X6)
             => h(j(X6)) = X6 )
          & ! [X2] :
              ( sorti1(X2)
             => ! [X3] :
                  ( sorti1(X3)
                 => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ( ( ! [X1] :
          ( sorti2(X1)
         => sorti1(j(X1)) )
      & ! [X0] :
          ( sorti1(X0)
         => sorti2(h(X0)) ) )
   => ~ ( ! [X4] :
            ( sorti2(X4)
           => ! [X5] :
                ( sorti2(X5)
               => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
        & ! [X7] :
            ( sorti1(X7)
           => j(h(X7)) = X7 )
        & ! [X6] :
            ( sorti2(X6)
           => h(j(X6)) = X6 )
        & ! [X2] :
            ( sorti1(X2)
           => ! [X3] :
                ( sorti1(X3)
               => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f153,plain,
    ( ~ sorti2(h(sK1))
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f152]) ).

fof(f152,plain,
    ( h(sK1) != h(sK1)
    | ~ sorti2(h(sK1))
    | ~ spl3_3 ),
    inference(superposition,[],[f44,f136]) ).

fof(f136,plain,
    h(sK1) = op2(h(sK1),h(sK1)),
    inference(forward_demodulation,[],[f82,f21]) ).

fof(f21,plain,
    op1(sK1,sK1) = sK1,
    inference(cnf_transformation,[],[f16]) ).

fof(f82,plain,
    h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
    inference(resolution,[],[f60,f20]) ).

fof(f60,plain,
    ! [X6] :
      ( ~ sorti1(X6)
      | op2(h(X6),h(sK1)) = h(op1(X6,sK1)) ),
    inference(resolution,[],[f26,f20]) ).

fof(f26,plain,
    ! [X6,X5] :
      ( ~ sorti1(X6)
      | ~ sorti1(X5)
      | h(op1(X5,X6)) = op2(h(X5),h(X6)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f44,plain,
    ( ! [X1] :
        ( op2(X1,X1) != X1
        | ~ sorti2(X1) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl3_3
  <=> ! [X1] :
        ( ~ sorti2(X1)
        | op2(X1,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f135,plain,
    ( ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f134]) ).

fof(f134,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f131]) ).

fof(f131,plain,
    ( sK0 != sK0
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(superposition,[],[f22,f126]) ).

fof(f126,plain,
    ( sK0 = op1(sK0,sK0)
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(forward_demodulation,[],[f125,f47]) ).

fof(f47,plain,
    sK0 = j(h(sK0)),
    inference(resolution,[],[f28,f23]) ).

fof(f23,plain,
    sorti1(sK0),
    inference(cnf_transformation,[],[f16]) ).

fof(f28,plain,
    ! [X3] :
      ( ~ sorti1(X3)
      | j(h(X3)) = X3 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f125,plain,
    ( op1(sK0,sK0) = j(h(sK0))
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(forward_demodulation,[],[f112,f78]) ).

fof(f78,plain,
    ( h(sK0) = h(op1(sK0,sK0))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f76,f72]) ).

fof(f72,plain,
    ( op2(h(sK0),h(sK0)) = h(sK0)
    | ~ spl3_2 ),
    inference(resolution,[],[f50,f23]) ).

fof(f50,plain,
    ( ! [X0] :
        ( ~ sorti1(X0)
        | h(X0) = op2(h(X0),h(X0)) )
    | ~ spl3_2 ),
    inference(resolution,[],[f40,f27]) ).

fof(f40,plain,
    ( ! [X0] :
        ( ~ sorti2(X0)
        | op2(X0,X0) = X0 )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl3_2
  <=> ! [X0] :
        ( ~ sorti2(X0)
        | op2(X0,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f76,plain,
    op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
    inference(resolution,[],[f59,f23]) ).

fof(f59,plain,
    ! [X5] :
      ( ~ sorti1(X5)
      | op2(h(X5),h(sK0)) = h(op1(X5,sK0)) ),
    inference(resolution,[],[f26,f23]) ).

fof(f112,plain,
    ( op1(sK0,sK0) = j(h(op1(sK0,sK0)))
    | ~ spl3_4 ),
    inference(resolution,[],[f87,f28]) ).

fof(f87,plain,
    ( sorti1(op1(sK0,sK0))
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f86,plain,
    ( spl3_4
  <=> sorti1(op1(sK0,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f22,plain,
    sK0 != op1(sK0,sK0),
    inference(cnf_transformation,[],[f16]) ).

fof(f101,plain,
    spl3_4,
    inference(avatar_contradiction_clause,[],[f100]) ).

fof(f100,plain,
    ( $false
    | spl3_4 ),
    inference(resolution,[],[f99,f23]) ).

fof(f99,plain,
    ( ~ sorti1(sK0)
    | spl3_4 ),
    inference(duplicate_literal_removal,[],[f98]) ).

fof(f98,plain,
    ( ~ sorti1(sK0)
    | ~ sorti1(sK0)
    | spl3_4 ),
    inference(resolution,[],[f88,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( sorti1(op1(X0,X1))
      | ~ sorti1(X1)
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ sorti1(X1)
          | sorti1(op1(X0,X1)) )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( sorti1(X0)
     => ! [X1] :
          ( sorti1(X1)
         => sorti1(op1(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(f88,plain,
    ( ~ sorti1(op1(sK0,sK0))
    | spl3_4 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f45,plain,
    ( ~ spl3_1
    | spl3_3 ),
    inference(avatar_split_clause,[],[f33,f43,f35]) ).

fof(f35,plain,
    ( spl3_1
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f33,plain,
    ! [X1] :
      ( ~ sorti2(X1)
      | op2(X1,X1) != X1
      | ~ sP2 ),
    inference(general_splitting,[],[f24,f32_D]) ).

fof(f32,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | op2(X0,X0) = X0
      | sP2 ),
    inference(cnf_transformation,[],[f32_D]) ).

fof(f32_D,plain,
    ( ! [X0] :
        ( ~ sorti2(X0)
        | op2(X0,X0) = X0 )
  <=> ~ sP2 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ sorti2(X0)
      | op2(X0,X0) = X0
      | op2(X1,X1) != X1
      | ~ sorti2(X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( ! [X0] :
        ( ~ sorti2(X0)
        | op2(X0,X0) = X0 )
    | ! [X1] :
        ( op2(X1,X1) != X1
        | ~ sorti2(X1) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ( ! [X1] :
        ( ~ sorti2(X1)
        | op2(X1,X1) = X1 )
    | ! [X0] :
        ( op2(X0,X0) != X0
        | ~ sorti2(X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ~ ( ? [X0] :
          ( op2(X0,X0) = X0
          & sorti2(X0) )
      & ? [X1] :
          ( op2(X1,X1) != X1
          & sorti2(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f41,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f32,f39,f35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : ALG203+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n027.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   : Mon Aug 29 15:14:00 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.49  % (5406)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.49  % (5414)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (5424)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.50  % (5411)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (5414)First to succeed.
% 0.19/0.50  % (5419)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.51  % (5414)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (5414)------------------------------
% 0.19/0.51  % (5414)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (5414)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (5414)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (5414)Memory used [KB]: 5500
% 0.19/0.51  % (5414)Time elapsed: 0.103 s
% 0.19/0.51  % (5414)Instructions burned: 6 (million)
% 0.19/0.51  % (5414)------------------------------
% 0.19/0.51  % (5414)------------------------------
% 0.19/0.51  % (5403)Success in time 0.169 s
%------------------------------------------------------------------------------