TSTP Solution File: KRS101+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : KRS101+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : n006.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 17:30:48 EDT 2022

% Result   : Unsatisfiable 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   51 (   5 unt;   0 def)
%            Number of atoms       :  286 (  46 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  375 ( 140   ~; 121   |;  94   &)
%                                         (   7 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-1 aty)
%            Number of variables   :  147 (  99   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f205,plain,
    $false,
    inference(resolution,[],[f204,f94]) ).

fof(f94,plain,
    cUnsatisfiable(i2003_11_14_17_20_36582),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    cUnsatisfiable(i2003_11_14_17_20_36582),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f204,plain,
    ~ cUnsatisfiable(i2003_11_14_17_20_36582),
    inference(trivial_inequality_removal,[],[f203]) ).

fof(f203,plain,
    ( sK5(i2003_11_14_17_20_36582) != sK5(i2003_11_14_17_20_36582)
    | ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
    inference(superposition,[],[f92,f201]) ).

fof(f201,plain,
    sK5(i2003_11_14_17_20_36582) = sK6(i2003_11_14_17_20_36582),
    inference(resolution,[],[f200,f94]) ).

fof(f200,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK6(X0) = sK5(X0) ),
    inference(duplicate_literal_removal,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK6(X0) = sK5(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f198,f89]) ).

fof(f89,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ( ( rs(sK4(X0),sK6(X0))
          & sK6(X0) != sK5(X0)
          & rs(sK4(X0),sK5(X0))
          & rr(X0,sK4(X0))
          & sP0(X0)
          & ! [X4] :
              ( ~ rr(X0,X4)
              | cd(X4) ) )
        | ~ cUnsatisfiable(X0) )
      & ( cUnsatisfiable(X0)
        | ! [X5] :
            ( ! [X6,X7] :
                ( ~ rs(X5,X7)
                | X6 = X7
                | ~ rs(X5,X6) )
            | ~ rr(X0,X5) )
        | ~ sP0(X0)
        | ( rr(X0,sK7(X0))
          & ~ cd(sK7(X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f64,f67,f66,f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2,X3] :
              ( rs(X1,X3)
              & X2 != X3
              & rs(X1,X2) )
          & rr(X0,X1) )
     => ( ? [X3,X2] :
            ( rs(sK4(X0),X3)
            & X2 != X3
            & rs(sK4(X0),X2) )
        & rr(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0] :
      ( ? [X3,X2] :
          ( rs(sK4(X0),X3)
          & X2 != X3
          & rs(sK4(X0),X2) )
     => ( rs(sK4(X0),sK6(X0))
        & sK6(X0) != sK5(X0)
        & rs(sK4(X0),sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0] :
      ( ? [X8] :
          ( rr(X0,X8)
          & ~ cd(X8) )
     => ( rr(X0,sK7(X0))
        & ~ cd(sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0] :
      ( ( ( ? [X1] :
              ( ? [X2,X3] :
                  ( rs(X1,X3)
                  & X2 != X3
                  & rs(X1,X2) )
              & rr(X0,X1) )
          & sP0(X0)
          & ! [X4] :
              ( ~ rr(X0,X4)
              | cd(X4) ) )
        | ~ cUnsatisfiable(X0) )
      & ( cUnsatisfiable(X0)
        | ! [X5] :
            ( ! [X6,X7] :
                ( ~ rs(X5,X7)
                | X6 = X7
                | ~ rs(X5,X6) )
            | ~ rr(X0,X5) )
        | ~ sP0(X0)
        | ? [X8] :
            ( rr(X0,X8)
            & ~ cd(X8) ) ) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ( ? [X1] :
              ( ? [X2,X3] :
                  ( rs(X1,X3)
                  & X2 != X3
                  & rs(X1,X2) )
              & rr(X0,X1) )
          & sP0(X0)
          & ! [X7] :
              ( ~ rr(X0,X7)
              | cd(X7) ) )
        | ~ cUnsatisfiable(X0) )
      & ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ! [X2,X3] :
                ( ~ rs(X1,X3)
                | X2 = X3
                | ~ rs(X1,X2) )
            | ~ rr(X0,X1) )
        | ~ sP0(X0)
        | ? [X7] :
            ( rr(X0,X7)
            & ~ cd(X7) ) ) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ( ( ? [X1] :
              ( ? [X2,X3] :
                  ( rs(X1,X3)
                  & X2 != X3
                  & rs(X1,X2) )
              & rr(X0,X1) )
          & sP0(X0)
          & ! [X7] :
              ( ~ rr(X0,X7)
              | cd(X7) ) )
        | ~ cUnsatisfiable(X0) )
      & ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ! [X2,X3] :
                ( ~ rs(X1,X3)
                | X2 = X3
                | ~ rs(X1,X2) )
            | ~ rr(X0,X1) )
        | ~ sP0(X0)
        | ? [X7] :
            ( rr(X0,X7)
            & ~ cd(X7) ) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( ? [X2,X3] :
                ( rs(X1,X3)
                & X2 != X3
                & rs(X1,X2) )
            & rr(X0,X1) )
        & sP0(X0)
        & ! [X7] :
            ( ~ rr(X0,X7)
            | cd(X7) ) )
    <=> cUnsatisfiable(X0) ),
    inference(definition_folding,[],[f52,f53]) ).

fof(f53,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ! [X4] :
          ( cc(X4)
          | ! [X6,X5] :
              ( ~ rs(X4,X6)
              | ~ rs(X4,X5)
              | X5 = X6 )
          | ~ rr(X0,X4) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f52,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( ? [X2,X3] :
                ( rs(X1,X3)
                & X2 != X3
                & rs(X1,X2) )
            & rr(X0,X1) )
        & ! [X4] :
            ( cc(X4)
            | ! [X6,X5] :
                ( ~ rs(X4,X6)
                | ~ rs(X4,X5)
                | X5 = X6 )
            | ~ rr(X0,X4) )
        & ! [X7] :
            ( ~ rr(X0,X7)
            | cd(X7) ) )
    <=> cUnsatisfiable(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X4] :
            ( cc(X4)
            | ! [X6,X5] :
                ( ~ rs(X4,X6)
                | ~ rs(X4,X5)
                | X5 = X6 )
            | ~ rr(X0,X4) )
        & ! [X7] :
            ( ~ rr(X0,X7)
            | cd(X7) )
        & ? [X1] :
            ( ? [X2,X3] :
                ( X2 != X3
                & rs(X1,X2)
                & rs(X1,X3) )
            & rr(X0,X1) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X4] :
            ( rr(X0,X4)
           => ( cc(X4)
              | ~ ? [X5,X6] :
                    ( X5 != X6
                    & rs(X4,X6)
                    & rs(X4,X5) ) ) )
        & ! [X7] :
            ( rr(X0,X7)
           => cd(X7) )
        & ? [X1] :
            ( ~ ! [X2,X3] :
                  ( ( rs(X1,X2)
                    & rs(X1,X3) )
                 => X2 = X3 )
            & rr(X0,X1) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3] :
      ( ( ? [X4] :
            ( rr(X3,X4)
            & ~ ! [X5,X6] :
                  ( ( rs(X4,X5)
                    & rs(X4,X6) )
                 => X5 = X6 ) )
        & ! [X4] :
            ( rr(X3,X4)
           => ( cc(X4)
              | ~ ? [X5,X6] :
                    ( X5 != X6
                    & rs(X4,X6)
                    & rs(X4,X5) ) ) )
        & ! [X4] :
            ( rr(X3,X4)
           => cd(X4) ) )
    <=> cUnsatisfiable(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f198,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ~ cUnsatisfiable(X0)
      | sK6(X0) = sK5(X0) ),
    inference(duplicate_literal_removal,[],[f197]) ).

fof(f197,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ~ cUnsatisfiable(X0)
      | sK6(X0) = sK5(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f196,f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ~ cc(sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f127,f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( cc(X0)
     => ~ cd(X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3] :
      ( cc(X3)
     => ~ cd(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f127,plain,
    ! [X1] :
      ( cd(sK4(X1))
      | ~ cUnsatisfiable(X1) ),
    inference(duplicate_literal_removal,[],[f126]) ).

fof(f126,plain,
    ! [X1] :
      ( ~ cUnsatisfiable(X1)
      | cd(sK4(X1))
      | ~ cUnsatisfiable(X1) ),
    inference(resolution,[],[f88,f90]) ).

fof(f90,plain,
    ! [X0] :
      ( rr(X0,sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f88,plain,
    ! [X0,X4] :
      ( ~ rr(X0,X4)
      | cd(X4)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f196,plain,
    ! [X0] :
      ( cc(sK4(X0))
      | ~ sP0(X0)
      | sK6(X0) = sK5(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(duplicate_literal_removal,[],[f195]) ).

fof(f195,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sK6(X0) = sK5(X0)
      | cc(sK4(X0))
      | ~ sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[],[f190,f130]) ).

fof(f130,plain,
    ! [X1] :
      ( sP8(sK4(X1))
      | ~ sP0(X1)
      | ~ cUnsatisfiable(X1) ),
    inference(resolution,[],[f118,f90]) ).

fof(f118,plain,
    ! [X0,X4] :
      ( ~ rr(X0,X4)
      | sP8(X4)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f118_D]) ).

fof(f118_D,plain,
    ! [X4] :
      ( ! [X0] :
          ( ~ rr(X0,X4)
          | ~ sP0(X0) )
    <=> ~ sP8(X4) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).

fof(f190,plain,
    ! [X1] :
      ( ~ sP8(sK4(X1))
      | sK6(X1) = sK5(X1)
      | ~ cUnsatisfiable(X1)
      | cc(sK4(X1)) ),
    inference(duplicate_literal_removal,[],[f188]) ).

fof(f188,plain,
    ! [X1] :
      ( ~ sP8(sK4(X1))
      | ~ cUnsatisfiable(X1)
      | ~ cUnsatisfiable(X1)
      | sK6(X1) = sK5(X1)
      | cc(sK4(X1)) ),
    inference(resolution,[],[f143,f93]) ).

fof(f93,plain,
    ! [X0] :
      ( rs(sK4(X0),sK6(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f143,plain,
    ! [X4,X5] :
      ( ~ rs(sK4(X4),X5)
      | sK5(X4) = X5
      | cc(sK4(X4))
      | ~ cUnsatisfiable(X4)
      | ~ sP8(sK4(X4)) ),
    inference(resolution,[],[f119,f91]) ).

fof(f91,plain,
    ! [X0] :
      ( rs(sK4(X0),sK5(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f119,plain,
    ! [X6,X4,X5] :
      ( ~ rs(X4,X6)
      | cc(X4)
      | ~ sP8(X4)
      | X5 = X6
      | ~ rs(X4,X5) ),
    inference(general_splitting,[],[f80,f118_D]) ).

fof(f80,plain,
    ! [X0,X6,X4,X5] :
      ( cc(X4)
      | ~ rs(X4,X5)
      | ~ rs(X4,X6)
      | X5 = X6
      | ~ rr(X0,X4)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( ~ cc(sK1(X0))
          & rs(sK1(X0),sK2(X0))
          & rs(sK1(X0),sK3(X0))
          & sK3(X0) != sK2(X0)
          & rr(X0,sK1(X0)) ) )
      & ( ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( ~ rs(X4,X5)
                | ~ rs(X4,X6)
                | X5 = X6 )
            | ~ rr(X0,X4) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f58,f60,f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cc(X1)
          & ? [X2,X3] :
              ( rs(X1,X2)
              & rs(X1,X3)
              & X2 != X3 )
          & rr(X0,X1) )
     => ( ~ cc(sK1(X0))
        & ? [X3,X2] :
            ( rs(sK1(X0),X2)
            & rs(sK1(X0),X3)
            & X2 != X3 )
        & rr(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X3,X2] :
          ( rs(sK1(X0),X2)
          & rs(sK1(X0),X3)
          & X2 != X3 )
     => ( rs(sK1(X0),sK2(X0))
        & rs(sK1(X0),sK3(X0))
        & sK3(X0) != sK2(X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1] :
            ( ~ cc(X1)
            & ? [X2,X3] :
                ( rs(X1,X2)
                & rs(X1,X3)
                & X2 != X3 )
            & rr(X0,X1) ) )
      & ( ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( ~ rs(X4,X5)
                | ~ rs(X4,X6)
                | X5 = X6 )
            | ~ rr(X0,X4) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X4] :
            ( ~ cc(X4)
            & ? [X6,X5] :
                ( rs(X4,X6)
                & rs(X4,X5)
                & X5 != X6 )
            & rr(X0,X4) ) )
      & ( ! [X4] :
            ( cc(X4)
            | ! [X6,X5] :
                ( ~ rs(X4,X6)
                | ~ rs(X4,X5)
                | X5 = X6 )
            | ~ rr(X0,X4) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f92,plain,
    ! [X0] :
      ( sK6(X0) != sK5(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : KRS101+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 00:32:25 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.52  % (22122)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53  % (22106)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53  % (22106)First to succeed.
% 0.19/0.53  % (22106)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (22106)------------------------------
% 0.19/0.53  % (22106)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (22106)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (22106)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (22106)Memory used [KB]: 5500
% 0.19/0.53  % (22106)Time elapsed: 0.145 s
% 0.19/0.53  % (22106)Instructions burned: 5 (million)
% 0.19/0.53  % (22106)------------------------------
% 0.19/0.53  % (22106)------------------------------
% 0.19/0.53  % (22095)Success in time 0.184 s
%------------------------------------------------------------------------------