TSTP Solution File: SYO889_16 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 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 : n002.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 : Mon May 22 15:45:51 EDT 2023

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   45 (   5 unt;   9 typ;   0 def)
%            Number of atoms       :  176 (   0 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  189 (  74   ~;  64   |;  34   &)
%                                         (   5 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   25 (  25 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   7 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   60 (;  36   !;  24   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    '$ki_world': $tType ).

tff(func_def_0,type,
    '$ki_local_world': '$ki_world' ).

tff(func_def_1,type,
    sK0: '$ki_world' > $i ).

tff(func_def_2,type,
    sK1: '$ki_world' ).

tff(func_def_4,type,
    sK3: ( '$ki_world' * $i ) > '$ki_world' ).

tff(pred_def_1,type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(pred_def_2,type,
    a: ( '$ki_world' * $i ) > $o ).

tff(pred_def_3,type,
    b: ( '$ki_world' * $i ) > $o ).

tff(pred_def_4,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(f111,plain,
    $false,
    inference(avatar_sat_refutation,[],[f59,f61,f84,f106,f108,f110]) ).

tff(f110,plain,
    spl4_8,
    inference(avatar_contradiction_clause,[],[f109]) ).

tff(f109,plain,
    ( $false
    | spl4_8 ),
    inference(resolution,[],[f105,f23]) ).

tff(f23,plain,
    '$ki_exists_in_world_$i'(sK1,sK2),
    inference(cnf_transformation,[],[f12]) ).

tff(f12,plain,
    ( ! [X6: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',X6)
        | ! [X7] :
            ( ~ '$ki_exists_in_world_$i'(X6,X7)
            | ! [X8: '$ki_world'] :
                ( ~ b(X8,X7)
                | ~ a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) ) ) )
    & ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ? [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
                & b(X2,X1) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X3)
        & ? [X4] :
            ( '$ki_exists_in_world_$i'(X3,X4)
            & ! [X5: '$ki_world'] :
                ( a(X5,X4)
                | ~ '$ki_accessible'(X3,X5) ) ) ) ),
    inference(flattening,[],[f11]) ).

tff(f11,plain,
    ( ! [X6: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',X6)
        | ! [X7] :
            ( ~ '$ki_exists_in_world_$i'(X6,X7)
            | ! [X8: '$ki_world'] :
                ( ~ b(X8,X7)
                | ~ a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) ) ) )
    & ? [X3: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X3)
        & ? [X4] :
            ( '$ki_exists_in_world_$i'(X3,X4)
            & ! [X5: '$ki_world'] :
                ( a(X5,X4)
                | ~ '$ki_accessible'(X3,X5) ) ) )
    & ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ? [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
                & b(X2,X1) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ~ ( ( ? [X3: '$ki_world'] :
            ( ? [X4] :
                ( '$ki_exists_in_world_$i'(X3,X4)
                & ! [X5: '$ki_world'] :
                    ( '$ki_accessible'(X3,X5)
                   => a(X5,X4) ) )
            & '$ki_accessible'('$ki_local_world',X3) )
        & ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ! [X1] :
                ( '$ki_exists_in_world_$i'(X0,X1)
               => ? [X2: '$ki_world'] :
                    ( '$ki_accessible'(X0,X2)
                    & b(X2,X1) ) ) ) )
     => ? [X6: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X6)
          & ? [X7] :
              ( '$ki_exists_in_world_$i'(X6,X7)
              & ? [X8: '$ki_world'] :
                  ( a(X8,X7)
                  & '$ki_accessible'(X6,X8)
                  & b(X8,X7) ) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,negated_conjecture,
    ~ ( ( ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ! [X3] :
                ( '$ki_exists_in_world_$i'(X0,X3)
               => ? [X4: '$ki_world'] :
                    ( '$ki_accessible'(X0,X4)
                    & b(X4,X3) ) ) )
        & ? [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
            & ? [X3] :
                ( ! [X4: '$ki_world'] :
                    ( '$ki_accessible'(X0,X4)
                   => a(X4,X3) )
                & '$ki_exists_in_world_$i'(X0,X3) ) ) )
     => ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
              & ? [X4: '$ki_world'] :
                  ( b(X4,X3)
                  & '$ki_accessible'(X0,X4)
                  & a(X4,X3) ) )
          & '$ki_accessible'('$ki_local_world',X0) ) ),
    inference(negated_conjecture,[],[f5]) ).

tff(f5,conjecture,
    ( ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ! [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
             => ? [X4: '$ki_world'] :
                  ( '$ki_accessible'(X0,X4)
                  & b(X4,X3) ) ) )
      & ? [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
          & ? [X3] :
              ( ! [X4: '$ki_world'] :
                  ( '$ki_accessible'(X0,X4)
                 => a(X4,X3) )
              & '$ki_exists_in_world_$i'(X0,X3) ) ) )
   => ? [X0: '$ki_world'] :
        ( ? [X3] :
            ( '$ki_exists_in_world_$i'(X0,X3)
            & ? [X4: '$ki_world'] :
                ( b(X4,X3)
                & '$ki_accessible'(X0,X4)
                & a(X4,X3) ) )
        & '$ki_accessible'('$ki_local_world',X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f105,plain,
    ( ~ '$ki_exists_in_world_$i'(sK1,sK2)
    | spl4_8 ),
    inference(avatar_component_clause,[],[f103]) ).

tff(f103,plain,
    ( spl4_8
  <=> '$ki_exists_in_world_$i'(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

tff(f108,plain,
    ( ~ spl4_8
    | ~ spl4_2
    | spl4_7 ),
    inference(avatar_split_clause,[],[f107,f99,f48,f103]) ).

tff(f48,plain,
    ( spl4_2
  <=> '$ki_accessible'('$ki_local_world',sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

tff(f99,plain,
    ( spl4_7
  <=> '$ki_accessible'(sK1,sK3(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

tff(f107,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK1)
    | ~ '$ki_exists_in_world_$i'(sK1,sK2)
    | spl4_7 ),
    inference(resolution,[],[f101,f21]) ).

tff(f21,plain,
    ! [X0: '$ki_world',X1: $i] :
      ( '$ki_accessible'(X0,sK3(X0,X1))
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f12]) ).

tff(f101,plain,
    ( ~ '$ki_accessible'(sK1,sK3(sK1,sK2))
    | spl4_7 ),
    inference(avatar_component_clause,[],[f99]) ).

tff(f106,plain,
    ( ~ spl4_7
    | ~ spl4_2
    | ~ spl4_8
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(avatar_split_clause,[],[f97,f82,f57,f103,f48,f99]) ).

tff(f57,plain,
    ( spl4_4
  <=> ! [X2] :
        ( ~ '$ki_exists_in_world_$i'(sK1,X2)
        | a(sK3(sK1,X2),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

tff(f82,plain,
    ( spl4_5
  <=> ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(sK1,X0)
        | ~ a(X0,sK2)
        | ~ b(X0,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

tff(f97,plain,
    ( ~ '$ki_exists_in_world_$i'(sK1,sK2)
    | ~ '$ki_accessible'('$ki_local_world',sK1)
    | ~ '$ki_accessible'(sK1,sK3(sK1,sK2))
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(duplicate_literal_removal,[],[f96]) ).

tff(f96,plain,
    ( ~ '$ki_accessible'(sK1,sK3(sK1,sK2))
    | ~ '$ki_exists_in_world_$i'(sK1,sK2)
    | ~ '$ki_accessible'('$ki_local_world',sK1)
    | ~ '$ki_exists_in_world_$i'(sK1,sK2)
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(resolution,[],[f89,f58]) ).

tff(f58,plain,
    ( ! [X2: $i] :
        ( a(sK3(sK1,X2),sK2)
        | ~ '$ki_exists_in_world_$i'(sK1,X2) )
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f57]) ).

tff(f89,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ a(sK3(X0,sK2),sK2)
        | ~ '$ki_accessible'(sK1,sK3(X0,sK2))
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_exists_in_world_$i'(X0,sK2) )
    | ~ spl4_5 ),
    inference(resolution,[],[f83,f20]) ).

tff(f20,plain,
    ! [X0: '$ki_world',X1: $i] :
      ( b(sK3(X0,X1),X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f12]) ).

tff(f83,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ b(X0,sK2)
        | ~ a(X0,sK2)
        | ~ '$ki_accessible'(sK1,X0) )
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f82]) ).

tff(f84,plain,
    ( ~ spl4_2
    | spl4_5 ),
    inference(avatar_split_clause,[],[f74,f82,f48]) ).

tff(f74,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'(sK1,X0)
      | ~ b(X0,sK2)
      | ~ '$ki_accessible'('$ki_local_world',sK1)
      | ~ a(X0,sK2) ),
    inference(resolution,[],[f19,f23]) ).

tff(f19,plain,
    ! [X8: '$ki_world',X6: '$ki_world',X7: $i] :
      ( ~ '$ki_exists_in_world_$i'(X6,X7)
      | ~ '$ki_accessible'('$ki_local_world',X6)
      | ~ '$ki_accessible'(X6,X8)
      | ~ b(X8,X7)
      | ~ a(X8,X7) ),
    inference(cnf_transformation,[],[f12]) ).

tff(f61,plain,
    spl4_2,
    inference(avatar_contradiction_clause,[],[f60]) ).

tff(f60,plain,
    ( $false
    | spl4_2 ),
    inference(resolution,[],[f50,f24]) ).

tff(f24,plain,
    '$ki_accessible'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f12]) ).

tff(f50,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK1)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f48]) ).

tff(f59,plain,
    ( spl4_4
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f41,f48,f57]) ).

tff(f41,plain,
    ! [X2: $i] :
      ( ~ '$ki_accessible'('$ki_local_world',sK1)
      | ~ '$ki_exists_in_world_$i'(sK1,X2)
      | a(sK3(sK1,X2),sK2) ),
    inference(resolution,[],[f21,f22]) ).

tff(f22,plain,
    ! [X5: '$ki_world'] :
      ( ~ '$ki_accessible'(sK1,X5)
      | a(X5,sK2) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.13  % 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 : n002.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   : Mon May 22 13:24:07 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.51  % (19464)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.51  TRYING [1]
% 0.20/0.52  % (19472)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52  TRYING [2]
% 0.20/0.52  TRYING [3]
% 0.20/0.52  % (19473)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (19480)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (19467)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  TRYING [4]
% 0.20/0.52  TRYING [5]
% 0.20/0.52  % (19488)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.52  % (19467)First to succeed.
% 0.20/0.52  % (19465)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (19465)Refutation not found, incomplete strategy% (19465)------------------------------
% 0.20/0.52  % (19465)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (19465)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (19465)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52  
% 0.20/0.52  % (19465)Memory used [KB]: 5373
% 0.20/0.52  % (19465)Time elapsed: 0.117 s
% 0.20/0.52  % (19465)------------------------------
% 0.20/0.52  % (19465)------------------------------
% 0.20/0.53  % (19466)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)
% 0.20/0.53  % (19468)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (19471)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (19469)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53  % (19478)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)
% 0.20/0.53  TRYING [6]
% 0.20/0.53  % (19486)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.53  % (19482)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (19481)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.53  TRYING [7]
% 0.20/0.54  % (19485)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.54  % (19487)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.54  % (19475)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54  TRYING [8]
% 0.20/0.54  % (19476)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54  % (19483)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)
% 0.20/0.54  % (19472)Instruction limit reached!
% 0.20/0.54  % (19472)------------------------------
% 0.20/0.54  % (19472)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (19472)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (19472)Termination reason: Unknown
% 0.20/0.54  % (19472)Termination phase: Saturation
% 0.20/0.54  
% 0.20/0.54  % (19472)Memory used [KB]: 5373
% 0.20/0.54  % (19472)Time elapsed: 0.143 s
% 0.20/0.54  % (19472)Instructions burned: 3 (million)
% 0.20/0.54  % (19472)------------------------------
% 0.20/0.54  % (19472)------------------------------
% 0.20/0.54  % (19474)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54  % (19467)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (19467)------------------------------
% 0.20/0.54  % (19467)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (19467)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (19467)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (19467)Memory used [KB]: 5500
% 0.20/0.54  % (19467)Time elapsed: 0.126 s
% 0.20/0.54  % (19467)Instructions burned: 2 (million)
% 0.20/0.54  % (19467)------------------------------
% 0.20/0.54  % (19467)------------------------------
% 0.20/0.54  % (19463)Success in time 0.194 s
%------------------------------------------------------------------------------