TSTP Solution File: LCL536+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n021.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 17:43:02 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   53 (  15 unt;   0 def)
%            Number of atoms       :  106 (   6 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   93 (  40   ~;  35   |;   0   &)
%                                         (  11 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   15 (  13 usr;  13 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   31 (  29   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f539,plain,
    $false,
    inference(avatar_sat_refutation,[],[f358,f378,f403,f411,f458,f459,f460,f463,f538]) ).

fof(f538,plain,
    ( ~ spl1_29
    | ~ spl1_34
    | spl1_39
    | ~ spl1_42 ),
    inference(avatar_contradiction_clause,[],[f536]) ).

fof(f536,plain,
    ( $false
    | ~ spl1_29
    | ~ spl1_34
    | spl1_39
    | ~ spl1_42 ),
    inference(resolution,[],[f481,f398]) ).

fof(f398,plain,
    ( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
    | spl1_39 ),
    inference(avatar_component_clause,[],[f396]) ).

fof(f396,plain,
    ( spl1_39
  <=> is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).

fof(f481,plain,
    ( ! [X9] : is_a_theorem(strict_implies(possibly(X9),necessarily(possibly(X9))))
    | ~ spl1_29
    | ~ spl1_34
    | ~ spl1_42 ),
    inference(resolution,[],[f466,f410]) ).

fof(f410,plain,
    ( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
    | ~ spl1_42 ),
    inference(avatar_component_clause,[],[f409]) ).

fof(f409,plain,
    ( spl1_42
  <=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).

fof(f466,plain,
    ( ! [X0,X1] :
        ( ~ is_a_theorem(implies(X0,X1))
        | is_a_theorem(strict_implies(X0,X1)) )
    | ~ spl1_29
    | ~ spl1_34 ),
    inference(superposition,[],[f377,f353]) ).

fof(f353,plain,
    ( ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0))
    | ~ spl1_29 ),
    inference(avatar_component_clause,[],[f352]) ).

fof(f352,plain,
    ( spl1_29
  <=> ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).

fof(f377,plain,
    ( ! [X0] :
        ( is_a_theorem(necessarily(X0))
        | ~ is_a_theorem(X0) )
    | ~ spl1_34 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f376,plain,
    ( spl1_34
  <=> ! [X0] :
        ( ~ is_a_theorem(X0)
        | is_a_theorem(necessarily(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).

fof(f463,plain,
    spl1_33,
    inference(avatar_split_clause,[],[f210,f372]) ).

fof(f372,plain,
    ( spl1_33
  <=> necessitation ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).

fof(f210,plain,
    necessitation,
    inference(cnf_transformation,[],[f78]) ).

fof(f78,axiom,
    necessitation,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_necessitation) ).

fof(f460,plain,
    spl1_41,
    inference(avatar_split_clause,[],[f197,f405]) ).

fof(f405,plain,
    ( spl1_41
  <=> axiom_5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).

fof(f197,plain,
    axiom_5,
    inference(cnf_transformation,[],[f81]) ).

fof(f81,axiom,
    axiom_5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_5) ).

fof(f459,plain,
    spl1_30,
    inference(avatar_split_clause,[],[f192,f355]) ).

fof(f355,plain,
    ( spl1_30
  <=> op_strict_implies ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).

fof(f192,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f85]) ).

fof(f85,axiom,
    op_strict_implies,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).

fof(f458,plain,
    ~ spl1_40,
    inference(avatar_split_clause,[],[f182,f400]) ).

fof(f400,plain,
    ( spl1_40
  <=> axiom_m10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).

fof(f182,plain,
    ~ axiom_m10,
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ~ axiom_m10,
    inference(flattening,[],[f89]) ).

fof(f89,negated_conjecture,
    ~ axiom_m10,
    inference(negated_conjecture,[],[f88]) ).

fof(f88,conjecture,
    axiom_m10,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).

fof(f411,plain,
    ( ~ spl1_41
    | spl1_42 ),
    inference(avatar_split_clause,[],[f183,f409,f405]) ).

fof(f183,plain,
    ! [X0] :
      ( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
      | ~ axiom_5 ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ( ~ axiom_5
    | ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
    inference(ennf_transformation,[],[f120]) ).

fof(f120,plain,
    ( axiom_5
   => ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
    inference(unused_predicate_definition_removal,[],[f58]) ).

fof(f58,axiom,
    ( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
  <=> axiom_5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f403,plain,
    ( ~ spl1_39
    | spl1_40 ),
    inference(avatar_split_clause,[],[f215,f400,f396]) ).

fof(f215,plain,
    ( axiom_m10
    | ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ( axiom_m10
    | ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f157,f175]) ).

fof(f175,plain,
    ( ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
   => ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ( axiom_m10
    | ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
    inference(ennf_transformation,[],[f119]) ).

fof(f119,plain,
    ( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
   => axiom_m10 ),
    inference(unused_predicate_definition_removal,[],[f72]) ).

fof(f72,axiom,
    ( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
  <=> axiom_m10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m10) ).

fof(f378,plain,
    ( ~ spl1_33
    | spl1_34 ),
    inference(avatar_split_clause,[],[f198,f376,f372]) ).

fof(f198,plain,
    ! [X0] :
      ( ~ is_a_theorem(X0)
      | is_a_theorem(necessarily(X0))
      | ~ necessitation ),
    inference(cnf_transformation,[],[f156]) ).

fof(f156,plain,
    ( ! [X0] :
        ( is_a_theorem(necessarily(X0))
        | ~ is_a_theorem(X0) )
    | ~ necessitation ),
    inference(ennf_transformation,[],[f123]) ).

fof(f123,plain,
    ( necessitation
   => ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f50,axiom,
    ( necessitation
  <=> ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).

fof(f358,plain,
    ( spl1_29
    | ~ spl1_30 ),
    inference(avatar_split_clause,[],[f232,f355,f352]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( ~ op_strict_implies
      | strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ( ~ op_strict_implies
    | ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
    inference(rectify,[],[f143]) ).

fof(f143,plain,
    ( ~ op_strict_implies
    | ! [X1,X0] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ( op_strict_implies
   => ! [X1,X0] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n021.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 02:03:40 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.51  % (27286)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (27295)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.52  % (27302)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.52  % (27294)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52  % (27294)Refutation not found, incomplete strategy% (27294)------------------------------
% 0.19/0.52  % (27294)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27287)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.52  % (27294)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27294)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (27294)Memory used [KB]: 6012
% 0.19/0.52  % (27294)Time elapsed: 0.003 s
% 0.19/0.52  % (27294)Instructions burned: 2 (million)
% 0.19/0.52  % (27294)------------------------------
% 0.19/0.52  % (27294)------------------------------
% 0.19/0.52  % (27302)Refutation not found, incomplete strategy% (27302)------------------------------
% 0.19/0.52  % (27302)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27302)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27302)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (27302)Memory used [KB]: 6012
% 0.19/0.52  % (27302)Time elapsed: 0.004 s
% 0.19/0.52  % (27302)Instructions burned: 2 (million)
% 0.19/0.52  % (27302)------------------------------
% 0.19/0.52  % (27302)------------------------------
% 0.19/0.52  % (27277)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.52  % (27286)Refutation not found, incomplete strategy% (27286)------------------------------
% 0.19/0.52  % (27286)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27286)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27286)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (27286)Memory used [KB]: 6012
% 0.19/0.52  % (27286)Time elapsed: 0.004 s
% 0.19/0.52  % (27277)Refutation not found, incomplete strategy% (27277)------------------------------
% 0.19/0.52  % (27277)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27277)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27277)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (27277)Memory used [KB]: 6012
% 0.19/0.52  % (27277)Time elapsed: 0.002 s
% 0.19/0.52  % (27277)Instructions burned: 2 (million)
% 0.19/0.52  % (27277)------------------------------
% 0.19/0.52  % (27277)------------------------------
% 0.19/0.52  % (27286)Instructions burned: 1 (million)
% 0.19/0.52  % (27286)------------------------------
% 0.19/0.52  % (27286)------------------------------
% 0.19/0.52  % (27278)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.52  % (27279)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.52  % (27278)Refutation not found, incomplete strategy% (27278)------------------------------
% 0.19/0.52  % (27278)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27278)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27278)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (27278)Memory used [KB]: 1535
% 0.19/0.52  % (27278)Time elapsed: 0.002 s
% 0.19/0.52  % (27278)Instructions burned: 1 (million)
% 0.19/0.52  % (27278)------------------------------
% 0.19/0.52  % (27278)------------------------------
% 0.19/0.52  % (27279)Refutation not found, incomplete strategy% (27279)------------------------------
% 0.19/0.52  % (27279)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27279)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27279)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (27279)Memory used [KB]: 6012
% 0.19/0.52  % (27279)Time elapsed: 0.002 s
% 0.19/0.52  % (27279)------------------------------
% 0.19/0.52  % (27279)------------------------------
% 0.19/0.53  % (27282)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.53  % (27275)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.53  % (27273)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.53  % (27300)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.53  % (27295)First to succeed.
% 0.19/0.53  % (27295)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (27295)------------------------------
% 0.19/0.53  % (27295)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (27295)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (27295)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (27295)Memory used [KB]: 6268
% 0.19/0.53  % (27295)Time elapsed: 0.083 s
% 0.19/0.53  % (27295)Instructions burned: 8 (million)
% 0.19/0.53  % (27295)------------------------------
% 0.19/0.53  % (27295)------------------------------
% 0.19/0.53  % (27272)Success in time 0.182 s
%------------------------------------------------------------------------------