TSTP Solution File: ALG211+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ALG211+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_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 15:40:40 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   60 (   9 unt;   0 def)
%            Number of atoms       :  170 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  182 (  72   ~;  54   |;  35   &)
%                                         (   6 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-3 aty)
%            Number of variables   :  121 (  97   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f116,plain,
    $false,
    inference(avatar_sat_refutation,[],[f58,f67,f115]) ).

fof(f115,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f114]) ).

fof(f114,plain,
    ( $false
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f107,f79]) ).

fof(f79,plain,
    a_subset_of(sK0(sK3),vec_to_class(sK3)),
    inference(unit_resulting_resolution,[],[f59,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ basis_of(X1,X0)
      | a_subset_of(X1,vec_to_class(X0)) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( lin_ind_subset(X1,X0)
        & a_subset_of(X1,vec_to_class(X0)) )
      | ~ basis_of(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ( lin_ind_subset(X0,X1)
        & a_subset_of(X0,vec_to_class(X1)) )
      | ~ basis_of(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( basis_of(X0,X1)
     => ( lin_ind_subset(X0,X1)
        & a_subset_of(X0,vec_to_class(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).

fof(f59,plain,
    basis_of(sK0(sK3),sK3),
    inference(unit_resulting_resolution,[],[f47,f34]) ).

fof(f34,plain,
    ! [X0] :
      ( basis_of(sK0(X0),X0)
      | ~ a_vector_space(X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( ~ a_vector_space(X0)
      | basis_of(sK0(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ? [X1] : basis_of(X1,X0)
     => basis_of(sK0(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0] :
      ( ~ a_vector_space(X0)
      | ? [X1] : basis_of(X1,X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( a_vector_space(X0)
     => ? [X1] : basis_of(X1,X0) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X5] :
      ( a_vector_space(X5)
     => ? [X0] : basis_of(X0,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).

fof(f47,plain,
    a_vector_space(sK3),
    inference(unit_resulting_resolution,[],[f43,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ a_vector_subspace_of(X1,X0)
      | a_vector_space(X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( a_vector_space(X1)
      | ~ a_vector_subspace_of(X1,X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( a_vector_space(X0)
      | ~ a_vector_subspace_of(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X0] :
      ( a_vector_subspace_of(X0,X1)
     => a_vector_space(X0) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X5,X0] :
      ( a_vector_subspace_of(X5,X0)
     => a_vector_space(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).

fof(f43,plain,
    a_vector_subspace_of(sK3,sK2),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ( a_vector_space(sK2)
    & a_vector_subspace_of(sK3,sK2)
    & ! [X2,X3] :
        ( ~ basis_of(union(X2,X3),sK2)
        | ~ basis_of(X2,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f31,f32]) ).

fof(f32,plain,
    ( ? [X0,X1] :
        ( a_vector_space(X0)
        & a_vector_subspace_of(X1,X0)
        & ! [X2,X3] :
            ( ~ basis_of(union(X2,X3),X0)
            | ~ basis_of(X2,X1) ) )
   => ( a_vector_space(sK2)
      & a_vector_subspace_of(sK3,sK2)
      & ! [X3,X2] :
          ( ~ basis_of(union(X2,X3),sK2)
          | ~ basis_of(X2,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( a_vector_space(X0)
      & a_vector_subspace_of(X1,X0)
      & ! [X2,X3] :
          ( ~ basis_of(union(X2,X3),X0)
          | ~ basis_of(X2,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ? [X1,X0] :
      ( a_vector_space(X1)
      & a_vector_subspace_of(X0,X1)
      & ! [X2,X3] :
          ( ~ basis_of(union(X2,X3),X1)
          | ~ basis_of(X2,X0) ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ? [X0,X1] :
      ( ! [X2,X3] :
          ( ~ basis_of(union(X2,X3),X1)
          | ~ basis_of(X2,X0) )
      & a_vector_subspace_of(X0,X1)
      & a_vector_space(X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ~ ! [X0,X1] :
        ( ( a_vector_subspace_of(X0,X1)
          & a_vector_space(X1) )
       => ? [X3,X2] :
            ( basis_of(X2,X0)
            & basis_of(union(X2,X3),X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X6,X1] :
        ( ( a_vector_space(X1)
          & a_vector_subspace_of(X6,X1) )
       => ? [X7,X8] :
            ( basis_of(union(X7,X8),X1)
            & basis_of(X7,X6) ) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X6,X1] :
      ( ( a_vector_space(X1)
        & a_vector_subspace_of(X6,X1) )
     => ? [X7,X8] :
          ( basis_of(union(X7,X8),X1)
          & basis_of(X7,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).

fof(f107,plain,
    ( ~ a_subset_of(sK0(sK3),vec_to_class(sK3))
    | ~ spl4_1 ),
    inference(unit_resulting_resolution,[],[f43,f77,f83,f39]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( lin_ind_subset(X2,X1)
      | ~ a_subset_of(X2,vec_to_class(X0))
      | ~ a_vector_subspace_of(X0,X1)
      | ~ lin_ind_subset(X2,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ~ a_subset_of(X2,vec_to_class(X0))
      | ~ a_vector_subspace_of(X0,X1)
      | ( ( lin_ind_subset(X2,X1)
          | ~ lin_ind_subset(X2,X0) )
        & ( lin_ind_subset(X2,X0)
          | ~ lin_ind_subset(X2,X1) ) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( ~ a_subset_of(X1,vec_to_class(X2))
      | ~ a_vector_subspace_of(X2,X0)
      | ( ( lin_ind_subset(X1,X0)
          | ~ lin_ind_subset(X1,X2) )
        & ( lin_ind_subset(X1,X2)
          | ~ lin_ind_subset(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X2,X0,X1] :
      ( ~ a_subset_of(X1,vec_to_class(X2))
      | ~ a_vector_subspace_of(X2,X0)
      | ( lin_ind_subset(X1,X0)
      <=> lin_ind_subset(X1,X2) ) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( lin_ind_subset(X1,X0)
      <=> lin_ind_subset(X1,X2) )
      | ~ a_vector_subspace_of(X2,X0)
      | ~ a_subset_of(X1,vec_to_class(X2)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ( a_vector_subspace_of(X2,X0)
        & a_subset_of(X1,vec_to_class(X2)) )
     => ( lin_ind_subset(X1,X0)
      <=> lin_ind_subset(X1,X2) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X7,X6] :
      ( ( a_subset_of(X7,vec_to_class(X6))
        & a_vector_subspace_of(X6,X1) )
     => ( lin_ind_subset(X7,X1)
      <=> lin_ind_subset(X7,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).

fof(f83,plain,
    lin_ind_subset(sK0(sK3),sK3),
    inference(resolution,[],[f59,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ basis_of(X1,X0)
      | lin_ind_subset(X1,X0) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f77,plain,
    ( ~ lin_ind_subset(sK0(sK3),sK2)
    | ~ spl4_1 ),
    inference(unit_resulting_resolution,[],[f59,f54]) ).

fof(f54,plain,
    ( ! [X0] :
        ( ~ lin_ind_subset(X0,sK2)
        | ~ basis_of(X0,sK3) )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f53,plain,
    ( spl4_1
  <=> ! [X0] :
        ( ~ lin_ind_subset(X0,sK2)
        | ~ basis_of(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f67,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f66]) ).

fof(f66,plain,
    ( $false
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f61,f44]) ).

fof(f44,plain,
    a_vector_space(sK2),
    inference(cnf_transformation,[],[f33]) ).

fof(f61,plain,
    ( ~ a_vector_space(sK2)
    | ~ spl4_2 ),
    inference(unit_resulting_resolution,[],[f57,f34]) ).

fof(f57,plain,
    ( ! [X1] : ~ basis_of(X1,sK2)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl4_2
  <=> ! [X1] : ~ basis_of(X1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f58,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f51,f56,f53]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ basis_of(X1,sK2)
      | ~ lin_ind_subset(X0,sK2)
      | ~ basis_of(X0,sK3) ),
    inference(resolution,[],[f42,f36]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( ~ basis_of(X1,X2)
      | ~ lin_ind_subset(X0,X2)
      | basis_of(union(X0,sK1(X0,X1,X2)),X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( a_subset_of(sK1(X0,X1,X2),X1)
        & basis_of(union(X0,sK1(X0,X1,X2)),X2) )
      | ~ basis_of(X1,X2)
      | ~ lin_ind_subset(X0,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( a_subset_of(X3,X1)
          & basis_of(union(X0,X3),X2) )
     => ( a_subset_of(sK1(X0,X1,X2),X1)
        & basis_of(union(X0,sK1(X0,X1,X2)),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( a_subset_of(X3,X1)
          & basis_of(union(X0,X3),X2) )
      | ~ basis_of(X1,X2)
      | ~ lin_ind_subset(X0,X2) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X1,X2,X0] :
      ( ? [X3] :
          ( a_subset_of(X3,X2)
          & basis_of(union(X1,X3),X0) )
      | ~ basis_of(X2,X0)
      | ~ lin_ind_subset(X1,X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X2,X0,X1] :
      ( ? [X3] :
          ( a_subset_of(X3,X2)
          & basis_of(union(X1,X3),X0) )
      | ~ lin_ind_subset(X1,X0)
      | ~ basis_of(X2,X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X2,X0,X1] :
      ( ( lin_ind_subset(X1,X0)
        & basis_of(X2,X0) )
     => ? [X3] :
          ( a_subset_of(X3,X2)
          & basis_of(union(X1,X3),X0) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X2,X3] :
      ( ( lin_ind_subset(X2,X1)
        & basis_of(X3,X1) )
     => ? [X4] :
          ( basis_of(union(X2,X4),X1)
          & a_subset_of(X4,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).

fof(f42,plain,
    ! [X2,X3] :
      ( ~ basis_of(union(X2,X3),sK2)
      | ~ basis_of(X2,sK3) ),
    inference(cnf_transformation,[],[f33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ALG211+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_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   : Mon Aug 29 14:55:40 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (32581)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)
% 0.19/0.51  % (32582)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)
% 0.19/0.51  % (32580)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)
% 0.19/0.51  % (32581)Refutation not found, incomplete strategy% (32581)------------------------------
% 0.19/0.51  % (32581)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (32581)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (32581)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (32581)Memory used [KB]: 1407
% 0.19/0.51  % (32581)Time elapsed: 0.112 s
% 0.19/0.51  % (32581)Instructions burned: 2 (million)
% 0.19/0.51  % (32581)------------------------------
% 0.19/0.51  % (32581)------------------------------
% 0.19/0.51  % (32580)Refutation not found, incomplete strategy% (32580)------------------------------
% 0.19/0.51  % (32580)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (32580)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (32580)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (32580)Memory used [KB]: 5884
% 0.19/0.51  % (32580)Time elapsed: 0.116 s
% 0.19/0.51  % (32580)Instructions burned: 2 (million)
% 0.19/0.51  % (32580)------------------------------
% 0.19/0.51  % (32580)------------------------------
% 0.19/0.51  % (32602)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  % (32583)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (32594)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51  % (32594)Instruction limit reached!
% 0.19/0.51  % (32594)------------------------------
% 0.19/0.51  % (32594)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (32583)First to succeed.
% 0.19/0.51  % (32594)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (32594)Termination reason: Unknown
% 0.19/0.51  % (32594)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (32594)Memory used [KB]: 5884
% 0.19/0.51  % (32594)Time elapsed: 0.003 s
% 0.19/0.51  % (32594)Instructions burned: 2 (million)
% 0.19/0.51  % (32594)------------------------------
% 0.19/0.51  % (32594)------------------------------
% 0.19/0.51  % (32602)Also succeeded, but the first one will report.
% 0.19/0.52  % (32583)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (32583)------------------------------
% 0.19/0.52  % (32583)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (32583)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (32583)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (32583)Memory used [KB]: 6012
% 0.19/0.52  % (32583)Time elapsed: 0.079 s
% 0.19/0.52  % (32583)Instructions burned: 3 (million)
% 0.19/0.52  % (32583)------------------------------
% 0.19/0.52  % (32583)------------------------------
% 0.19/0.52  % (32574)Success in time 0.167 s
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