TSTP Solution File: ALG211+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 30 16:06:39 EDT 2023

% Result   : Theorem 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   40 (   5 unt;  11 typ;   0 def)
%            Number of atoms       :   81 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   89 (  37   ~;  31   |;  13   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-3 aty)
%            Number of variables   :   58 (   6 sgn;  28   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    basis_of: ( $i * $i ) > $o ).

tff(decl_23,type,
    lin_ind_subset: ( $i * $i ) > $o ).

tff(decl_24,type,
    vec_to_class: $i > $i ).

tff(decl_25,type,
    a_subset_of: ( $i * $i ) > $o ).

tff(decl_26,type,
    union: ( $i * $i ) > $i ).

tff(decl_27,type,
    a_vector_space: $i > $o ).

tff(decl_28,type,
    a_vector_subspace_of: ( $i * $i ) > $o ).

tff(decl_29,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_30,type,
    esk2_1: $i > $i ).

tff(decl_31,type,
    esk3_0: $i ).

tff(decl_32,type,
    esk4_0: $i ).

fof(bg_2_4_3,conjecture,
    ! [X7,X2] :
      ( ( a_vector_subspace_of(X7,X2)
        & a_vector_space(X2) )
     => ? [X8,X9] :
          ( basis_of(union(X8,X9),X2)
          & basis_of(X8,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).

fof(bg_2_4_2,axiom,
    ! [X7,X2,X8] :
      ( ( a_vector_subspace_of(X7,X2)
        & a_subset_of(X8,vec_to_class(X7)) )
     => ( lin_ind_subset(X8,X7)
      <=> lin_ind_subset(X8,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).

fof(basis_of,axiom,
    ! [X1,X2] :
      ( basis_of(X1,X2)
     => ( lin_ind_subset(X1,X2)
        & a_subset_of(X1,vec_to_class(X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).

fof(bg_2_2_5,axiom,
    ! [X3,X4,X2] :
      ( ( lin_ind_subset(X3,X2)
        & basis_of(X4,X2) )
     => ? [X5] :
          ( a_subset_of(X5,X4)
          & basis_of(union(X3,X5),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).

fof(bg_2_4_a,axiom,
    ! [X6,X1] :
      ( a_vector_subspace_of(X6,X1)
     => a_vector_space(X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).

fof(bg_remark_63_a,axiom,
    ! [X6] :
      ( a_vector_space(X6)
     => ? [X1] : basis_of(X1,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X7,X2] :
        ( ( a_vector_subspace_of(X7,X2)
          & a_vector_space(X2) )
       => ? [X8,X9] :
            ( basis_of(union(X8,X9),X2)
            & basis_of(X8,X7) ) ),
    inference(assume_negation,[status(cth)],[bg_2_4_3]) ).

fof(c_0_7,plain,
    ! [X20,X21,X22] :
      ( ( ~ lin_ind_subset(X22,X20)
        | lin_ind_subset(X22,X21)
        | ~ a_vector_subspace_of(X20,X21)
        | ~ a_subset_of(X22,vec_to_class(X20)) )
      & ( ~ lin_ind_subset(X22,X21)
        | lin_ind_subset(X22,X20)
        | ~ a_vector_subspace_of(X20,X21)
        | ~ a_subset_of(X22,vec_to_class(X20)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_2])])]) ).

fof(c_0_8,plain,
    ! [X10,X11] :
      ( ( lin_ind_subset(X10,X11)
        | ~ basis_of(X10,X11) )
      & ( a_subset_of(X10,vec_to_class(X11))
        | ~ basis_of(X10,X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[basis_of])])]) ).

fof(c_0_9,negated_conjecture,
    ! [X25,X26] :
      ( a_vector_subspace_of(esk3_0,esk4_0)
      & a_vector_space(esk4_0)
      & ( ~ basis_of(union(X25,X26),esk4_0)
        | ~ basis_of(X25,esk3_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_10,plain,
    ! [X12,X13,X14] :
      ( ( a_subset_of(esk1_3(X12,X13,X14),X13)
        | ~ lin_ind_subset(X12,X14)
        | ~ basis_of(X13,X14) )
      & ( basis_of(union(X12,esk1_3(X12,X13,X14)),X14)
        | ~ lin_ind_subset(X12,X14)
        | ~ basis_of(X13,X14) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_2_5])])])]) ).

cnf(c_0_11,plain,
    ( lin_ind_subset(X1,X3)
    | ~ lin_ind_subset(X1,X2)
    | ~ a_vector_subspace_of(X2,X3)
    | ~ a_subset_of(X1,vec_to_class(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( a_subset_of(X1,vec_to_class(X2))
    | ~ basis_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( lin_ind_subset(X1,X2)
    | ~ basis_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( ~ basis_of(union(X1,X2),esk4_0)
    | ~ basis_of(X1,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( basis_of(union(X1,esk1_3(X1,X2,X3)),X3)
    | ~ lin_ind_subset(X1,X3)
    | ~ basis_of(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( lin_ind_subset(X1,X2)
    | ~ a_vector_subspace_of(X3,X2)
    | ~ basis_of(X1,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    a_vector_subspace_of(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_18,plain,
    ! [X18,X19] :
      ( ~ a_vector_subspace_of(X18,X19)
      | a_vector_space(X18) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_a])]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ lin_ind_subset(X1,esk4_0)
    | ~ basis_of(X1,esk3_0)
    | ~ basis_of(X2,esk4_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    ( lin_ind_subset(X1,esk4_0)
    | ~ basis_of(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_21,plain,
    ! [X16] :
      ( ~ a_vector_space(X16)
      | basis_of(esk2_1(X16),X16) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_remark_63_a])])]) ).

cnf(c_0_22,plain,
    ( a_vector_space(X1)
    | ~ a_vector_subspace_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ basis_of(X1,esk3_0)
    | ~ basis_of(X2,esk4_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( basis_of(esk2_1(X1),X1)
    | ~ a_vector_space(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    a_vector_space(esk3_0),
    inference(spm,[status(thm)],[c_0_22,c_0_17]) ).

cnf(c_0_26,negated_conjecture,
    ~ basis_of(X1,esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_27,negated_conjecture,
    a_vector_space(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n003.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 28 03:32:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.007000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.009000 s
%------------------------------------------------------------------------------