TSTP Solution File: ALG211+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n019.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 : Tue Aug 22 10:32:21 EDT 2023

% Result   : Theorem 3.26s 1.87s
% Output   : CNFRefutation 3.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   38 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   59 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   59 (  27   ~;  19   |;   6   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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   :   44 (;  40   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ lin_ind_subset > basis_of > a_vector_subspace_of > a_subset_of > a_vector_space > union > #nlpp > vec_to_class > #skF_1 > #skF_2 > #skF_3 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a_vector_subspace_of,type,
    a_vector_subspace_of: ( $i * $i ) > $o ).

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

tff('#skF_1',type,
    '#skF_1': ( $i * $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': $i > $i ).

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

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $i ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff(f_72,negated_conjecture,
    ~ ! [W,V] :
        ( ( a_vector_subspace_of(W,V)
          & a_vector_space(V) )
       => ? [E,F] :
            ( basis_of(union(E,F),V)
            & basis_of(E,W) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_3) ).

tff(f_48,axiom,
    ! [A] :
      ( a_vector_space(A)
     => ? [B] : basis_of(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_remark_63_a) ).

tff(f_53,axiom,
    ! [A,B] :
      ( a_vector_subspace_of(A,B)
     => a_vector_space(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_a) ).

tff(f_32,axiom,
    ! [B,V] :
      ( basis_of(B,V)
     => ( lin_ind_subset(B,V)
        & a_subset_of(B,vec_to_class(V)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',basis_of) ).

tff(f_62,axiom,
    ! [W,V,E] :
      ( ( a_vector_subspace_of(W,V)
        & a_subset_of(E,vec_to_class(W)) )
     => ( lin_ind_subset(E,W)
      <=> lin_ind_subset(E,V) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_2) ).

tff(f_42,axiom,
    ! [S,T,V] :
      ( ( lin_ind_subset(S,V)
        & basis_of(T,V) )
     => ? [U] :
          ( a_subset_of(U,T)
          & basis_of(union(S,U),V) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_2_5) ).

tff(c_20,plain,
    a_vector_space('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_10,plain,
    ! [A_7] :
      ( basis_of('#skF_2'(A_7),A_7)
      | ~ a_vector_space(A_7) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_22,plain,
    a_vector_subspace_of('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_23,plain,
    ! [A_18,B_19] :
      ( a_vector_space(A_18)
      | ~ a_vector_subspace_of(A_18,B_19) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_27,plain,
    a_vector_space('#skF_3'),
    inference(resolution,[status(thm)],[c_22,c_23]) ).

tff(c_4,plain,
    ! [B_1,V_2] :
      ( lin_ind_subset(B_1,V_2)
      | ~ basis_of(B_1,V_2) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_2,plain,
    ! [B_1,V_2] :
      ( a_subset_of(B_1,vec_to_class(V_2))
      | ~ basis_of(B_1,V_2) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_33,plain,
    ! [E_30,V_31,W_32] :
      ( lin_ind_subset(E_30,V_31)
      | ~ lin_ind_subset(E_30,W_32)
      | ~ a_subset_of(E_30,vec_to_class(W_32))
      | ~ a_vector_subspace_of(W_32,V_31) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_41,plain,
    ! [B_33,V_34,V_35] :
      ( lin_ind_subset(B_33,V_34)
      | ~ lin_ind_subset(B_33,V_35)
      | ~ a_vector_subspace_of(V_35,V_34)
      | ~ basis_of(B_33,V_35) ),
    inference(resolution,[status(thm)],[c_2,c_33]) ).

tff(c_45,plain,
    ! [B_36,V_37,V_38] :
      ( lin_ind_subset(B_36,V_37)
      | ~ a_vector_subspace_of(V_38,V_37)
      | ~ basis_of(B_36,V_38) ),
    inference(resolution,[status(thm)],[c_4,c_41]) ).

tff(c_48,plain,
    ! [B_36] :
      ( lin_ind_subset(B_36,'#skF_4')
      | ~ basis_of(B_36,'#skF_3') ),
    inference(resolution,[status(thm)],[c_22,c_45]) ).

tff(c_65,plain,
    ! [S_46,T_47,V_48] :
      ( basis_of(union(S_46,'#skF_1'(S_46,T_47,V_48)),V_48)
      | ~ basis_of(T_47,V_48)
      | ~ lin_ind_subset(S_46,V_48) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_18,plain,
    ! [E_16,F_17] :
      ( ~ basis_of(E_16,'#skF_3')
      | ~ basis_of(union(E_16,F_17),'#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_70,plain,
    ! [S_46,T_47] :
      ( ~ basis_of(S_46,'#skF_3')
      | ~ basis_of(T_47,'#skF_4')
      | ~ lin_ind_subset(S_46,'#skF_4') ),
    inference(resolution,[status(thm)],[c_65,c_18]) ).

tff(c_72,plain,
    ! [S_49] :
      ( ~ basis_of(S_49,'#skF_3')
      | ~ lin_ind_subset(S_49,'#skF_4') ),
    inference(splitLeft,[status(thm)],[c_70]) ).

tff(c_82,plain,
    ! [B_50] : ~ basis_of(B_50,'#skF_3'),
    inference(resolution,[status(thm)],[c_48,c_72]) ).

tff(c_90,plain,
    ~ a_vector_space('#skF_3'),
    inference(resolution,[status(thm)],[c_10,c_82]) ).

tff(c_95,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_27,c_90]) ).

tff(c_97,plain,
    ! [T_51] : ~ basis_of(T_51,'#skF_4'),
    inference(splitRight,[status(thm)],[c_70]) ).

tff(c_105,plain,
    ~ a_vector_space('#skF_4'),
    inference(resolution,[status(thm)],[c_10,c_97]) ).

tff(c_110,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_105]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 20:19:17 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.26/1.87  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.26/1.87  
% 3.26/1.87  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.34/1.91  
% 3.34/1.91  Inference rules
% 3.34/1.91  ----------------------
% 3.34/1.91  #Ref     : 0
% 3.34/1.91  #Sup     : 16
% 3.34/1.91  #Fact    : 0
% 3.34/1.91  #Define  : 0
% 3.34/1.91  #Split   : 1
% 3.34/1.91  #Chain   : 0
% 3.34/1.91  #Close   : 0
% 3.34/1.91  
% 3.34/1.91  Ordering : KBO
% 3.34/1.91  
% 3.34/1.91  Simplification rules
% 3.34/1.91  ----------------------
% 3.34/1.91  #Subsume      : 8
% 3.34/1.91  #Demod        : 2
% 3.34/1.91  #Tautology    : 0
% 3.34/1.91  #SimpNegUnit  : 0
% 3.34/1.91  #BackRed      : 0
% 3.34/1.91  
% 3.34/1.91  #Partial instantiations: 0
% 3.34/1.91  #Strategies tried      : 1
% 3.34/1.91  
% 3.34/1.91  Timing (in seconds)
% 3.34/1.91  ----------------------
% 3.34/1.91  Preprocessing        : 0.44
% 3.34/1.91  Parsing              : 0.25
% 3.34/1.91  CNF conversion       : 0.03
% 3.34/1.91  Main loop            : 0.30
% 3.34/1.91  Inferencing          : 0.13
% 3.34/1.91  Reduction            : 0.06
% 3.34/1.92  Demodulation         : 0.04
% 3.34/1.92  BG Simplification    : 0.02
% 3.34/1.92  Subsumption          : 0.06
% 3.34/1.92  Abstraction          : 0.01
% 3.34/1.92  MUC search           : 0.00
% 3.34/1.92  Cooper               : 0.00
% 3.34/1.92  Total                : 0.80
% 3.34/1.92  Index Insertion      : 0.00
% 3.34/1.92  Index Deletion       : 0.00
% 3.34/1.92  Index Matching       : 0.00
% 3.34/1.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------