TSTP Solution File: ANA027-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA027-2 : TPTP v8.1.2. Released v3.2.0.
% 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 : n010.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 10:32:50 EDT 2023

% Result   : Unsatisfiable 2.97s 1.74s
% Output   : CNFRefutation 2.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   62 (  23 unt;  15 typ;   0 def)
%            Number of atoms       :   82 (   3 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   77 (  42   ~;  35   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  12   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   49 (;  49   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__abs > class_OrderedGroup_Ocomm__monoid__add > class_LOrder_Ojoin__semilorder > c_plus > c_minus > #nlpp > v_k > v_g > v_f > v_x > t_b > c_0

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(v_x,type,
    v_x: $i ).

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

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

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

tff(c_0,type,
    c_0: $i ).

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

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

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

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

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

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

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

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

tff(t_b,type,
    t_b: $i ).

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

tff(f_30,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file(unknown,unknown) ).

tff(f_87,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__idom(T)
      | class_OrderedGroup_Olordered__ab__group__abs(T) ),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [T] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
      | class_OrderedGroup_Opordered__ab__group__add(T) ),
    file(unknown,unknown) ).

tff(f_82,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__idom(T)
      | class_OrderedGroup_Ocomm__monoid__add(T) ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    ! [T_a,V_y] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
      | ( c_plus(c_0,V_y,T_a) = V_y ) ),
    file(unknown,unknown) ).

tff(f_51,axiom,
    ! [T_a,V_a,V_b,V_c] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
      | ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
      | c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
    file(unknown,unknown) ).

tff(f_29,axiom,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    file(unknown,unknown) ).

tff(f_26,axiom,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
    file(unknown,unknown) ).

tff(f_43,axiom,
    ! [T_a,V_a,V_c,V_b] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
      | ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
      | c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [T] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
      | class_LOrder_Ojoin__semilorder(T) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [T] :
      ( ~ class_LOrder_Ojoin__semilorder(T)
      | class_Orderings_Oorder(T) ),
    file(unknown,unknown) ).

tff(f_27,axiom,
    c_lessequals(v_g(v_x),v_k(v_x),t_b),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [T_a,V_y,V_z,V_x] :
      ( ~ class_Orderings_Oorder(T_a)
      | ~ c_lessequals(V_y,V_z,T_a)
      | ~ c_lessequals(V_x,V_y,T_a)
      | c_lessequals(V_x,V_z,T_a) ),
    file(unknown,unknown) ).

tff(c_8,plain,
    class_Ring__and__Field_Oordered__idom(t_b),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_27,plain,
    ! [T_20] :
      ( class_OrderedGroup_Olordered__ab__group__abs(T_20)
      | ~ class_Ring__and__Field_Oordered__idom(T_20) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_31,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(resolution,[status(thm)],[c_8,c_27]) ).

tff(c_20,plain,
    ! [T_16] :
      ( class_OrderedGroup_Opordered__ab__group__add(T_16)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_16) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_32,plain,
    ! [T_21] :
      ( class_OrderedGroup_Ocomm__monoid__add(T_21)
      | ~ class_Ring__and__Field_Oordered__idom(T_21) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_36,plain,
    class_OrderedGroup_Ocomm__monoid__add(t_b),
    inference(resolution,[status(thm)],[c_8,c_32]) ).

tff(c_44,plain,
    ! [V_y_25,T_a_26] :
      ( ( c_plus(c_0,V_y_25,T_a_26) = V_y_25 )
      | ~ class_OrderedGroup_Ocomm__monoid__add(T_a_26) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_47,plain,
    ! [V_y_25] : ( c_plus(c_0,V_y_25,t_b) = V_y_25 ),
    inference(resolution,[status(thm)],[c_36,c_44]) ).

tff(c_81,plain,
    ! [V_a_36,V_c_37,V_b_38,T_a_39] :
      ( c_lessequals(V_a_36,c_minus(V_c_37,V_b_38,T_a_39),T_a_39)
      | ~ c_lessequals(c_plus(V_a_36,V_b_38,T_a_39),V_c_37,T_a_39)
      | ~ class_OrderedGroup_Opordered__ab__group__add(T_a_39) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_87,plain,
    ! [V_c_37,V_y_25] :
      ( c_lessequals(c_0,c_minus(V_c_37,V_y_25,t_b),t_b)
      | ~ c_lessequals(V_y_25,V_c_37,t_b)
      | ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
    inference(superposition,[status(thm),theory(equality)],[c_47,c_81]) ).

tff(c_90,plain,
    ~ class_OrderedGroup_Opordered__ab__group__add(t_b),
    inference(splitLeft,[status(thm)],[c_87]) ).

tff(c_93,plain,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(resolution,[status(thm)],[c_20,c_90]) ).

tff(c_97,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_31,c_93]) ).

tff(c_100,plain,
    ! [V_c_41,V_y_42] :
      ( c_lessequals(c_0,c_minus(V_c_41,V_y_42,t_b),t_b)
      | ~ c_lessequals(V_y_42,V_c_41,t_b) ),
    inference(splitRight,[status(thm)],[c_87]) ).

tff(c_6,plain,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_109,plain,
    ~ c_lessequals(v_g(v_x),v_f(v_x),t_b),
    inference(resolution,[status(thm)],[c_100,c_6]) ).

tff(c_2,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_99,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b),
    inference(splitRight,[status(thm)],[c_87]) ).

tff(c_64,plain,
    ! [V_a_32,V_b_33,T_a_34,V_c_35] :
      ( c_lessequals(c_plus(V_a_32,V_b_33,T_a_34),V_c_35,T_a_34)
      | ~ c_lessequals(V_a_32,c_minus(V_c_35,V_b_33,T_a_34),T_a_34)
      | ~ class_OrderedGroup_Opordered__ab__group__add(T_a_34) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_69,plain,
    ! [V_y_25,V_c_35] :
      ( c_lessequals(V_y_25,V_c_35,t_b)
      | ~ c_lessequals(c_0,c_minus(V_c_35,V_y_25,t_b),t_b)
      | ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
    inference(superposition,[status(thm),theory(equality)],[c_47,c_64]) ).

tff(c_115,plain,
    ! [V_y_44,V_c_45] :
      ( c_lessequals(V_y_44,V_c_45,t_b)
      | ~ c_lessequals(c_0,c_minus(V_c_45,V_y_44,t_b),t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_99,c_69]) ).

tff(c_123,plain,
    c_lessequals(v_k(v_x),v_f(v_x),t_b),
    inference(resolution,[status(thm)],[c_2,c_115]) ).

tff(c_38,plain,
    ! [T_23] :
      ( class_LOrder_Ojoin__semilorder(T_23)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_23) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_42,plain,
    class_LOrder_Ojoin__semilorder(t_b),
    inference(resolution,[status(thm)],[c_31,c_38]) ).

tff(c_18,plain,
    ! [T_15] :
      ( class_Orderings_Oorder(T_15)
      | ~ class_LOrder_Ojoin__semilorder(T_15) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_4,plain,
    c_lessequals(v_g(v_x),v_k(v_x),t_b),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_57,plain,
    ! [V_x_28,V_z_29,T_a_30,V_y_31] :
      ( c_lessequals(V_x_28,V_z_29,T_a_30)
      | ~ c_lessequals(V_x_28,V_y_31,T_a_30)
      | ~ c_lessequals(V_y_31,V_z_29,T_a_30)
      | ~ class_Orderings_Oorder(T_a_30) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_63,plain,
    ! [V_z_29] :
      ( c_lessequals(v_g(v_x),V_z_29,t_b)
      | ~ c_lessequals(v_k(v_x),V_z_29,t_b)
      | ~ class_Orderings_Oorder(t_b) ),
    inference(resolution,[status(thm)],[c_4,c_57]) ).

tff(c_71,plain,
    ~ class_Orderings_Oorder(t_b),
    inference(splitLeft,[status(thm)],[c_63]) ).

tff(c_74,plain,
    ~ class_LOrder_Ojoin__semilorder(t_b),
    inference(resolution,[status(thm)],[c_18,c_71]) ).

tff(c_78,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_42,c_74]) ).

tff(c_79,plain,
    ! [V_z_29] :
      ( c_lessequals(v_g(v_x),V_z_29,t_b)
      | ~ c_lessequals(v_k(v_x),V_z_29,t_b) ),
    inference(splitRight,[status(thm)],[c_63]) ).

tff(c_126,plain,
    c_lessequals(v_g(v_x),v_f(v_x),t_b),
    inference(resolution,[status(thm)],[c_123,c_79]) ).

tff(c_132,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_109,c_126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ANA027-2 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 15:20:29 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 2.97/1.74  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.97/1.74  
% 2.97/1.74  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.97/1.78  
% 2.97/1.78  Inference rules
% 2.97/1.78  ----------------------
% 2.97/1.78  #Ref     : 0
% 2.97/1.78  #Sup     : 20
% 2.97/1.78  #Fact    : 0
% 2.97/1.78  #Define  : 0
% 2.97/1.78  #Split   : 2
% 2.97/1.78  #Chain   : 0
% 2.97/1.78  #Close   : 0
% 2.97/1.78  
% 2.97/1.78  Ordering : KBO
% 2.97/1.78  
% 2.97/1.78  Simplification rules
% 2.97/1.78  ----------------------
% 2.97/1.78  #Subsume      : 0
% 2.97/1.78  #Demod        : 5
% 2.97/1.78  #Tautology    : 4
% 2.97/1.78  #SimpNegUnit  : 1
% 2.97/1.78  #BackRed      : 0
% 2.97/1.78  
% 2.97/1.78  #Partial instantiations: 0
% 2.97/1.78  #Strategies tried      : 1
% 2.97/1.78  
% 2.97/1.78  Timing (in seconds)
% 2.97/1.78  ----------------------
% 2.97/1.78  Preprocessing        : 0.44
% 2.97/1.78  Parsing              : 0.24
% 2.97/1.78  CNF conversion       : 0.02
% 2.97/1.78  Main loop            : 0.26
% 2.97/1.78  Inferencing          : 0.11
% 2.97/1.78  Reduction            : 0.07
% 2.97/1.78  Demodulation         : 0.04
% 2.97/1.78  BG Simplification    : 0.01
% 2.97/1.78  Subsumption          : 0.05
% 2.97/1.78  Abstraction          : 0.01
% 2.97/1.78  MUC search           : 0.00
% 2.97/1.78  Cooper               : 0.00
% 2.97/1.78  Total                : 0.75
% 2.97/1.78  Index Insertion      : 0.00
% 2.97/1.79  Index Deletion       : 0.00
% 2.97/1.79  Index Matching       : 0.00
% 2.97/1.79  BG Taut test         : 0.00
%------------------------------------------------------------------------------