TSTP Solution File: ANA023-10 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA023-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n016.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 10:32:49 EDT 2023

% Result   : Unsatisfiable 3.59s 1.93s
% Output   : CNFRefutation 3.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   66 (  49 unt;  17 typ;   0 def)
%            Number of atoms       :   49 (  48 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   25 (  13   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   4 con; 0-4 aty)
%            Number of variables   :   56 (;  56   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ifeq2 > ifeq > c_plus > c_minus > c_lessequals > #nlpp > v_k > v_g > v_f > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Ocomm__monoid__add > v_x > true > t_b > c_0

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(ifeq2,type,
    ifeq2: ( $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(f_38,axiom,
    c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
    file(unknown,unknown) ).

tff(f_47,axiom,
    class_Ring__and__Field_Oordered__idom(t_b) = true,
    file(unknown,unknown) ).

tff(f_42,axiom,
    ! [T] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Ocomm__monoid__add(T),true) = true ),
    file(unknown,unknown) ).

tff(f_26,axiom,
    ! [A,B,C] : ( ifeq(A,A,B,C) = B ),
    file(unknown,unknown) ).

tff(f_28,axiom,
    ! [T_a,V_y] : ( ifeq2(class_OrderedGroup_Ocomm__monoid__add(T_a),true,c_plus(c_0,V_y,T_a),V_y) = V_y ),
    file(unknown,unknown) ).

tff(f_24,axiom,
    ! [A,B,C] : ( ifeq2(A,A,B,C) = B ),
    file(unknown,unknown) ).

tff(f_46,axiom,
    ! [T] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [T_a,V_a,V_c,V_b] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true ),
    file(unknown,unknown) ).

tff(f_44,axiom,
    ! [T] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true ),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [T] : ( ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
    file(unknown,unknown) ).

tff(f_34,axiom,
    ! [T_a,V_x,V_y,V_z] : ( ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ! [T_a,V_a,V_b,V_c] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true ),
    file(unknown,unknown) ).

tff(c_18,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_28,plain,
    class_Ring__and__Field_Oordered__idom(t_b) = true,
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_65,plain,
    ! [T_32] : ( ifeq(class_Ring__and__Field_Oordered__idom(T_32),true,class_OrderedGroup_Ocomm__monoid__add(T_32),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_72,plain,
    ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_28,c_65]) ).

tff(c_4,plain,
    ! [A_4,B_5,C_6] : ( ifeq(A_4,A_4,B_5,C_6) = B_5 ),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_106,plain,
    class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_72,c_4]) ).

tff(c_144,plain,
    ! [T_a_35,V_y_36] : ( ifeq2(class_OrderedGroup_Ocomm__monoid__add(T_a_35),true,c_plus(c_0,V_y_36,T_a_35),V_y_36) = V_y_36 ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_191,plain,
    ! [V_y_37] : ( ifeq2(true,true,c_plus(c_0,V_y_37,t_b),V_y_37) = V_y_37 ),
    inference(superposition,[status(thm),theory(equality)],[c_106,c_144]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3] : ( ifeq2(A_1,A_1,B_2,C_3) = B_2 ),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_197,plain,
    ! [V_y_37] : ( c_plus(c_0,V_y_37,t_b) = V_y_37 ),
    inference(superposition,[status(thm),theory(equality)],[c_191,c_2]) ).

tff(c_55,plain,
    ! [T_31] : ( ifeq(class_Ring__and__Field_Oordered__idom(T_31),true,class_OrderedGroup_Opordered__ab__group__add(T_31),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_62,plain,
    ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_28,c_55]) ).

tff(c_78,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_62,c_4]) ).

tff(c_14,plain,
    c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_227,plain,
    ! [T_a_39,V_a_40,V_c_41,V_b_42] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a_39),true,ifeq(c_lessequals(V_a_40,c_minus(V_c_41,V_b_42,T_a_39),T_a_39),true,c_lessequals(c_plus(V_a_40,V_b_42,T_a_39),V_c_41,T_a_39),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_234,plain,
    ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_14,c_227]) ).

tff(c_243,plain,
    c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
    inference(demodulation,[status(thm),theory(equality)],[c_197,c_4,c_78,c_4,c_234]) ).

tff(c_124,plain,
    ! [T_34] : ( ifeq(class_Ring__and__Field_Oordered__idom(T_34),true,class_Orderings_Olinorder(T_34),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_131,plain,
    ifeq(true,true,class_Orderings_Olinorder(t_b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_28,c_124]) ).

tff(c_137,plain,
    class_Orderings_Olinorder(t_b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_131,c_4]) ).

tff(c_20,plain,
    ! [T_21] : ( ifeq(class_Orderings_Olinorder(T_21),true,class_Orderings_Oorder(T_21),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_164,plain,
    ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_137,c_20]) ).

tff(c_173,plain,
    class_Orderings_Oorder(t_b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_164,c_4]) ).

tff(c_16,plain,
    c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_354,plain,
    ! [T_a_51,V_x_52,V_y_53,V_z_54] : ( ifeq(class_Orderings_Oorder(T_a_51),true,ifeq(c_lessequals(V_x_52,V_y_53,T_a_51),true,ifeq(c_lessequals(V_y_53,V_z_54,T_a_51),true,c_lessequals(V_x_52,V_z_54,T_a_51),true),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_394,plain,
    ! [V_x_52] : ( ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(V_x_52,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(V_x_52,v_f(v_x),t_b),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_354]) ).

tff(c_430,plain,
    ! [V_x_56] : ( ifeq(c_lessequals(V_x_56,v_k(v_x),t_b),true,c_lessequals(V_x_56,v_f(v_x),t_b),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_173,c_4,c_394]) ).

tff(c_437,plain,
    ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_243,c_430]) ).

tff(c_450,plain,
    c_lessequals(v_g(v_x),v_f(v_x),t_b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_437,c_4]) ).

tff(c_270,plain,
    ! [T_a_45,V_a_46,V_b_47,V_c_48] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a_45),true,ifeq(c_lessequals(c_plus(V_a_46,V_b_47,T_a_45),V_c_48,T_a_45),true,c_lessequals(V_a_46,c_minus(V_c_48,V_b_47,T_a_45),T_a_45),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_280,plain,
    ! [V_y_37,V_c_48] : ( ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(V_y_37,V_c_48,t_b),true,c_lessequals(c_0,c_minus(V_c_48,V_y_37,t_b),t_b),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_197,c_270]) ).

tff(c_287,plain,
    ! [V_y_37,V_c_48] : ( ifeq(c_lessequals(V_y_37,V_c_48,t_b),true,c_lessequals(c_0,c_minus(V_c_48,V_y_37,t_b),t_b),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_78,c_280]) ).

tff(c_474,plain,
    ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_450,c_287]) ).

tff(c_624,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_474,c_4]) ).

tff(c_631,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_624]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ANA023-10 : TPTP v8.1.2. Released v7.5.0.
% 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
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 15:58:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.59/1.93  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.93  
% 3.62/1.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.62/1.98  
% 3.62/1.98  Inference rules
% 3.62/1.98  ----------------------
% 3.62/1.98  #Ref     : 0
% 3.62/1.98  #Sup     : 181
% 3.62/1.98  #Fact    : 0
% 3.62/1.98  #Define  : 0
% 3.62/1.98  #Split   : 0
% 3.62/1.98  #Chain   : 0
% 3.62/1.98  #Close   : 0
% 3.62/1.98  
% 3.62/1.98  Ordering : KBO
% 3.62/1.98  
% 3.62/1.98  Simplification rules
% 3.62/1.98  ----------------------
% 3.62/1.98  #Subsume      : 0
% 3.62/1.98  #Demod        : 163
% 3.62/1.98  #Tautology    : 133
% 3.62/1.98  #SimpNegUnit  : 1
% 3.62/1.98  #BackRed      : 9
% 3.62/1.98  
% 3.62/1.98  #Partial instantiations: 0
% 3.62/1.98  #Strategies tried      : 1
% 3.62/1.98  
% 3.62/1.98  Timing (in seconds)
% 3.62/1.98  ----------------------
% 3.62/1.98  Preprocessing        : 0.45
% 3.62/1.98  Parsing              : 0.25
% 3.62/1.98  CNF conversion       : 0.02
% 3.62/1.98  Main loop            : 0.43
% 3.62/1.98  Inferencing          : 0.16
% 3.62/1.98  Reduction            : 0.16
% 3.62/1.98  Demodulation         : 0.12
% 3.62/1.98  BG Simplification    : 0.02
% 3.62/1.98  Subsumption          : 0.07
% 3.62/1.98  Abstraction          : 0.02
% 3.62/1.98  MUC search           : 0.00
% 3.62/1.98  Cooper               : 0.00
% 3.62/1.98  Total                : 0.95
% 3.62/1.98  Index Insertion      : 0.00
% 3.62/1.98  Index Deletion       : 0.00
% 3.62/1.98  Index Matching       : 0.00
% 3.62/1.98  BG Taut test         : 0.00
%------------------------------------------------------------------------------