TSTP Solution File: ANA043-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA043-2 : 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 : n020.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 10:32:53 EDT 2023

% Result   : Unsatisfiable 5.87s 2.54s
% Output   : CNFRefutation 6.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   46 (  14 unt;  16 typ;   0 def)
%            Number of atoms       :   56 (   2 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   61 (  35   ~;  26   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  13   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   38 (;  38   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Oordered__idom > class_OrderedGroup_Olordered__ab__group__abs > class_OrderedGroup_Oab__semigroup__mult > c_times > v_l > v_k > c_HOL_Oabs > #nlpp > v_xa > v_x > v_h > v_f > v_c > t_b > c_0

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(c_times,type,
    c_times: ( $i * $i * $i ) > $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_Ring__and__Field_Opordered__semiring,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

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

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

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

tff(f_31,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file(unknown,unknown) ).

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

tff(f_36,axiom,
    ! [T_a,V_a] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
      | c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
    file(unknown,unknown) ).

tff(f_27,axiom,
    ! [V_U] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__idom(T)
      | class_Ring__and__Field_Opordered__semiring(T) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__idom(T)
      | class_OrderedGroup_Oab__semigroup__mult(T) ),
    file(unknown,unknown) ).

tff(f_41,axiom,
    ! [T_a,V_a,V_b,V_c] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
      | ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [T_a,V_a,V_b,V_c] :
      ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
      | ~ c_lessequals(V_a,V_b,T_a)
      | ~ c_lessequals(c_0,V_c,T_a)
      | c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [V_U] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b),
    file(unknown,unknown) ).

tff(c_6,plain,
    class_Ring__and__Field_Oordered__idom(t_b),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_20,plain,
    ! [T_17] :
      ( class_OrderedGroup_Olordered__ab__group__abs(T_17)
      | ~ class_Ring__and__Field_Oordered__idom(T_17) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_24,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(resolution,[status(thm)],[c_6,c_20]) ).

tff(c_8,plain,
    ! [V_a_4,T_a_3] :
      ( c_lessequals(c_0,c_HOL_Oabs(V_a_4,T_a_3),T_a_3)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_3) ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_2,plain,
    ! [V_U_1] : c_lessequals(c_HOL_Oabs(v_f(V_U_1),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U_1),t_b),t_b),t_b),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_16,plain,
    ! [T_14] :
      ( class_Ring__and__Field_Opordered__semiring(T_14)
      | ~ class_Ring__and__Field_Oordered__idom(T_14) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_25,plain,
    ! [T_18] :
      ( class_OrderedGroup_Oab__semigroup__mult(T_18)
      | ~ class_Ring__and__Field_Oordered__idom(T_18) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_29,plain,
    class_OrderedGroup_Oab__semigroup__mult(t_b),
    inference(resolution,[status(thm)],[c_6,c_25]) ).

tff(c_10,plain,
    ! [V_b_7,V_a_6,V_c_8,T_a_5] :
      ( ( c_times(V_b_7,c_times(V_a_6,V_c_8,T_a_5),T_a_5) = c_times(V_a_6,c_times(V_b_7,V_c_8,T_a_5),T_a_5) )
      | ~ class_OrderedGroup_Oab__semigroup__mult(T_a_5) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_89,plain,
    ! [V_c_26,V_a_27,T_a_28,V_b_29] :
      ( c_lessequals(c_times(V_c_26,V_a_27,T_a_28),c_times(V_c_26,V_b_29,T_a_28),T_a_28)
      | ~ c_lessequals(c_0,V_c_26,T_a_28)
      | ~ c_lessequals(V_a_27,V_b_29,T_a_28)
      | ~ class_Ring__and__Field_Opordered__semiring(T_a_28) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_863,plain,
    ! [V_a_51,V_c_55,V_a_52,V_b_53,T_a_54] :
      ( c_lessequals(c_times(V_a_52,V_a_51,T_a_54),c_times(V_b_53,c_times(V_a_52,V_c_55,T_a_54),T_a_54),T_a_54)
      | ~ c_lessequals(c_0,V_a_52,T_a_54)
      | ~ c_lessequals(V_a_51,c_times(V_b_53,V_c_55,T_a_54),T_a_54)
      | ~ class_Ring__and__Field_Opordered__semiring(T_a_54)
      | ~ class_OrderedGroup_Oab__semigroup__mult(T_a_54) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_89]) ).

tff(c_4,plain,
    ! [V_U_2] : ~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(V_U_2),v_xa(V_U_2)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U_2),v_xa(V_U_2))),t_b),t_b),c_times(V_U_2,c_times(c_HOL_Oabs(v_l(v_x(V_U_2),v_xa(V_U_2)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U_2),v_xa(V_U_2))),t_b),t_b),t_b),t_b),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_867,plain,
    ! [V_b_53] :
      ( ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(V_b_53),v_xa(V_b_53)),t_b),t_b)
      | ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(V_b_53),v_xa(V_b_53))),t_b),c_times(V_b_53,c_HOL_Oabs(v_h(v_k(v_x(V_b_53),v_xa(V_b_53))),t_b),t_b),t_b)
      | ~ class_Ring__and__Field_Opordered__semiring(t_b)
      | ~ class_OrderedGroup_Oab__semigroup__mult(t_b) ),
    inference(resolution,[status(thm)],[c_863,c_4]) ).

tff(c_942,plain,
    ! [V_b_53] :
      ( ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(V_b_53),v_xa(V_b_53)),t_b),t_b)
      | ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(V_b_53),v_xa(V_b_53))),t_b),c_times(V_b_53,c_HOL_Oabs(v_h(v_k(v_x(V_b_53),v_xa(V_b_53))),t_b),t_b),t_b)
      | ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_29,c_867]) ).

tff(c_2025,plain,
    ~ class_Ring__and__Field_Opordered__semiring(t_b),
    inference(splitLeft,[status(thm)],[c_942]) ).

tff(c_2028,plain,
    ~ class_Ring__and__Field_Oordered__idom(t_b),
    inference(resolution,[status(thm)],[c_16,c_2025]) ).

tff(c_2032,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2028]) ).

tff(c_2035,plain,
    ! [V_b_68] :
      ( ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(V_b_68),v_xa(V_b_68)),t_b),t_b)
      | ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(V_b_68),v_xa(V_b_68))),t_b),c_times(V_b_68,c_HOL_Oabs(v_h(v_k(v_x(V_b_68),v_xa(V_b_68))),t_b),t_b),t_b) ),
    inference(splitRight,[status(thm)],[c_942]) ).

tff(c_2040,plain,
    ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b),
    inference(resolution,[status(thm)],[c_2,c_2035]) ).

tff(c_2043,plain,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(resolution,[status(thm)],[c_8,c_2040]) ).

tff(c_2047,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_2043]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ANA043-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % 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
% 0.19/0.36  % Computer : n020.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit : 300
% 0.19/0.36  % WCLimit  : 300
% 0.19/0.36  % DateTime : Thu Aug  3 15:29:52 EDT 2023
% 0.19/0.36  % CPUTime  : 
% 5.87/2.54  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.87/2.55  
% 5.87/2.55  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.31/2.58  
% 6.31/2.58  Inference rules
% 6.31/2.58  ----------------------
% 6.31/2.58  #Ref     : 0
% 6.31/2.58  #Sup     : 634
% 6.31/2.58  #Fact    : 0
% 6.31/2.58  #Define  : 0
% 6.31/2.58  #Split   : 1
% 6.31/2.58  #Chain   : 0
% 6.31/2.58  #Close   : 0
% 6.31/2.58  
% 6.31/2.58  Ordering : KBO
% 6.31/2.58  
% 6.31/2.58  Simplification rules
% 6.31/2.58  ----------------------
% 6.31/2.58  #Subsume      : 95
% 6.31/2.58  #Demod        : 3
% 6.31/2.58  #Tautology    : 40
% 6.31/2.58  #SimpNegUnit  : 0
% 6.31/2.58  #BackRed      : 0
% 6.31/2.58  
% 6.31/2.58  #Partial instantiations: 0
% 6.31/2.58  #Strategies tried      : 1
% 6.31/2.58  
% 6.31/2.58  Timing (in seconds)
% 6.31/2.58  ----------------------
% 6.31/2.58  Preprocessing        : 0.49
% 6.31/2.58  Parsing              : 0.26
% 6.31/2.58  CNF conversion       : 0.03
% 6.31/2.59  Main loop            : 0.96
% 6.31/2.59  Inferencing          : 0.46
% 6.31/2.59  Reduction            : 0.18
% 6.31/2.59  Demodulation         : 0.13
% 6.31/2.59  BG Simplification    : 0.09
% 6.31/2.59  Subsumption          : 0.16
% 6.31/2.59  Abstraction          : 0.08
% 6.31/2.59  MUC search           : 0.00
% 6.31/2.59  Cooper               : 0.00
% 6.31/2.59  Total                : 1.50
% 6.31/2.59  Index Insertion      : 0.00
% 6.31/2.59  Index Deletion       : 0.00
% 6.31/2.59  Index Matching       : 0.00
% 6.31/2.59  BG Taut test         : 0.00
%------------------------------------------------------------------------------