TSTP Solution File: ANA015-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA015-2 : 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 : 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 : Tue Aug 22 10:32:47 EDT 2023

% Result   : Unsatisfiable 49.13s 15.92s
% Output   : CNFRefutation 49.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   68 (  25 unt;  17 typ;   0 def)
%            Number of atoms       :   90 (   4 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   96 (  57   ~;  39   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  13   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   53 (;  53   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Ofield > class_OrderedGroup_Osemigroup__mult > class_OrderedGroup_Olordered__ab__group__abs > c_times > c_HOL_Oinverse > c_HOL_Oabs > #nlpp > v_x > v_g > v_f > v_d > v_c > t_a > c_0

%Foreground sorts:

%Background operators:

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

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

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

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

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_Ofield,type,
    class_Ring__and__Field_Ofield: $i > $o ).

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_Osemigroup__mult,type,
    class_OrderedGroup_Osemigroup__mult: $i > $o ).

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

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

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

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(f_53,axiom,
    ! [V_U] : c_lessequals(c_HOL_Oabs(v_g(V_U),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
    file(unknown,unknown) ).

tff(f_82,axiom,
    class_Ring__and__Field_Oordered__field(t_a),
    file(unknown,unknown) ).

tff(f_76,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_Ring__and__Field_Opordered__semiring(T) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_Ring__and__Field_Oordered__idom(T) ),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [T_a,V_a,V_b] :
      ( ~ class_Ring__and__Field_Oordered__idom(T_a)
      | ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [V_U] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U)),t_a),t_a),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),
    file(unknown,unknown) ).

tff(f_51,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_81,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_OrderedGroup_Olordered__ab__group__abs(T) ),
    file(unknown,unknown) ).

tff(f_30,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_66,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_Ring__and__Field_Ofield(T) ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Ofield(T)
      | class_OrderedGroup_Osemigroup__mult(T) ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    ! [T_a,V_a,V_b,V_c] :
      ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
      | ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
    file(unknown,unknown) ).

tff(c_10,plain,
    ! [V_U_14] : c_lessequals(c_HOL_Oabs(v_g(V_U_14),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U_14),t_a),t_a),t_a),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_24,plain,
    class_Ring__and__Field_Oordered__field(t_a),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_20,plain,
    ! [T_19] :
      ( class_Ring__and__Field_Opordered__semiring(T_19)
      | ~ class_Ring__and__Field_Oordered__field(T_19) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_18,plain,
    ! [T_18] :
      ( class_Ring__and__Field_Oordered__idom(T_18)
      | ~ class_Ring__and__Field_Oordered__field(T_18) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_6,plain,
    ! [V_a_8,T_a_7,V_b_9] :
      ( ( c_times(c_HOL_Oabs(V_a_8,T_a_7),c_HOL_Oabs(V_b_9,T_a_7),T_a_7) = c_HOL_Oabs(c_times(V_a_8,V_b_9,T_a_7),T_a_7) )
      | ~ class_Ring__and__Field_Oordered__idom(T_a_7) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_71,plain,
    ! [V_U_36] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U_36)),t_a),t_a),c_times(V_U_36,c_HOL_Oabs(v_f(v_x(V_U_36)),t_a),t_a),t_a),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_75,plain,
    ! [V_a_8] :
      ( ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_HOL_Oabs(V_a_8,t_a))),t_a),t_a),c_HOL_Oabs(c_times(V_a_8,v_f(v_x(c_HOL_Oabs(V_a_8,t_a))),t_a),t_a),t_a)
      | ~ class_Ring__and__Field_Oordered__idom(t_a) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_71]) ).

tff(c_183,plain,
    ~ class_Ring__and__Field_Oordered__idom(t_a),
    inference(splitLeft,[status(thm)],[c_75]) ).

tff(c_261,plain,
    ~ class_Ring__and__Field_Oordered__field(t_a),
    inference(resolution,[status(thm)],[c_18,c_183]) ).

tff(c_265,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_261]) ).

tff(c_267,plain,
    class_Ring__and__Field_Oordered__idom(t_a),
    inference(splitRight,[status(thm)],[c_75]) ).

tff(c_82,plain,
    ! [V_c_37,V_a_38,T_a_39,V_b_40] :
      ( c_lessequals(c_times(V_c_37,V_a_38,T_a_39),c_times(V_c_37,V_b_40,T_a_39),T_a_39)
      | ~ c_lessequals(c_0,V_c_37,T_a_39)
      | ~ c_lessequals(V_a_38,V_b_40,T_a_39)
      | ~ class_Ring__and__Field_Opordered__semiring(T_a_39) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_891,plain,
    ! [V_a_84,V_b_85,T_a_86,V_b_87] :
      ( c_lessequals(c_HOL_Oabs(c_times(V_a_84,V_b_85,T_a_86),T_a_86),c_times(c_HOL_Oabs(V_a_84,T_a_86),V_b_87,T_a_86),T_a_86)
      | ~ c_lessequals(c_0,c_HOL_Oabs(V_a_84,T_a_86),T_a_86)
      | ~ c_lessequals(c_HOL_Oabs(V_b_85,T_a_86),V_b_87,T_a_86)
      | ~ class_Ring__and__Field_Opordered__semiring(T_a_86)
      | ~ class_Ring__and__Field_Oordered__idom(T_a_86) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_82]) ).

tff(c_12,plain,
    ! [V_U_15] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U_15)),t_a),t_a),c_times(V_U_15,c_HOL_Oabs(v_f(v_x(V_U_15)),t_a),t_a),t_a),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_899,plain,
    ( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
    | ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
    | ~ class_Ring__and__Field_Opordered__semiring(t_a)
    | ~ class_Ring__and__Field_Oordered__idom(t_a) ),
    inference(resolution,[status(thm)],[c_891,c_12]) ).

tff(c_951,plain,
    ( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
    | ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
    | ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_267,c_899]) ).

tff(c_1031,plain,
    ~ class_Ring__and__Field_Opordered__semiring(t_a),
    inference(splitLeft,[status(thm)],[c_951]) ).

tff(c_1034,plain,
    ~ class_Ring__and__Field_Oordered__field(t_a),
    inference(resolution,[status(thm)],[c_20,c_1031]) ).

tff(c_1038,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_1034]) ).

tff(c_1040,plain,
    class_Ring__and__Field_Opordered__semiring(t_a),
    inference(splitRight,[status(thm)],[c_951]) ).

tff(c_25,plain,
    ! [T_21] :
      ( class_OrderedGroup_Olordered__ab__group__abs(T_21)
      | ~ class_Ring__and__Field_Oordered__field(T_21) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_29,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_a),
    inference(resolution,[status(thm)],[c_24,c_25]) ).

tff(c_2,plain,
    ! [V_a_2,T_a_1] :
      ( c_lessequals(c_0,c_HOL_Oabs(V_a_2,T_a_1),T_a_1)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_1) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_1039,plain,
    ( ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
    | ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
    inference(splitRight,[status(thm)],[c_951]) ).

tff(c_1120,plain,
    ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a),
    inference(splitLeft,[status(thm)],[c_1039]) ).

tff(c_1123,plain,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
    inference(resolution,[status(thm)],[c_2,c_1120]) ).

tff(c_1127,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29,c_1123]) ).

tff(c_1129,plain,
    c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a),
    inference(splitRight,[status(thm)],[c_1039]) ).

tff(c_31,plain,
    ! [T_23] :
      ( class_Ring__and__Field_Ofield(T_23)
      | ~ class_Ring__and__Field_Oordered__field(T_23) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_35,plain,
    class_Ring__and__Field_Ofield(t_a),
    inference(resolution,[status(thm)],[c_24,c_31]) ).

tff(c_37,plain,
    ! [T_25] :
      ( class_OrderedGroup_Osemigroup__mult(T_25)
      | ~ class_Ring__and__Field_Ofield(T_25) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_41,plain,
    class_OrderedGroup_Osemigroup__mult(t_a),
    inference(resolution,[status(thm)],[c_35,c_37]) ).

tff(c_4,plain,
    ! [V_a_4,V_b_5,T_a_3,V_c_6] :
      ( ( c_times(c_times(V_a_4,V_b_5,T_a_3),V_c_6,T_a_3) = c_times(V_a_4,c_times(V_b_5,V_c_6,T_a_3),T_a_3) )
      | ~ class_OrderedGroup_Osemigroup__mult(T_a_3) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_79,plain,
    ! [V_a_4,V_b_5] :
      ( ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),c_times(V_a_4,c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),t_a),t_a)
      | ~ class_OrderedGroup_Osemigroup__mult(t_a) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_71]) ).

tff(c_81,plain,
    ! [V_a_4,V_b_5] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),c_times(V_a_4,c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),t_a),t_a),
    inference(demodulation,[status(thm),theory(equality)],[c_41,c_79]) ).

tff(c_895,plain,
    ! [V_b_5] :
      ( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
      | ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),t_a),t_a)
      | ~ class_Ring__and__Field_Opordered__semiring(t_a)
      | ~ class_Ring__and__Field_Oordered__idom(t_a) ),
    inference(resolution,[status(thm)],[c_891,c_81]) ).

tff(c_948,plain,
    ! [V_b_5] :
      ( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
      | ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),t_a),t_a)
      | ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_267,c_895]) ).

tff(c_101716,plain,
    ! [V_b_596] : ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_596,t_a))),t_a),c_times(V_b_596,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_596,t_a))),t_a),t_a),t_a),
    inference(demodulation,[status(thm),theory(equality)],[c_1040,c_1129,c_948]) ).

tff(c_102135,plain,
    $false,
    inference(resolution,[status(thm)],[c_10,c_101716]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ANA015-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14  % 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
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 15:32:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 49.13/15.92  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.13/15.93  
% 49.13/15.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.30/15.96  
% 49.30/15.96  Inference rules
% 49.30/15.96  ----------------------
% 49.30/15.96  #Ref     : 0
% 49.30/15.96  #Sup     : 23335
% 49.30/15.96  #Fact    : 0
% 49.30/15.96  #Define  : 0
% 49.30/15.96  #Split   : 3
% 49.30/15.96  #Chain   : 0
% 49.30/15.96  #Close   : 0
% 49.30/15.96  
% 49.30/15.96  Ordering : KBO
% 49.30/15.96  
% 49.30/15.96  Simplification rules
% 49.30/15.96  ----------------------
% 49.30/15.96  #Subsume      : 337
% 49.30/15.96  #Demod        : 42217
% 49.30/15.96  #Tautology    : 172
% 49.30/15.96  #SimpNegUnit  : 0
% 49.30/15.96  #BackRed      : 0
% 49.30/15.96  
% 49.30/15.96  #Partial instantiations: 0
% 49.30/15.96  #Strategies tried      : 1
% 49.30/15.96  
% 49.30/15.96  Timing (in seconds)
% 49.30/15.96  ----------------------
% 49.30/15.96  Preprocessing        : 0.44
% 49.30/15.96  Parsing              : 0.24
% 49.30/15.96  CNF conversion       : 0.02
% 49.30/15.96  Main loop            : 14.47
% 49.30/15.96  Inferencing          : 7.22
% 49.30/15.96  Reduction            : 2.75
% 49.30/15.96  Demodulation         : 2.25
% 49.30/15.96  BG Simplification    : 0.84
% 49.30/15.96  Subsumption          : 3.12
% 49.30/15.96  Abstraction          : 0.90
% 49.30/15.96  MUC search           : 0.00
% 49.30/15.96  Cooper               : 0.00
% 49.30/15.96  Total                : 14.97
% 49.30/15.96  Index Insertion      : 0.00
% 49.30/15.96  Index Deletion       : 0.00
% 49.30/15.97  Index Matching       : 0.00
% 49.30/15.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------