TSTP Solution File: ANA025-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA025-2 : 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 : n022.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 5.29s 2.22s
% Output   : CNFRefutation 5.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   89 (  26 unt;  16 typ;   0 def)
%            Number of atoms       :  169 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  195 (  99   ~;  96   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  13   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   97 (;  97   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Olordered__ab__group__abs > class_LOrder_Ojoin__semilorder > c_minus > c_Orderings_Omax > c_HOL_Oabs > #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(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

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

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(c_less,type,
    c_less: ( $i * $i * $i ) > $o ).

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

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

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

tff(f_92,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__idom(T)
      | class_Orderings_Olinorder(T) ),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ! [T_a,V_y,V_x] :
      ( ~ class_Orderings_Olinorder(T_a)
      | c_less(V_y,V_x,T_a)
      | c_lessequals(V_x,V_y,T_a) ),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__idom(T)
      | class_OrderedGroup_Olordered__ab__group__abs(T) ),
    file(unknown,unknown) ).

tff(f_81,axiom,
    ! [T] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
      | class_LOrder_Ojoin__semilorder(T) ),
    file(unknown,unknown) ).

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

tff(f_67,axiom,
    ! [T_a,V_x,V_y] :
      ( ~ class_Orderings_Oorder(T_a)
      | ~ c_less(V_x,V_y,T_a)
      | c_lessequals(V_x,V_y,T_a) ),
    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_59,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(f_48,axiom,
    ! [T_b,V_y,V_z,V_x] :
      ( ~ class_Orderings_Olinorder(T_b)
      | ~ c_lessequals(V_y,V_z,T_b)
      | ~ c_lessequals(V_x,V_z,T_b)
      | c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    file(unknown,unknown) ).

tff(c_24,plain,
    class_Ring__and__Field_Oordered__idom(t_b),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_36,plain,
    ! [T_24] :
      ( class_Orderings_Olinorder(T_24)
      | ~ class_Ring__and__Field_Oordered__idom(T_24) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_40,plain,
    class_Orderings_Olinorder(t_b),
    inference(resolution,[status(thm)],[c_24,c_36]) ).

tff(c_42,plain,
    ! [V_x_27,V_y_28,T_a_29] :
      ( c_lessequals(V_x_27,V_y_28,T_a_29)
      | c_less(V_y_28,V_x_27,T_a_29)
      | ~ class_Orderings_Olinorder(T_a_29) ),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_12,plain,
    ~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_45,plain,
    ( c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
    | ~ class_Orderings_Olinorder(t_b) ),
    inference(resolution,[status(thm)],[c_42,c_12]) ).

tff(c_48,plain,
    c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_45]) ).

tff(c_25,plain,
    ! [T_21] :
      ( class_OrderedGroup_Olordered__ab__group__abs(T_21)
      | ~ class_Ring__and__Field_Oordered__idom(T_21) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

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

tff(c_30,plain,
    ! [T_22] :
      ( class_LOrder_Ojoin__semilorder(T_22)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_22) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_34,plain,
    class_LOrder_Ojoin__semilorder(t_b),
    inference(resolution,[status(thm)],[c_29,c_30]) ).

tff(c_16,plain,
    ! [T_17] :
      ( class_Orderings_Oorder(T_17)
      | ~ class_LOrder_Ojoin__semilorder(T_17) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_49,plain,
    ! [V_x_30,V_y_31,T_a_32] :
      ( c_lessequals(V_x_30,V_y_31,T_a_32)
      | ~ c_less(V_x_30,V_y_31,T_a_32)
      | ~ class_Orderings_Oorder(T_a_32) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_53,plain,
    ( ~ c_less(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | ~ class_Orderings_Oorder(t_b) ),
    inference(resolution,[status(thm)],[c_49,c_12]) ).

tff(c_54,plain,
    ~ class_Orderings_Oorder(t_b),
    inference(splitLeft,[status(thm)],[c_53]) ).

tff(c_57,plain,
    ~ class_LOrder_Ojoin__semilorder(t_b),
    inference(resolution,[status(thm)],[c_16,c_54]) ).

tff(c_61,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_57]) ).

tff(c_63,plain,
    class_Orderings_Oorder(t_b),
    inference(splitRight,[status(thm)],[c_53]) ).

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_4,plain,
    ! [V_x_5,V_y_4,T_a_3] :
      ( c_lessequals(V_x_5,V_y_4,T_a_3)
      | c_less(V_y_4,V_x_5,T_a_3)
      | ~ class_Orderings_Olinorder(T_a_3) ),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_10,plain,
    ! [V_x_15,V_y_16,T_a_14] :
      ( c_lessequals(V_x_15,V_y_16,T_a_14)
      | ~ c_less(V_x_15,V_y_16,T_a_14)
      | ~ class_Orderings_Oorder(T_a_14) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_64,plain,
    ! [V_x_33,V_z_34,T_a_35,V_y_36] :
      ( c_lessequals(V_x_33,V_z_34,T_a_35)
      | ~ c_lessequals(V_x_33,V_y_36,T_a_35)
      | ~ c_lessequals(V_y_36,V_z_34,T_a_35)
      | ~ class_Orderings_Oorder(T_a_35) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_74,plain,
    ! [V_x_37,V_z_38,T_a_39,V_y_40] :
      ( c_lessequals(V_x_37,V_z_38,T_a_39)
      | ~ c_lessequals(V_y_40,V_z_38,T_a_39)
      | ~ c_less(V_x_37,V_y_40,T_a_39)
      | ~ class_Orderings_Oorder(T_a_39) ),
    inference(resolution,[status(thm)],[c_10,c_64]) ).

tff(c_186,plain,
    ! [V_x_66,V_y_67,T_a_68,V_x_69] :
      ( c_lessequals(V_x_66,V_y_67,T_a_68)
      | ~ c_less(V_x_66,V_x_69,T_a_68)
      | ~ class_Orderings_Oorder(T_a_68)
      | c_less(V_y_67,V_x_69,T_a_68)
      | ~ class_Orderings_Olinorder(T_a_68) ),
    inference(resolution,[status(thm)],[c_4,c_74]) ).

tff(c_190,plain,
    ! [V_y_67] :
      ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),V_y_67,t_b)
      | ~ class_Orderings_Oorder(t_b)
      | c_less(V_y_67,c_0,t_b)
      | ~ class_Orderings_Olinorder(t_b) ),
    inference(resolution,[status(thm)],[c_48,c_186]) ).

tff(c_195,plain,
    ! [V_y_70] :
      ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),V_y_70,t_b)
      | c_less(V_y_70,c_0,t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_63,c_190]) ).

tff(c_8,plain,
    ! [V_x_13,V_z_12,T_a_10,V_y_11] :
      ( c_lessequals(V_x_13,V_z_12,T_a_10)
      | ~ c_lessequals(V_x_13,V_y_11,T_a_10)
      | ~ c_lessequals(V_y_11,V_z_12,T_a_10)
      | ~ class_Orderings_Oorder(T_a_10) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_201,plain,
    ! [V_z_12,V_y_70] :
      ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),V_z_12,t_b)
      | ~ c_lessequals(V_y_70,V_z_12,t_b)
      | ~ class_Orderings_Oorder(t_b)
      | c_less(V_y_70,c_0,t_b) ),
    inference(resolution,[status(thm)],[c_195,c_8]) ).

tff(c_639,plain,
    ! [V_z_99,V_y_100] :
      ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),V_z_99,t_b)
      | ~ c_lessequals(V_y_100,V_z_99,t_b)
      | c_less(V_y_100,c_0,t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_63,c_201]) ).

tff(c_670,plain,
    ! [V_a_2] :
      ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(V_a_2,t_b),t_b)
      | c_less(c_0,c_0,t_b)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(resolution,[status(thm)],[c_2,c_639]) ).

tff(c_698,plain,
    ! [V_a_2] :
      ( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(V_a_2,t_b),t_b)
      | c_less(c_0,c_0,t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_29,c_670]) ).

tff(c_699,plain,
    c_less(c_0,c_0,t_b),
    inference(splitLeft,[status(thm)],[c_698]) ).

tff(c_81,plain,
    ! [V_x_37,V_y_16,T_a_14,V_x_15] :
      ( c_lessequals(V_x_37,V_y_16,T_a_14)
      | ~ c_less(V_x_37,V_x_15,T_a_14)
      | ~ c_less(V_x_15,V_y_16,T_a_14)
      | ~ class_Orderings_Oorder(T_a_14) ),
    inference(resolution,[status(thm)],[c_10,c_74]) ).

tff(c_705,plain,
    ! [V_y_16] :
      ( c_lessequals(c_0,V_y_16,t_b)
      | ~ c_less(c_0,V_y_16,t_b)
      | ~ class_Orderings_Oorder(t_b) ),
    inference(resolution,[status(thm)],[c_699,c_81]) ).

tff(c_835,plain,
    ! [V_y_108] :
      ( c_lessequals(c_0,V_y_108,t_b)
      | ~ c_less(c_0,V_y_108,t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_63,c_705]) ).

tff(c_845,plain,
    ! [V_z_12,V_y_108] :
      ( c_lessequals(c_0,V_z_12,t_b)
      | ~ c_lessequals(V_y_108,V_z_12,t_b)
      | ~ class_Orderings_Oorder(t_b)
      | ~ c_less(c_0,V_y_108,t_b) ),
    inference(resolution,[status(thm)],[c_835,c_8]) ).

tff(c_1618,plain,
    ! [V_z_131,V_y_132] :
      ( c_lessequals(c_0,V_z_131,t_b)
      | ~ c_lessequals(V_y_132,V_z_131,t_b)
      | ~ c_less(c_0,V_y_132,t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_63,c_845]) ).

tff(c_1671,plain,
    ! [V_a_2] :
      ( c_lessequals(c_0,c_HOL_Oabs(V_a_2,t_b),t_b)
      | ~ c_less(c_0,c_0,t_b)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(resolution,[status(thm)],[c_2,c_1618]) ).

tff(c_1725,plain,
    ! [V_a_133] : c_lessequals(c_0,c_HOL_Oabs(V_a_133,t_b),t_b),
    inference(demodulation,[status(thm),theory(equality)],[c_29,c_699,c_1671]) ).

tff(c_71,plain,
    ! [V_x_15,V_z_34,T_a_14,V_y_16] :
      ( c_lessequals(V_x_15,V_z_34,T_a_14)
      | ~ c_lessequals(V_y_16,V_z_34,T_a_14)
      | ~ c_less(V_x_15,V_y_16,T_a_14)
      | ~ class_Orderings_Oorder(T_a_14) ),
    inference(resolution,[status(thm)],[c_10,c_64]) ).

tff(c_1739,plain,
    ! [V_x_15,V_a_133] :
      ( c_lessequals(V_x_15,c_HOL_Oabs(V_a_133,t_b),t_b)
      | ~ c_less(V_x_15,c_0,t_b)
      | ~ class_Orderings_Oorder(t_b) ),
    inference(resolution,[status(thm)],[c_1725,c_71]) ).

tff(c_1760,plain,
    ! [V_x_15,V_a_133] :
      ( c_lessequals(V_x_15,c_HOL_Oabs(V_a_133,t_b),t_b)
      | ~ c_less(V_x_15,c_0,t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_63,c_1739]) ).

tff(c_83,plain,
    ! [V_x_37,V_a_2,T_a_1] :
      ( c_lessequals(V_x_37,c_HOL_Oabs(V_a_2,T_a_1),T_a_1)
      | ~ c_less(V_x_37,c_0,T_a_1)
      | ~ class_Orderings_Oorder(T_a_1)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_1) ),
    inference(resolution,[status(thm)],[c_2,c_74]) ).

tff(c_6,plain,
    ! [V_x_9,V_y_7,T_b_6,V_z_8] :
      ( c_lessequals(c_Orderings_Omax(V_x_9,V_y_7,T_b_6),V_z_8,T_b_6)
      | ~ c_lessequals(V_x_9,V_z_8,T_b_6)
      | ~ c_lessequals(V_y_7,V_z_8,T_b_6)
      | ~ class_Orderings_Olinorder(T_b_6) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_14,plain,
    ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_137,plain,
    ( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
    | ~ class_Orderings_Olinorder(t_b) ),
    inference(resolution,[status(thm)],[c_6,c_14]) ).

tff(c_149,plain,
    ( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_137]) ).

tff(c_1211,plain,
    ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    inference(splitLeft,[status(thm)],[c_149]) ).

tff(c_1238,plain,
    ( ~ c_less(c_0,c_0,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(resolution,[status(thm)],[c_83,c_1211]) ).

tff(c_1269,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29,c_63,c_699,c_1238]) ).

tff(c_1270,plain,
    ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    inference(splitRight,[status(thm)],[c_149]) ).

tff(c_1899,plain,
    ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
    inference(resolution,[status(thm)],[c_1760,c_1270]) ).

tff(c_1939,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_48,c_1899]) ).

tff(c_1941,plain,
    ~ c_less(c_0,c_0,t_b),
    inference(splitRight,[status(thm)],[c_698]) ).

tff(c_156,plain,
    ! [V_x_59,V_z_60,T_a_61,V_y_62] :
      ( c_lessequals(V_x_59,V_z_60,T_a_61)
      | ~ c_lessequals(V_y_62,V_z_60,T_a_61)
      | ~ class_Orderings_Oorder(T_a_61)
      | c_less(V_y_62,V_x_59,T_a_61)
      | ~ class_Orderings_Olinorder(T_a_61) ),
    inference(resolution,[status(thm)],[c_4,c_64]) ).

tff(c_176,plain,
    ! [V_x_59,V_a_2,T_a_1] :
      ( c_lessequals(V_x_59,c_HOL_Oabs(V_a_2,T_a_1),T_a_1)
      | ~ class_Orderings_Oorder(T_a_1)
      | c_less(c_0,V_x_59,T_a_1)
      | ~ class_Orderings_Olinorder(T_a_1)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_1) ),
    inference(resolution,[status(thm)],[c_2,c_156]) ).

tff(c_1940,plain,
    ! [V_a_2] : c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(V_a_2,t_b),t_b),
    inference(splitRight,[status(thm)],[c_698]) ).

tff(c_2849,plain,
    ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    inference(demodulation,[status(thm),theory(equality)],[c_1940,c_149]) ).

tff(c_2858,plain,
    ( ~ class_Orderings_Oorder(t_b)
    | c_less(c_0,c_0,t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(resolution,[status(thm)],[c_176,c_2849]) ).

tff(c_2880,plain,
    c_less(c_0,c_0,t_b),
    inference(demodulation,[status(thm),theory(equality)],[c_29,c_40,c_63,c_2858]) ).

tff(c_2882,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1941,c_2880]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ANA025-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 15:28:03 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 5.29/2.22  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.29/2.23  
% 5.29/2.23  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.29/2.28  
% 5.29/2.28  Inference rules
% 5.29/2.28  ----------------------
% 5.29/2.28  #Ref     : 0
% 5.29/2.28  #Sup     : 571
% 5.29/2.28  #Fact    : 2
% 5.29/2.28  #Define  : 0
% 5.29/2.28  #Split   : 4
% 5.29/2.28  #Chain   : 0
% 5.29/2.28  #Close   : 0
% 5.29/2.28  
% 5.29/2.28  Ordering : KBO
% 5.29/2.28  
% 5.29/2.28  Simplification rules
% 5.29/2.28  ----------------------
% 5.29/2.28  #Subsume      : 105
% 5.29/2.28  #Demod        : 700
% 5.29/2.28  #Tautology    : 94
% 5.29/2.28  #SimpNegUnit  : 4
% 5.29/2.28  #BackRed      : 0
% 5.29/2.28  
% 5.29/2.28  #Partial instantiations: 0
% 5.29/2.28  #Strategies tried      : 1
% 5.29/2.28  
% 5.29/2.28  Timing (in seconds)
% 5.29/2.28  ----------------------
% 5.29/2.28  Preprocessing        : 0.42
% 5.29/2.28  Parsing              : 0.24
% 5.29/2.28  CNF conversion       : 0.02
% 5.29/2.28  Main loop            : 0.78
% 5.29/2.28  Inferencing          : 0.29
% 5.29/2.28  Reduction            : 0.23
% 5.29/2.28  Demodulation         : 0.16
% 5.29/2.28  BG Simplification    : 0.02
% 5.29/2.28  Subsumption          : 0.17
% 5.29/2.28  Abstraction          : 0.03
% 5.29/2.28  MUC search           : 0.00
% 5.29/2.28  Cooper               : 0.00
% 5.29/2.28  Total                : 1.27
% 5.29/2.28  Index Insertion      : 0.00
% 5.29/2.28  Index Deletion       : 0.00
% 5.29/2.28  Index Matching       : 0.00
% 5.29/2.28  BG Taut test         : 0.00
%------------------------------------------------------------------------------