TSTP Solution File: SET865-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET865-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n017.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 10:57:15 EDT 2023

% Result   : Unsatisfiable 2.74s 1.70s
% Output   : CNFRefutation 2.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   35 (   9 unt;  10 typ;   0 def)
%            Number of atoms       :   50 (   9 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   53 (  28   ~;  25   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :   40 (;  40   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Zorn_Omaxchain > c_Zorn_Ochain > c_Zorn_OHausdorff__1 > c_Union > #nlpp > v_x > tc_set > v_S > t_a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(c_Zorn_OHausdorff__1,type,
    c_Zorn_OHausdorff__1: ( $i * $i ) > $i ).

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

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

tff(f_56,axiom,
    ! [V_S,T_a] : c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ! [V_S,T_a] : c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [V_c,V_A,T_a,V_B] :
      ( ~ c_in(V_c,V_A,T_a)
      | ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | c_in(V_c,V_B,T_a) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [V_U] :
      ( c_in(c_Union(V_U,t_a),v_S,tc_set(t_a))
      | ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
    file(unknown,unknown) ).

tff(f_46,axiom,
    ! [V_U] :
      ( ( V_U != v_x(V_U) )
      | ~ c_in(V_U,v_S,tc_set(t_a)) ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    ! [V_U] :
      ( c_in(v_x(V_U),v_S,tc_set(t_a))
      | ~ c_in(V_U,v_S,tc_set(t_a)) ),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [V_U] :
      ( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
      | ~ c_in(V_U,v_S,tc_set(t_a)) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [V_u,V_S,T_a,V_c] :
      ( ~ c_in(V_u,V_S,tc_set(T_a))
      | ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
      | ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
      | ( c_Union(V_c,T_a) = V_u ) ),
    file(unknown,unknown) ).

tff(c_12,plain,
    ! [V_S_9,T_a_10] : c_in(c_Zorn_OHausdorff__1(V_S_9,T_a_10),c_Zorn_Omaxchain(V_S_9,T_a_10),tc_set(tc_set(T_a_10))),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_16,plain,
    ! [V_S_15,T_a_16] : c_lessequals(c_Zorn_Omaxchain(V_S_15,T_a_16),c_Zorn_Ochain(V_S_15,T_a_16),tc_set(tc_set(tc_set(T_a_16)))),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_32,plain,
    ! [V_c_26,V_B_27,T_a_28,V_A_29] :
      ( c_in(V_c_26,V_B_27,T_a_28)
      | ~ c_lessequals(V_A_29,V_B_27,tc_set(T_a_28))
      | ~ c_in(V_c_26,V_A_29,T_a_28) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_44,plain,
    ! [V_c_33,V_S_34,T_a_35] :
      ( c_in(V_c_33,c_Zorn_Ochain(V_S_34,T_a_35),tc_set(tc_set(T_a_35)))
      | ~ c_in(V_c_33,c_Zorn_Omaxchain(V_S_34,T_a_35),tc_set(tc_set(T_a_35))) ),
    inference(resolution,[status(thm)],[c_16,c_32]) ).

tff(c_49,plain,
    ! [V_S_36,T_a_37] : c_in(c_Zorn_OHausdorff__1(V_S_36,T_a_37),c_Zorn_Ochain(V_S_36,T_a_37),tc_set(tc_set(T_a_37))),
    inference(resolution,[status(thm)],[c_12,c_44]) ).

tff(c_2,plain,
    ! [V_U_1] :
      ( ~ c_in(V_U_1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
      | c_in(c_Union(V_U_1,t_a),v_S,tc_set(t_a)) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_54,plain,
    c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
    inference(resolution,[status(thm)],[c_49,c_2]) ).

tff(c_8,plain,
    ! [V_U_4] :
      ( ~ c_in(V_U_4,v_S,tc_set(t_a))
      | ( v_x(V_U_4) != V_U_4 ) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_65,plain,
    v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) != c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),
    inference(resolution,[status(thm)],[c_54,c_8]) ).

tff(c_4,plain,
    ! [V_U_2] :
      ( ~ c_in(V_U_2,v_S,tc_set(t_a))
      | c_in(v_x(V_U_2),v_S,tc_set(t_a)) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_6,plain,
    ! [V_U_3] :
      ( ~ c_in(V_U_3,v_S,tc_set(t_a))
      | c_lessequals(V_U_3,v_x(V_U_3),tc_set(t_a)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_66,plain,
    ! [V_c_38,T_a_39,V_u_40,V_S_41] :
      ( ( c_Union(V_c_38,T_a_39) = V_u_40 )
      | ~ c_lessequals(c_Union(V_c_38,T_a_39),V_u_40,tc_set(T_a_39))
      | ~ c_in(V_c_38,c_Zorn_Omaxchain(V_S_41,T_a_39),tc_set(tc_set(T_a_39)))
      | ~ c_in(V_u_40,V_S_41,tc_set(T_a_39)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_73,plain,
    ! [V_c_45,V_S_46] :
      ( ( v_x(c_Union(V_c_45,t_a)) = c_Union(V_c_45,t_a) )
      | ~ c_in(V_c_45,c_Zorn_Omaxchain(V_S_46,t_a),tc_set(tc_set(t_a)))
      | ~ c_in(v_x(c_Union(V_c_45,t_a)),V_S_46,tc_set(t_a))
      | ~ c_in(c_Union(V_c_45,t_a),v_S,tc_set(t_a)) ),
    inference(resolution,[status(thm)],[c_6,c_66]) ).

tff(c_79,plain,
    ! [V_c_47] :
      ( ( v_x(c_Union(V_c_47,t_a)) = c_Union(V_c_47,t_a) )
      | ~ c_in(V_c_47,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
      | ~ c_in(c_Union(V_c_47,t_a),v_S,tc_set(t_a)) ),
    inference(resolution,[status(thm)],[c_4,c_73]) ).

tff(c_83,plain,
    ( ( v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) = c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) )
    | ~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) ),
    inference(resolution,[status(thm)],[c_12,c_79]) ).

tff(c_86,plain,
    v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) = c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_83]) ).

tff(c_88,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_65,c_86]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET865-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % 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 15:36:36 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 2.74/1.70  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/1.71  
% 2.84/1.71  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.99/1.75  
% 2.99/1.75  Inference rules
% 2.99/1.75  ----------------------
% 2.99/1.75  #Ref     : 0
% 2.99/1.75  #Sup     : 13
% 2.99/1.75  #Fact    : 0
% 2.99/1.75  #Define  : 0
% 2.99/1.75  #Split   : 0
% 2.99/1.75  #Chain   : 0
% 2.99/1.75  #Close   : 0
% 2.99/1.75  
% 2.99/1.75  Ordering : KBO
% 2.99/1.75  
% 2.99/1.75  Simplification rules
% 2.99/1.75  ----------------------
% 2.99/1.75  #Subsume      : 0
% 2.99/1.75  #Demod        : 1
% 2.99/1.75  #Tautology    : 0
% 2.99/1.75  #SimpNegUnit  : 1
% 2.99/1.75  #BackRed      : 0
% 2.99/1.75  
% 2.99/1.75  #Partial instantiations: 0
% 2.99/1.75  #Strategies tried      : 1
% 2.99/1.75  
% 2.99/1.75  Timing (in seconds)
% 2.99/1.75  ----------------------
% 2.99/1.76  Preprocessing        : 0.44
% 2.99/1.76  Parsing              : 0.24
% 2.99/1.76  CNF conversion       : 0.03
% 2.99/1.76  Main loop            : 0.23
% 2.99/1.76  Inferencing          : 0.10
% 2.99/1.76  Reduction            : 0.05
% 2.99/1.76  Demodulation         : 0.04
% 2.99/1.76  BG Simplification    : 0.01
% 2.99/1.76  Subsumption          : 0.05
% 2.99/1.76  Abstraction          : 0.01
% 2.99/1.76  MUC search           : 0.00
% 2.99/1.76  Cooper               : 0.00
% 2.99/1.76  Total                : 0.73
% 2.99/1.76  Index Insertion      : 0.00
% 2.99/1.76  Index Deletion       : 0.00
% 2.99/1.76  Index Matching       : 0.00
% 2.99/1.76  BG Taut test         : 0.00
%------------------------------------------------------------------------------