TSTP Solution File: COM011-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COM011-2 : 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 : n009.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 10:35:17 EDT 2023

% Result   : Unsatisfiable 5.69s 2.52s
% Output   : CNFRefutation 5.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   56 (  15 unt;  15 typ;   0 def)
%            Number of atoms       :   77 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   69 (  33   ~;  36   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  11   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   92 (;  92   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_union > c_minus > c_WFair_OleadsTo > c_WFair_Oensures > c_UNITY_Oconstrains > c_Main_OsubsetI__1 > c_WFair_Otransient > #nlpp > tc_set > tc_UNITY_Oprogram > v_F > v_B > v_A > t_a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(c_Main_OsubsetI__1,type,
    c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

tff(f_64,axiom,
    ! [V_F,V_A,V_B,T_a] :
      ( ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
      | c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    file(unknown,unknown) ).

tff(f_29,axiom,
    ~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
    file(unknown,unknown) ).

tff(f_26,axiom,
    c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
    file(unknown,unknown) ).

tff(f_27,axiom,
    c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ! [V_A,V_B,T_a] :
      ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
      | c_lessequals(V_A,V_B,tc_set(T_a)) ),
    file(unknown,unknown) ).

tff(f_34,axiom,
    ! [V_c,V_A,V_B,T_a] :
      ( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
      | c_in(V_c,V_A,T_a) ),
    file(unknown,unknown) ).

tff(f_43,axiom,
    ! [V_A,V_B,T_a] :
      ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
      | c_lessequals(V_A,V_B,tc_set(T_a)) ),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [V_F,V_A,T_a,V_B] :
      ( ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a))
      | ~ c_lessequals(V_B,V_A,tc_set(T_a))
      | c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    file(unknown,unknown) ).

tff(f_51,axiom,
    ! [V_F,V_B,T_a,V_A_H,V_A] :
      ( ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
      | ~ c_lessequals(V_B,V_A,tc_set(T_a))
      | c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [V_F,V_A,V_B,T_a] :
      ( ~ c_in(V_F,c_UNITY_Oconstrains(c_minus(V_A,V_B,tc_set(T_a)),c_union(V_A,V_B,T_a),T_a),tc_UNITY_Oprogram(T_a))
      | ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
      | c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    file(unknown,unknown) ).

tff(c_34,plain,
    ! [V_F_40,V_A_41,V_B_42,T_a_43] :
      ( c_in(V_F_40,c_WFair_OleadsTo(V_A_41,V_B_42,T_a_43),tc_UNITY_Oprogram(T_a_43))
      | ~ c_in(V_F_40,c_WFair_Oensures(V_A_41,V_B_42,T_a_43),tc_UNITY_Oprogram(T_a_43)) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_6,plain,
    ~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_42,plain,
    ~ c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
    inference(resolution,[status(thm)],[c_34,c_6]) ).

tff(c_2,plain,
    c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_4,plain,
    c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_23,plain,
    ! [V_A_35,V_B_36,T_a_37] :
      ( c_lessequals(V_A_35,V_B_36,tc_set(T_a_37))
      | c_in(c_Main_OsubsetI__1(V_A_35,V_B_36,T_a_37),V_A_35,T_a_37) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_8,plain,
    ! [V_c_1,V_A_2,T_a_4,V_B_3] :
      ( c_in(V_c_1,V_A_2,T_a_4)
      | ~ c_in(V_c_1,c_minus(V_A_2,V_B_3,tc_set(T_a_4)),T_a_4) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_50,plain,
    ! [V_A_48,V_B_49,T_a_50,V_B_51] :
      ( c_in(c_Main_OsubsetI__1(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_B_51,T_a_50),V_A_48,T_a_50)
      | c_lessequals(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_B_51,tc_set(T_a_50)) ),
    inference(resolution,[status(thm)],[c_23,c_8]) ).

tff(c_12,plain,
    ! [V_A_8,V_B_9,T_a_10] :
      ( c_lessequals(V_A_8,V_B_9,tc_set(T_a_10))
      | ~ c_in(c_Main_OsubsetI__1(V_A_8,V_B_9,T_a_10),V_B_9,T_a_10) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_63,plain,
    ! [V_A_52,V_B_53,T_a_54] : c_lessequals(c_minus(V_A_52,V_B_53,tc_set(T_a_54)),V_A_52,tc_set(T_a_54)),
    inference(resolution,[status(thm)],[c_50,c_12]) ).

tff(c_20,plain,
    ! [V_F_24,V_B_27,T_a_26,V_A_25] :
      ( c_in(V_F_24,c_WFair_Otransient(V_B_27,T_a_26),tc_UNITY_Oprogram(T_a_26))
      | ~ c_lessequals(V_B_27,V_A_25,tc_set(T_a_26))
      | ~ c_in(V_F_24,c_WFair_Otransient(V_A_25,T_a_26),tc_UNITY_Oprogram(T_a_26)) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_66,plain,
    ! [V_F_24,V_A_52,V_B_53,T_a_54] :
      ( c_in(V_F_24,c_WFair_Otransient(c_minus(V_A_52,V_B_53,tc_set(T_a_54)),T_a_54),tc_UNITY_Oprogram(T_a_54))
      | ~ c_in(V_F_24,c_WFair_Otransient(V_A_52,T_a_54),tc_UNITY_Oprogram(T_a_54)) ),
    inference(resolution,[status(thm)],[c_63,c_20]) ).

tff(c_10,plain,
    ! [V_A_5,V_B_6,T_a_7] :
      ( c_lessequals(V_A_5,V_B_6,tc_set(T_a_7))
      | c_in(c_Main_OsubsetI__1(V_A_5,V_B_6,T_a_7),V_A_5,T_a_7) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_72,plain,
    ! [V_A_H_63,V_B_59,V_A_61,T_a_62,V_F_60] :
      ( c_in(V_F_60,c_UNITY_Oconstrains(V_B_59,V_A_H_63,T_a_62),tc_UNITY_Oprogram(T_a_62))
      | ~ c_lessequals(V_B_59,V_A_61,tc_set(T_a_62))
      | ~ c_in(V_F_60,c_UNITY_Oconstrains(V_A_61,V_A_H_63,T_a_62),tc_UNITY_Oprogram(T_a_62)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_163,plain,
    ! [V_A_83,V_A_H_85,V_B_86,V_F_84,T_a_82] :
      ( c_in(V_F_84,c_UNITY_Oconstrains(V_A_83,V_A_H_85,T_a_82),tc_UNITY_Oprogram(T_a_82))
      | ~ c_in(V_F_84,c_UNITY_Oconstrains(V_B_86,V_A_H_85,T_a_82),tc_UNITY_Oprogram(T_a_82))
      | c_in(c_Main_OsubsetI__1(V_A_83,V_B_86,T_a_82),V_A_83,T_a_82) ),
    inference(resolution,[status(thm)],[c_10,c_72]) ).

tff(c_178,plain,
    ! [V_A_87] :
      ( c_in(v_F,c_UNITY_Oconstrains(V_A_87,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
      | c_in(c_Main_OsubsetI__1(V_A_87,v_A,t_a),V_A_87,t_a) ),
    inference(resolution,[status(thm)],[c_2,c_163]) ).

tff(c_308,plain,
    ! [V_A_119,V_B_120] :
      ( c_in(c_Main_OsubsetI__1(c_minus(V_A_119,V_B_120,tc_set(t_a)),v_A,t_a),V_A_119,t_a)
      | c_in(v_F,c_UNITY_Oconstrains(c_minus(V_A_119,V_B_120,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
    inference(resolution,[status(thm)],[c_178,c_8]) ).

tff(c_16,plain,
    ! [V_F_16,V_A_17,V_B_18,T_a_19] :
      ( c_in(V_F_16,c_WFair_Oensures(V_A_17,V_B_18,T_a_19),tc_UNITY_Oprogram(T_a_19))
      | ~ c_in(V_F_16,c_WFair_Otransient(c_minus(V_A_17,V_B_18,tc_set(T_a_19)),T_a_19),tc_UNITY_Oprogram(T_a_19))
      | ~ c_in(V_F_16,c_UNITY_Oconstrains(c_minus(V_A_17,V_B_18,tc_set(T_a_19)),c_union(V_A_17,V_B_18,T_a_19),T_a_19),tc_UNITY_Oprogram(T_a_19)) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_319,plain,
    ( c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a))
    | ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
    | c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a) ),
    inference(resolution,[status(thm)],[c_308,c_16]) ).

tff(c_324,plain,
    ( ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
    | c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a) ),
    inference(negUnitSimplification,[status(thm)],[c_42,c_319]) ).

tff(c_325,plain,
    ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
    inference(splitLeft,[status(thm)],[c_324]) ).

tff(c_333,plain,
    ~ c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
    inference(resolution,[status(thm)],[c_66,c_325]) ).

tff(c_338,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_333]) ).

tff(c_340,plain,
    c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
    inference(splitRight,[status(thm)],[c_324]) ).

tff(c_61,plain,
    ! [V_A_48,V_B_49,T_a_50] : c_lessequals(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_A_48,tc_set(T_a_50)),
    inference(resolution,[status(thm)],[c_50,c_12]) ).

tff(c_81,plain,
    ! [V_A_H_63,V_B_49,V_A_48,T_a_50,V_F_60] :
      ( c_in(V_F_60,c_UNITY_Oconstrains(c_minus(V_A_48,V_B_49,tc_set(T_a_50)),V_A_H_63,T_a_50),tc_UNITY_Oprogram(T_a_50))
      | ~ c_in(V_F_60,c_UNITY_Oconstrains(V_A_48,V_A_H_63,T_a_50),tc_UNITY_Oprogram(T_a_50)) ),
    inference(resolution,[status(thm)],[c_61,c_72]) ).

tff(c_90,plain,
    ! [V_F_69,V_A_70,V_B_71,T_a_72] :
      ( c_in(V_F_69,c_WFair_Oensures(V_A_70,V_B_71,T_a_72),tc_UNITY_Oprogram(T_a_72))
      | ~ c_in(V_F_69,c_WFair_Otransient(c_minus(V_A_70,V_B_71,tc_set(T_a_72)),T_a_72),tc_UNITY_Oprogram(T_a_72))
      | ~ c_in(V_F_69,c_UNITY_Oconstrains(c_minus(V_A_70,V_B_71,tc_set(T_a_72)),c_union(V_A_70,V_B_71,T_a_72),T_a_72),tc_UNITY_Oprogram(T_a_72)) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_2018,plain,
    ! [V_F_290,V_A_291,V_B_292,T_a_293] :
      ( c_in(V_F_290,c_WFair_Oensures(V_A_291,V_B_292,T_a_293),tc_UNITY_Oprogram(T_a_293))
      | ~ c_in(V_F_290,c_WFair_Otransient(c_minus(V_A_291,V_B_292,tc_set(T_a_293)),T_a_293),tc_UNITY_Oprogram(T_a_293))
      | ~ c_in(V_F_290,c_UNITY_Oconstrains(V_A_291,c_union(V_A_291,V_B_292,T_a_293),T_a_293),tc_UNITY_Oprogram(T_a_293)) ),
    inference(resolution,[status(thm)],[c_81,c_90]) ).

tff(c_2069,plain,
    ( c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a))
    | ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
    inference(resolution,[status(thm)],[c_340,c_2018]) ).

tff(c_2104,plain,
    c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2069]) ).

tff(c_2106,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_2104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COM011-2 : 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
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 23:27:54 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 5.69/2.52  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.69/2.52  
% 5.69/2.52  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.69/2.56  
% 5.69/2.56  Inference rules
% 5.69/2.56  ----------------------
% 5.69/2.56  #Ref     : 0
% 5.69/2.56  #Sup     : 465
% 5.69/2.56  #Fact    : 4
% 5.69/2.56  #Define  : 0
% 5.69/2.56  #Split   : 1
% 5.69/2.56  #Chain   : 0
% 5.69/2.56  #Close   : 0
% 5.69/2.56  
% 5.69/2.56  Ordering : KBO
% 5.69/2.56  
% 5.69/2.56  Simplification rules
% 5.69/2.56  ----------------------
% 5.69/2.56  #Subsume      : 21
% 5.69/2.56  #Demod        : 57
% 5.69/2.56  #Tautology    : 42
% 5.69/2.56  #SimpNegUnit  : 2
% 5.69/2.56  #BackRed      : 0
% 5.69/2.56  
% 5.69/2.56  #Partial instantiations: 0
% 5.69/2.56  #Strategies tried      : 1
% 5.69/2.56  
% 5.69/2.56  Timing (in seconds)
% 5.69/2.56  ----------------------
% 5.69/2.57  Preprocessing        : 0.46
% 5.69/2.57  Parsing              : 0.26
% 5.69/2.57  CNF conversion       : 0.02
% 5.69/2.57  Main loop            : 0.98
% 5.69/2.57  Inferencing          : 0.38
% 5.69/2.57  Reduction            : 0.23
% 5.69/2.57  Demodulation         : 0.17
% 5.69/2.57  BG Simplification    : 0.03
% 5.69/2.57  Subsumption          : 0.27
% 5.69/2.57  Abstraction          : 0.03
% 5.69/2.57  MUC search           : 0.00
% 5.69/2.57  Cooper               : 0.00
% 5.69/2.57  Total                : 1.50
% 5.69/2.57  Index Insertion      : 0.00
% 5.69/2.57  Index Deletion       : 0.00
% 5.69/2.57  Index Matching       : 0.00
% 5.69/2.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------