TSTP Solution File: LAT268-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LAT268-2 : 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 : n027.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 10:46:35 EDT 2023

% Result   : Unsatisfiable 2.84s 1.74s
% Output   : CNFRefutation 3.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   48 (  19 unt;  20 typ;   0 def)
%            Number of atoms       :   53 (   8 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   53 (  28   ~;  25   |;   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  :   29 (  11   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   9 con; 0-4 aty)
%            Number of variables   :   38 (;  38   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Pair > c_Tarski_Opotype_Opset > c_Tarski_Opotype_Oorder > c_Tarski_Olub > c_Tarski_Oglb > tc_prod > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_Odual > #nlpp > tc_set > v_x > v_r > v_cl > v_S > v_A > tc_Product__Type_Ounit > t_a > c_Tarski_OPartialOrder > c_Tarski_OCompleteLattice

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_27,axiom,
    c_in(v_x,v_S,t_a),
    file(unknown,unknown) ).

tff(f_26,axiom,
    c_lessequals(v_S,v_A,tc_set(t_a)),
    file(unknown,unknown) ).

tff(f_50,axiom,
    c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    file(unknown,unknown) ).

tff(f_51,axiom,
    c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    file(unknown,unknown) ).

tff(f_30,axiom,
    v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
    file(unknown,unknown) ).

tff(f_56,axiom,
    v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ! [V_cl,T_a] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [V_S,V_cl,T_a] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ),
    file(unknown,unknown) ).

tff(f_44,axiom,
    ! [V_x,V_S,T_a,V_cl] :
      ( ~ c_in(V_x,V_S,T_a)
      | ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
      | ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
      | ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
      | c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
    file(unknown,unknown) ).

tff(f_49,axiom,
    ! [V_x,V_y,T_a,V_cl] :
      ( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
      | c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ),
    file(unknown,unknown) ).

tff(f_29,axiom,
    ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    file(unknown,unknown) ).

tff(c_4,plain,
    c_in(v_x,v_S,t_a),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_2,plain,
    c_lessequals(v_S,v_A,tc_set(t_a)),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_14,plain,
    c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_16,plain,
    c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_8,plain,
    c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_22,plain,
    c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_20,plain,
    ! [V_cl_12,T_a_13] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl_12,T_a_13),T_a_13,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl_12,T_a_13,tc_Product__Type_Ounit) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_18,plain,
    ! [V_S_9,V_cl_10,T_a_11] : ( c_Tarski_Olub(V_S_9,c_Tarski_Odual(V_cl_10,T_a_11),T_a_11) = c_Tarski_Oglb(V_S_9,V_cl_10,T_a_11) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_50,plain,
    ! [V_x_23,V_S_24,V_cl_25,T_a_26] :
      ( c_in(c_Pair(V_x_23,c_Tarski_Olub(V_S_24,V_cl_25,T_a_26),T_a_26,T_a_26),c_Tarski_Opotype_Oorder(V_cl_25,T_a_26,tc_Product__Type_Ounit),tc_prod(T_a_26,T_a_26))
      | ~ c_lessequals(V_S_24,c_Tarski_Opotype_Opset(V_cl_25,T_a_26,tc_Product__Type_Ounit),tc_set(T_a_26))
      | ~ c_in(V_cl_25,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a_26,tc_Product__Type_Ounit))
      | ~ c_in(V_cl_25,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a_26,tc_Product__Type_Ounit))
      | ~ c_in(V_x_23,V_S_24,T_a_26) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_12,plain,
    ! [V_y_6,V_x_5,T_a_7,V_cl_8] :
      ( c_in(c_Pair(V_y_6,V_x_5,T_a_7,T_a_7),c_Tarski_Opotype_Oorder(V_cl_8,T_a_7,tc_Product__Type_Ounit),tc_prod(T_a_7,T_a_7))
      | ~ c_in(c_Pair(V_x_5,V_y_6,T_a_7,T_a_7),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl_8,T_a_7),T_a_7,tc_Product__Type_Ounit),tc_prod(T_a_7,T_a_7)) ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_54,plain,
    ! [V_S_24,V_cl_8,T_a_26,V_x_23] :
      ( c_in(c_Pair(c_Tarski_Olub(V_S_24,c_Tarski_Odual(V_cl_8,T_a_26),T_a_26),V_x_23,T_a_26,T_a_26),c_Tarski_Opotype_Oorder(V_cl_8,T_a_26,tc_Product__Type_Ounit),tc_prod(T_a_26,T_a_26))
      | ~ c_lessequals(V_S_24,c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl_8,T_a_26),T_a_26,tc_Product__Type_Ounit),tc_set(T_a_26))
      | ~ c_in(c_Tarski_Odual(V_cl_8,T_a_26),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a_26,tc_Product__Type_Ounit))
      | ~ c_in(c_Tarski_Odual(V_cl_8,T_a_26),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a_26,tc_Product__Type_Ounit))
      | ~ c_in(V_x_23,V_S_24,T_a_26) ),
    inference(resolution,[status(thm)],[c_50,c_12]) ).

tff(c_66,plain,
    ! [V_S_27,V_cl_28,T_a_29,V_x_30] :
      ( c_in(c_Pair(c_Tarski_Oglb(V_S_27,V_cl_28,T_a_29),V_x_30,T_a_29,T_a_29),c_Tarski_Opotype_Oorder(V_cl_28,T_a_29,tc_Product__Type_Ounit),tc_prod(T_a_29,T_a_29))
      | ~ c_lessequals(V_S_27,c_Tarski_Opotype_Opset(V_cl_28,T_a_29,tc_Product__Type_Ounit),tc_set(T_a_29))
      | ~ c_in(c_Tarski_Odual(V_cl_28,T_a_29),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a_29,tc_Product__Type_Ounit))
      | ~ c_in(c_Tarski_Odual(V_cl_28,T_a_29),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a_29,tc_Product__Type_Ounit))
      | ~ c_in(V_x_30,V_S_27,T_a_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_18,c_54]) ).

tff(c_73,plain,
    ! [V_S_27,V_x_30] :
      ( c_in(c_Pair(c_Tarski_Oglb(V_S_27,v_cl,t_a),V_x_30,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_lessequals(V_S_27,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
      | ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(V_x_30,V_S_27,t_a) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_66]) ).

tff(c_78,plain,
    ! [V_S_31,V_x_32] :
      ( c_in(c_Pair(c_Tarski_Oglb(V_S_31,v_cl,t_a),V_x_32,t_a,t_a),v_r,tc_prod(t_a,t_a))
      | ~ c_lessequals(V_S_31,v_A,tc_set(t_a))
      | ~ c_in(V_x_32,V_S_31,t_a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_16,c_8,c_73]) ).

tff(c_6,plain,
    ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_81,plain,
    ( ~ c_lessequals(v_S,v_A,tc_set(t_a))
    | ~ c_in(v_x,v_S,t_a) ),
    inference(resolution,[status(thm)],[c_78,c_6]) ).

tff(c_85,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_81]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LAT268-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.13/0.34  % Computer : n027.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 12:52:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 2.84/1.74  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/1.75  
% 2.84/1.75  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/1.79  
% 3.06/1.79  Inference rules
% 3.06/1.79  ----------------------
% 3.06/1.79  #Ref     : 0
% 3.06/1.79  #Sup     : 14
% 3.06/1.79  #Fact    : 0
% 3.06/1.79  #Define  : 0
% 3.06/1.79  #Split   : 1
% 3.06/1.79  #Chain   : 0
% 3.06/1.79  #Close   : 0
% 3.06/1.79  
% 3.06/1.79  Ordering : KBO
% 3.06/1.79  
% 3.06/1.79  Simplification rules
% 3.06/1.79  ----------------------
% 3.06/1.79  #Subsume      : 0
% 3.06/1.79  #Demod        : 10
% 3.06/1.79  #Tautology    : 8
% 3.06/1.79  #SimpNegUnit  : 0
% 3.06/1.79  #BackRed      : 0
% 3.06/1.79  
% 3.06/1.79  #Partial instantiations: 0
% 3.06/1.79  #Strategies tried      : 1
% 3.06/1.79  
% 3.06/1.79  Timing (in seconds)
% 3.06/1.79  ----------------------
% 3.06/1.79  Preprocessing        : 0.43
% 3.06/1.79  Parsing              : 0.24
% 3.06/1.79  CNF conversion       : 0.02
% 3.06/1.79  Main loop            : 0.22
% 3.06/1.79  Inferencing          : 0.09
% 3.06/1.79  Reduction            : 0.06
% 3.06/1.79  Demodulation         : 0.05
% 3.06/1.79  BG Simplification    : 0.01
% 3.06/1.79  Subsumption          : 0.04
% 3.06/1.79  Abstraction          : 0.01
% 3.06/1.79  MUC search           : 0.00
% 3.06/1.79  Cooper               : 0.00
% 3.06/1.79  Total                : 0.71
% 3.06/1.79  Index Insertion      : 0.00
% 3.06/1.79  Index Deletion       : 0.00
% 3.06/1.79  Index Matching       : 0.00
% 3.06/1.79  BG Taut test         : 0.00
%------------------------------------------------------------------------------