TSTP Solution File: SET825-2 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET825-2 : 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 10:57:05 EDT 2023

% Result   : Unsatisfiable 2.55s 1.64s
% Output   : CNFRefutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   35 (  14 unt;  12 typ;   0 def)
%            Number of atoms       :   38 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   29 (  14   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   7   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :   14 (;  14   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_in > v_Q > c_Pair > tc_prod > #nlpp > v_xa > v_x > c_Suc > v_n > v_m > tc_nat > c_Relation_OId > c_0

%Foreground sorts:

%Background operators:

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

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

tff(c_0,type,
    c_0: $i ).

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

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

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

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

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

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

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

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

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

tff(f_35,axiom,
    ~ v_Q(v_m),
    file(unknown,unknown) ).

tff(f_27,axiom,
    ! [V_a,T_a] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ! [V_U] :
      ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
      | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ! [V_a,V_b,T_a] :
      ( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))
      | ( V_a = V_b ) ),
    file(unknown,unknown) ).

tff(f_33,axiom,
    v_Q(v_n),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [V_U] :
      ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
      | ~ c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
      | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ),
    file(unknown,unknown) ).

tff(c_8,plain,
    ~ v_Q(v_m),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_2,plain,
    ! [V_a_1,T_a_2] : c_in(c_Pair(V_a_1,V_a_1,T_a_2,T_a_2),c_Relation_OId,tc_prod(T_a_2,T_a_2)),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_20,plain,
    ! [V_U_13] :
      ( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U_13,tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(v_x(V_U_13),v_xa(V_U_13),tc_nat,tc_nat),V_U_13,tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U_13,tc_prod(tc_nat,tc_nat)) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_4,plain,
    ! [V_b_4,V_a_3,T_a_5] :
      ( ( V_b_4 = V_a_3 )
      | ~ c_in(c_Pair(V_a_3,V_b_4,T_a_5,T_a_5),c_Relation_OId,tc_prod(T_a_5,T_a_5)) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_24,plain,
    ( ( v_xa(c_Relation_OId) = v_x(c_Relation_OId) )
    | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
    inference(resolution,[status(thm)],[c_20,c_4]) ).

tff(c_27,plain,
    ( ( v_xa(c_Relation_OId) = v_x(c_Relation_OId) )
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24]) ).

tff(c_29,plain,
    c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
    inference(splitLeft,[status(thm)],[c_27]) ).

tff(c_33,plain,
    v_n = v_m,
    inference(resolution,[status(thm)],[c_29,c_4]) ).

tff(c_6,plain,
    v_Q(v_n),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_37,plain,
    v_Q(v_m),
    inference(demodulation,[status(thm),theory(equality)],[c_33,c_6]) ).

tff(c_40,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_37]) ).

tff(c_42,plain,
    ~ c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
    inference(splitRight,[status(thm)],[c_27]) ).

tff(c_41,plain,
    v_xa(c_Relation_OId) = v_x(c_Relation_OId),
    inference(splitRight,[status(thm)],[c_27]) ).

tff(c_12,plain,
    ! [V_U_7] :
      ( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U_7,tc_prod(tc_nat,tc_nat))
      | ~ c_in(c_Pair(c_Suc(v_x(V_U_7)),c_Suc(v_xa(V_U_7)),tc_nat,tc_nat),V_U_7,tc_prod(tc_nat,tc_nat))
      | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U_7,tc_prod(tc_nat,tc_nat)) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_46,plain,
    ( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
    inference(superposition,[status(thm),theory(equality)],[c_41,c_12]) ).

tff(c_53,plain,
    c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_46]) ).

tff(c_57,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15  % Problem  : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.16  % 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
% 0.15/0.36  % Computer : n003.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % 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 16:27:38 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 2.55/1.64  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.55/1.65  
% 2.55/1.65  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.84/1.68  
% 2.84/1.68  Inference rules
% 2.84/1.68  ----------------------
% 2.84/1.68  #Ref     : 0
% 2.84/1.68  #Sup     : 7
% 2.84/1.68  #Fact    : 0
% 2.84/1.68  #Define  : 0
% 2.84/1.68  #Split   : 1
% 2.84/1.68  #Chain   : 0
% 2.84/1.68  #Close   : 0
% 2.84/1.68  
% 2.84/1.68  Ordering : KBO
% 2.84/1.68  
% 2.84/1.68  Simplification rules
% 2.84/1.68  ----------------------
% 2.84/1.68  #Subsume      : 0
% 2.84/1.68  #Demod        : 10
% 2.84/1.68  #Tautology    : 5
% 2.84/1.69  #SimpNegUnit  : 2
% 2.84/1.69  #BackRed      : 4
% 2.84/1.69  
% 2.84/1.69  #Partial instantiations: 0
% 2.84/1.69  #Strategies tried      : 1
% 2.84/1.69  
% 2.84/1.69  Timing (in seconds)
% 2.84/1.69  ----------------------
% 2.84/1.69  Preprocessing        : 0.42
% 2.84/1.69  Parsing              : 0.23
% 2.84/1.69  CNF conversion       : 0.02
% 2.84/1.69  Main loop            : 0.20
% 2.84/1.69  Inferencing          : 0.08
% 2.84/1.69  Reduction            : 0.05
% 2.84/1.69  Demodulation         : 0.03
% 2.84/1.69  BG Simplification    : 0.01
% 2.84/1.69  Subsumption          : 0.05
% 2.84/1.69  Abstraction          : 0.01
% 2.84/1.69  MUC search           : 0.00
% 2.84/1.69  Cooper               : 0.00
% 2.84/1.69  Total                : 0.67
% 2.84/1.69  Index Insertion      : 0.00
% 2.84/1.69  Index Deletion       : 0.00
% 2.84/1.69  Index Matching       : 0.00
% 2.84/1.69  BG Taut test         : 0.00
%------------------------------------------------------------------------------