TSTP Solution File: LAT270-2 by Beagle---0.9.47

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.47
% Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xms512M -Xmx4G -Xss10M -XX:MaxPermSize=384M -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 : n032.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  : 600s
% DateTime : Sun Jul 17 03:46:09 EDT 2022

% Result   : Unsatisfiable 1.30s 0.99s
% Output   : CNFRefutation 1.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   26 (  10 unt;  13 typ;   0 def)
%            Number of atoms       :   21 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    5 (   0 usr;   3 ari)
%            Number of type conns  :   17 (   7   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-4 aty)
%            Number of variables   :    6 (   6   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Tarski_Ointerval > #nlpp > tc_set > v_r > v_b > v_a > v_S > v_A > t_a

%Foreground sorts:

%Background operators:

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

tff('#nlpp',type,
    '#nlpp': ( $real * $real ) > $real ).

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

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

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

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

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

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

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

tff('#nlpp_001',type,
    '#nlpp': ( $rat * $rat ) > $rat ).

tff('#nlpp_002',type,
    '#nlpp': ( $int * $int ) > $int ).

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

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

tff(f_30,axiom,
    ~ c_lessequals(v_S,v_A,tc_set(t_a)),
    file(unknown,unknown) ).

tff(f_27,axiom,
    c_in(v_b,v_A,t_a),
    file(unknown,unknown) ).

tff(f_26,axiom,
    c_in(v_a,v_A,t_a),
    file(unknown,unknown) ).

tff(f_28,axiom,
    c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
    file(unknown,unknown) ).

tff(f_41,axiom,
    ! [V_b,V_a,V_S] :
      ( ~ c_in(V_b,v_A,t_a)
      | ~ c_in(V_a,v_A,t_a)
      | ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
      | c_lessequals(V_S,v_A,tc_set(t_a)) ),
    file(unknown,unknown) ).

tff(c_8,plain,
    ~ c_lessequals(v_S,v_A,tc_set(t_a)),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

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

tff(c_2,plain,
    c_in(v_a,v_A,t_a),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_6,plain,
    c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_11,plain,
    ! [V_S_4,V_a_5,V_b_6] :
      ( c_lessequals(V_S_4,v_A,tc_set(t_a))
      | ~ c_lessequals(V_S_4,c_Tarski_Ointerval(v_r,V_a_5,V_b_6,t_a),tc_set(t_a))
      | ~ c_in(V_a_5,v_A,t_a)
      | ~ c_in(V_b_6,v_A,t_a) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_14,plain,
    ( c_lessequals(v_S,v_A,tc_set(t_a))
    | ~ c_in(v_a,v_A,t_a)
    | ~ c_in(v_b,v_A,t_a) ),
    inference(resolution,[status(thm)],[c_6,c_11]) ).

tff(c_17,plain,
    c_lessequals(v_S,v_A,tc_set(t_a)),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2,c_14]) ).

tff(c_19,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.11  % Command  : java -Xms512M -Xmx4G -Xss10M -XX:MaxPermSize=384M -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
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Tue Jun 28 22:34:57 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.15/0.31  OpenJDK 64-Bit Server VM warning: ignoring option MaxPermSize=384M; support was removed in 8.0
% 1.30/0.99  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.30/0.99  
% 1.30/0.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.30/1.01  
% 1.30/1.01  Inference rules
% 1.30/1.01  ----------------------
% 1.30/1.01  #Ref     : 0
% 1.30/1.01  #Sup     : 1
% 1.30/1.01  #Fact    : 0
% 1.30/1.01  #Define  : 0
% 1.30/1.01  #Split   : 0
% 1.30/1.01  #Chain   : 0
% 1.30/1.01  #Close   : 0
% 1.30/1.01  
% 1.30/1.01  Ordering : KBO
% 1.30/1.01  
% 1.30/1.01  Simplification rules
% 1.30/1.01  ----------------------
% 1.30/1.01  #Subsume      : 0
% 1.30/1.01  #Demod        : 2
% 1.30/1.01  #Tautology    : 0
% 1.30/1.01  #SimpNegUnit  : 1
% 1.30/1.01  #BackRed      : 0
% 1.30/1.01  
% 1.30/1.01  #Partial instantiations: 0
% 1.30/1.01  #Strategies tried      : 1
% 1.30/1.01  
% 1.30/1.01  Timing (in seconds)
% 1.30/1.01  ----------------------
% 1.30/1.02  Preprocessing        : 0.25
% 1.30/1.02  Parsing              : 0.14
% 1.30/1.02  CNF conversion       : 0.01
% 1.30/1.02  Main loop            : 0.06
% 1.30/1.02  Inferencing          : 0.03
% 1.30/1.02  Reduction            : 0.02
% 1.30/1.02  Demodulation         : 0.02
% 1.30/1.02  BG Simplification    : 0.01
% 1.30/1.02  Subsumption          : 0.00
% 1.30/1.02  Abstraction          : 0.00
% 1.30/1.02  MUC search           : 0.00
% 1.30/1.02  Cooper               : 0.00
% 1.30/1.02  Total                : 0.35
% 1.30/1.02  Index Insertion      : 0.00
% 1.30/1.02  Index Deletion       : 0.00
% 1.30/1.02  Index Matching       : 0.00
% 1.30/1.02  BG Taut test         : 0.00
%------------------------------------------------------------------------------