TSTP Solution File: GRP125-1.003 by Beagle---0.9.47

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.47
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xms512M -Xmx4G -Xss10M -XX:MaxPermSize=384M -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 : 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  : 600s
% DateTime : Sat Jul 16 07:29:42 EDT 2022

% Result   : Unsatisfiable 2.12s 1.27s
% Output   : CNFRefutation 2.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   57 (  25 unt;   9 typ;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   93 (  41   ~;  52   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    5 (   0 usr;   3 ari)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   50 (  50   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > equalish > group_element > #nlpp > e_3 > e_2 > e_1

%Foreground sorts:

%Background operators:

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

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

tff(e_2,type,
    e_2: $i ).

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

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

tff(e_3,type,
    e_3: $i ).

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

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

tff(e_1,type,
    e_1: $i ).

tff(f_45,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_43,axiom,
    ~ equalish(e_3,e_1),
    file(unknown,unknown) ).

tff(f_33,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_32,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2)
      | product(X,Y,e_3) ),
    file(unknown,unknown) ).

tff(f_41,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ! [X] : product(X,X,X),
    file(unknown,unknown) ).

tff(f_81,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X,Y,Z1,Z2] :
      ( ~ product(X,Y,Z1)
      | ~ product(Y,X,Z2)
      | product(Z1,Z2,X) ),
    file(unknown,unknown) ).

tff(f_65,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(c_18,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_10,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_16,plain,
    ~ equalish(e_3,e_1),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_6,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_4,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_20,plain,
    ! [X_1,Y_2] :
      ( product(X_1,Y_2,e_3)
      | product(X_1,Y_2,e_2)
      | product(X_1,Y_2,e_1)
      | ~ group_element(Y_2)
      | ~ group_element(X_1) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_14,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_71,plain,
    ! [X_46,Y_47] :
      ( product(X_46,Y_47,e_3)
      | product(X_46,Y_47,e_2)
      | product(X_46,Y_47,e_1)
      | ~ group_element(Y_47)
      | ~ group_element(X_46) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_28,plain,
    ! [X_15] : product(X_15,X_15,X_15),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_52,plain,
    ! [W_34,Z_35,Y_36,X_37] :
      ( equalish(W_34,Z_35)
      | ~ product(Z_35,Y_36,X_37)
      | ~ product(W_34,Y_36,X_37) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_55,plain,
    ! [W_34,X_15] :
      ( equalish(W_34,X_15)
      | ~ product(W_34,X_15,X_15) ),
    inference(resolution,[status(thm)],[c_28,c_52]) ).

tff(c_80,plain,
    ! [X_46] :
      ( equalish(X_46,e_3)
      | product(X_46,e_3,e_2)
      | product(X_46,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_46) ),
    inference(resolution,[status(thm)],[c_71,c_55]) ).

tff(c_107,plain,
    ! [X_48] :
      ( equalish(X_48,e_3)
      | product(X_48,e_3,e_2)
      | product(X_48,e_3,e_1)
      | ~ group_element(X_48) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_80]) ).

tff(c_32,plain,
    ! [W_21,Z_22,X_23,Y_24] :
      ( equalish(W_21,Z_22)
      | ~ product(X_23,Z_22,Y_24)
      | ~ product(X_23,W_21,Y_24) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_35,plain,
    ! [W_21,X_15] :
      ( equalish(W_21,X_15)
      | ~ product(X_15,W_21,X_15) ),
    inference(resolution,[status(thm)],[c_28,c_32]) ).

tff(c_124,plain,
    ( equalish(e_3,e_2)
    | equalish(e_2,e_3)
    | product(e_2,e_3,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_107,c_35]) ).

tff(c_139,plain,
    ( equalish(e_3,e_2)
    | equalish(e_2,e_3)
    | product(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_124]) ).

tff(c_140,plain,
    product(e_2,e_3,e_1),
    inference(negUnitSimplification,[status(thm)],[c_14,c_18,c_139]) ).

tff(c_30,plain,
    ! [Z1_18,Z2_19,X_16,Y_17] :
      ( product(Z1_18,Z2_19,X_16)
      | ~ product(Y_17,X_16,Z2_19)
      | ~ product(X_16,Y_17,Z1_18) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_198,plain,
    ! [Z1_55] :
      ( product(Z1_55,e_1,e_3)
      | ~ product(e_3,e_2,Z1_55) ),
    inference(resolution,[status(thm)],[c_140,c_30]) ).

tff(c_201,plain,
    ( product(e_3,e_1,e_3)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1)
    | ~ group_element(e_2)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_20,c_198]) ).

tff(c_204,plain,
    ( product(e_3,e_1,e_3)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_201]) ).

tff(c_205,plain,
    product(e_3,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_204]) ).

tff(c_150,plain,
    ! [Z1_18] :
      ( product(Z1_18,e_1,e_3)
      | ~ product(e_3,e_2,Z1_18) ),
    inference(resolution,[status(thm)],[c_140,c_30]) ).

tff(c_216,plain,
    product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_205,c_150]) ).

tff(c_42,plain,
    ! [W_28,Z_29,X_30,Y_31] :
      ( equalish(W_28,Z_29)
      | ~ product(X_30,Y_31,Z_29)
      | ~ product(X_30,Y_31,W_28) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_45,plain,
    ! [W_28,X_15] :
      ( equalish(W_28,X_15)
      | ~ product(X_15,X_15,W_28) ),
    inference(resolution,[status(thm)],[c_28,c_42]) ).

tff(c_245,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_216,c_45]) ).

tff(c_259,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16,c_245]) ).

tff(c_260,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_1,e_3) ),
    inference(splitRight,[status(thm)],[c_204]) ).

tff(c_262,plain,
    product(e_3,e_1,e_3),
    inference(splitLeft,[status(thm)],[c_260]) ).

tff(c_273,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_262,c_35]) ).

tff(c_285,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_273]) ).

tff(c_286,plain,
    product(e_3,e_2,e_2),
    inference(splitRight,[status(thm)],[c_260]) ).

tff(c_294,plain,
    equalish(e_3,e_2),
    inference(resolution,[status(thm)],[c_286,c_55]) ).

tff(c_306,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_294]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13  % Command  : java -Xms512M -Xmx4G -Xss10M -XX:MaxPermSize=384M -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 : 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  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 23:28:32 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  OpenJDK 64-Bit Server VM warning: ignoring option MaxPermSize=384M; support was removed in 8.0
% 2.12/1.27  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.12/1.28  
% 2.12/1.28  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.12/1.30  
% 2.12/1.30  Inference rules
% 2.12/1.30  ----------------------
% 2.12/1.30  #Ref     : 0
% 2.12/1.30  #Sup     : 61
% 2.12/1.30  #Fact    : 0
% 2.12/1.30  #Define  : 0
% 2.12/1.30  #Split   : 2
% 2.12/1.30  #Chain   : 0
% 2.12/1.30  #Close   : 0
% 2.12/1.30  
% 2.12/1.30  Ordering : KBO
% 2.12/1.30  
% 2.12/1.30  Simplification rules
% 2.12/1.30  ----------------------
% 2.12/1.30  #Subsume      : 0
% 2.12/1.30  #Demod        : 27
% 2.12/1.30  #Tautology    : 12
% 2.12/1.30  #SimpNegUnit  : 8
% 2.12/1.30  #BackRed      : 0
% 2.12/1.30  
% 2.12/1.30  #Partial instantiations: 0
% 2.12/1.30  #Strategies tried      : 1
% 2.12/1.30  
% 2.12/1.30  Timing (in seconds)
% 2.12/1.30  ----------------------
% 2.12/1.30  Preprocessing        : 0.26
% 2.12/1.30  Parsing              : 0.15
% 2.12/1.30  CNF conversion       : 0.01
% 2.12/1.30  Main loop            : 0.25
% 2.12/1.30  Inferencing          : 0.09
% 2.12/1.30  Reduction            : 0.06
% 2.12/1.30  Demodulation         : 0.04
% 2.12/1.30  BG Simplification    : 0.01
% 2.12/1.30  Subsumption          : 0.07
% 2.12/1.30  Abstraction          : 0.01
% 2.12/1.30  MUC search           : 0.00
% 2.12/1.30  Cooper               : 0.00
% 2.12/1.30  Total                : 0.55
% 2.12/1.30  Index Insertion      : 0.00
% 2.12/1.30  Index Deletion       : 0.00
% 2.12/1.30  Index Matching       : 0.00
% 2.12/1.30  BG Taut test         : 0.00
%------------------------------------------------------------------------------