TSTP Solution File: KLE065+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE065+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n031.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 10:44:47 EDT 2023

% Result   : Theorem 19.37s 8.20s
% Output   : CNFRefutation 19.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   62 (  53 unt;   8 typ;   0 def)
%            Number of atoms       :   55 (  54 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    3 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   81 (;  81   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > zero > one > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

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

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

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

tff(f_127,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( multiplication(X0,X1) = zero )
       => ( multiplication(X0,domain(X1)) = zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

tff(f_63,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

tff(f_117,axiom,
    ! [X0] : ( addition(domain(X0),one) = one ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).

tff(f_52,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

tff(f_113,axiom,
    ! [X0] : ( addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).

tff(f_120,axiom,
    ! [X0,X1] : ( domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain5) ).

tff(f_115,axiom,
    ! [X0,X1] : ( domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).

tff(f_68,axiom,
    ! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

tff(f_75,axiom,
    ! [A] : ( multiplication(zero,A) = zero ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).

tff(f_118,axiom,
    domain(zero) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain4) ).

tff(f_61,axiom,
    ! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).

tff(f_65,axiom,
    ! [A] : ( multiplication(one,A) = A ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

tff(f_70,axiom,
    ! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

tff(c_38,plain,
    multiplication('#skF_1',domain('#skF_2')) != zero,
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_12,plain,
    ! [A_11] : ( multiplication(A_11,one) = A_11 ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_32,plain,
    ! [X0_26] : ( addition(domain(X0_26),one) = one ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_160,plain,
    ! [B_36,A_37] : ( addition(B_36,A_37) = addition(A_37,B_36) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_213,plain,
    ! [X0_26] : ( addition(one,domain(X0_26)) = one ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_160]) ).

tff(c_677,plain,
    ! [X0_56] : ( addition(X0_56,multiplication(domain(X0_56),X0_56)) = multiplication(domain(X0_56),X0_56) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_718,plain,
    multiplication(domain(one),one) = addition(one,domain(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_677]) ).

tff(c_734,plain,
    domain(one) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_12,c_718]) ).

tff(c_36,plain,
    ! [X0_27,X1_28] : ( addition(domain(X0_27),domain(X1_28)) = domain(addition(X0_27,X1_28)) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_752,plain,
    ! [X0_27] : ( addition(domain(X0_27),one) = domain(addition(X0_27,one)) ),
    inference(superposition,[status(thm),theory(equality)],[c_734,c_36]) ).

tff(c_836,plain,
    ! [X0_58] : ( domain(addition(X0_58,one)) = one ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_752]) ).

tff(c_30,plain,
    ! [X0_24,X1_25] : ( domain(multiplication(X0_24,domain(X1_25))) = domain(multiplication(X0_24,X1_25)) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_850,plain,
    ! [X0_24,X0_58] : ( domain(multiplication(X0_24,addition(X0_58,one))) = domain(multiplication(X0_24,one)) ),
    inference(superposition,[status(thm),theory(equality)],[c_836,c_30]) ).

tff(c_892,plain,
    ! [X0_24,X0_58] : ( domain(multiplication(X0_24,addition(X0_58,one))) = domain(X0_24) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_850]) ).

tff(c_1361,plain,
    ! [A_71,B_72,C_73] : ( addition(multiplication(A_71,B_72),multiplication(A_71,C_73)) = multiplication(A_71,addition(B_72,C_73)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_13990,plain,
    ! [A_179,B_180] : ( multiplication(A_179,addition(B_180,one)) = addition(multiplication(A_179,B_180),A_179) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1361]) ).

tff(c_305,plain,
    ! [X0_44,X1_45] : ( addition(domain(X0_44),domain(X1_45)) = domain(addition(X0_44,X1_45)) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_2,plain,
    ! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_2061,plain,
    ! [X1_85,X0_86] : ( addition(domain(X1_85),domain(X0_86)) = domain(addition(X0_86,X1_85)) ),
    inference(superposition,[status(thm),theory(equality)],[c_305,c_2]) ).

tff(c_2076,plain,
    ! [X1_85,X0_86] : ( domain(addition(X1_85,X0_86)) = domain(addition(X0_86,X1_85)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2061,c_36]) ).

tff(c_14105,plain,
    ! [A_179,B_180] : ( domain(multiplication(A_179,addition(B_180,one))) = domain(addition(A_179,multiplication(A_179,B_180))) ),
    inference(superposition,[status(thm),theory(equality)],[c_13990,c_2076]) ).

tff(c_14346,plain,
    ! [A_179,B_180] : ( domain(addition(A_179,multiplication(A_179,B_180))) = domain(A_179) ),
    inference(demodulation,[status(thm),theory(equality)],[c_892,c_14105]) ).

tff(c_22,plain,
    ! [A_20] : ( multiplication(zero,A_20) = zero ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_34,plain,
    domain(zero) = zero,
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_16270,plain,
    ! [A_192,C_193] : ( multiplication(A_192,addition(one,C_193)) = addition(A_192,multiplication(A_192,C_193)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_1361]) ).

tff(c_40,plain,
    multiplication('#skF_1','#skF_2') = zero,
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_906,plain,
    ! [A_59,B_60,C_61] : ( multiplication(multiplication(A_59,B_60),C_61) = multiplication(A_59,multiplication(B_60,C_61)) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_953,plain,
    ! [C_61] : ( multiplication('#skF_1',multiplication('#skF_2',C_61)) = multiplication(zero,C_61) ),
    inference(superposition,[status(thm),theory(equality)],[c_40,c_906]) ).

tff(c_967,plain,
    ! [C_61] : ( multiplication('#skF_1',multiplication('#skF_2',C_61)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_953]) ).

tff(c_16427,plain,
    ! [C_193] : ( multiplication('#skF_1',addition('#skF_2',multiplication('#skF_2',C_193))) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_16270,c_967]) ).

tff(c_14,plain,
    ! [A_12] : ( multiplication(one,A_12) = A_12 ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_1209,plain,
    ! [A_67,C_68,B_69] : ( addition(multiplication(A_67,C_68),multiplication(B_69,C_68)) = multiplication(addition(A_67,B_69),C_68) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_5481,plain,
    ! [B_116,A_117] : ( multiplication(addition(one,B_116),A_117) = addition(A_117,multiplication(B_116,A_117)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1209]) ).

tff(c_5651,plain,
    ! [A_117,X0_26] : ( addition(A_117,multiplication(domain(X0_26),A_117)) = multiplication(one,A_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_213,c_5481]) ).

tff(c_5707,plain,
    ! [A_117,X0_26] : ( addition(A_117,multiplication(domain(X0_26),A_117)) = A_117 ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_5651]) ).

tff(c_710,plain,
    ! [X0_24,X1_25] : ( addition(multiplication(X0_24,domain(X1_25)),multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25)))) = multiplication(domain(multiplication(X0_24,domain(X1_25))),multiplication(X0_24,domain(X1_25))) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_677]) ).

tff(c_732,plain,
    ! [X0_24,X1_25] : ( addition(multiplication(X0_24,domain(X1_25)),multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25)))) = multiplication(domain(multiplication(X0_24,X1_25)),multiplication(X0_24,domain(X1_25))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_710]) ).

tff(c_44754,plain,
    ! [X0_330,X1_331] : ( multiplication(domain(multiplication(X0_330,X1_331)),multiplication(X0_330,domain(X1_331))) = multiplication(X0_330,domain(X1_331)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5707,c_732]) ).

tff(c_45010,plain,
    ! [C_193] : ( multiplication(domain(zero),multiplication('#skF_1',domain(addition('#skF_2',multiplication('#skF_2',C_193))))) = multiplication('#skF_1',domain(addition('#skF_2',multiplication('#skF_2',C_193)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_16427,c_44754]) ).

tff(c_45248,plain,
    multiplication('#skF_1',domain('#skF_2')) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_14346,c_22,c_34,c_45010]) ).

tff(c_45250,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38,c_45248]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : KLE065+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15  % 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 : n031.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 23:43:15 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 19.37/8.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.45/8.21  
% 19.45/8.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.45/8.24  
% 19.45/8.24  Inference rules
% 19.45/8.24  ----------------------
% 19.45/8.24  #Ref     : 0
% 19.45/8.24  #Sup     : 11135
% 19.45/8.24  #Fact    : 0
% 19.45/8.24  #Define  : 0
% 19.45/8.24  #Split   : 0
% 19.45/8.24  #Chain   : 0
% 19.45/8.24  #Close   : 0
% 19.45/8.24  
% 19.45/8.24  Ordering : KBO
% 19.45/8.24  
% 19.45/8.24  Simplification rules
% 19.45/8.24  ----------------------
% 19.45/8.24  #Subsume      : 410
% 19.45/8.24  #Demod        : 17474
% 19.45/8.24  #Tautology    : 5534
% 19.45/8.24  #SimpNegUnit  : 1
% 19.45/8.24  #BackRed      : 1
% 19.45/8.24  
% 19.45/8.24  #Partial instantiations: 0
% 19.45/8.24  #Strategies tried      : 1
% 19.45/8.24  
% 19.45/8.24  Timing (in seconds)
% 19.45/8.24  ----------------------
% 19.45/8.24  Preprocessing        : 0.48
% 19.45/8.24  Parsing              : 0.26
% 19.45/8.24  CNF conversion       : 0.03
% 19.45/8.24  Main loop            : 6.70
% 19.45/8.24  Inferencing          : 1.05
% 19.45/8.24  Reduction            : 4.46
% 19.45/8.24  Demodulation         : 4.14
% 19.45/8.24  BG Simplification    : 0.16
% 19.45/8.24  Subsumption          : 0.82
% 19.45/8.24  Abstraction          : 0.25
% 19.45/8.24  MUC search           : 0.00
% 19.45/8.24  Cooper               : 0.00
% 19.45/8.24  Total                : 7.23
% 19.45/8.24  Index Insertion      : 0.00
% 19.45/8.24  Index Deletion       : 0.00
% 19.45/8.24  Index Matching       : 0.00
% 19.45/8.24  BG Taut test         : 0.00
%------------------------------------------------------------------------------