TSTP Solution File: KLE026+2 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE026+2 : 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/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 : n012.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 10:44:42 EDT 2023

% Result   : Theorem 6.17s 2.49s
% Output   : CNFRefutation 6.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   47 (  23 unt;  12 typ;   0 def)
%            Number of atoms       :   53 (  33 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   30 (  12   ~;   9   |;   3   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (;  48   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ leq > complement > test > multiplication > addition > #nlpp > c > zero > one > #skF_1 > #skF_2 > #skF_3 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_1',type,
    '#skF_1': $i > $i ).

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

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $i ).

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

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

tff('#skF_4',type,
    '#skF_4': $i ).

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

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

tff(f_80,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> ( addition(A,B) = B ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).

tff(f_180,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( test(X1)
          & test(X2) )
       => ( ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) )
         => leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

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

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

tff(f_127,axiom,
    ! [X0,X1] :
      ( test(X0)
     => ( ( c(X0) = X1 )
      <=> complement(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

tff(f_121,axiom,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( ( multiplication(X0,X1) = zero )
        & ( multiplication(X1,X0) = zero )
        & ( addition(X0,X1) = one ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).

tff(f_58,axiom,
    ! [A] : ( addition(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

tff(f_54,axiom,
    ! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).

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

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

tff(c_279,plain,
    ! [A_53,B_54] :
      ( leq(A_53,B_54)
      | ( addition(A_53,B_54) != B_54 ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_50,plain,
    ~ leq(multiplication('#skF_3','#skF_2'),multiplication('#skF_2','#skF_4')),
    inference(cnfTransformation,[status(thm)],[f_180]) ).

tff(c_283,plain,
    addition(multiplication('#skF_3','#skF_2'),multiplication('#skF_2','#skF_4')) != multiplication('#skF_2','#skF_4'),
    inference(resolution,[status(thm)],[c_279,c_50]) ).

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

tff(c_56,plain,
    test('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_180]) ).

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_42,plain,
    ! [X0_29] :
      ( complement(X0_29,c(X0_29))
      | ~ test(X0_29) ),
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_269,plain,
    ! [X0_51,X1_52] :
      ( ( addition(X0_51,X1_52) = one )
      | ~ complement(X1_52,X0_51) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_275,plain,
    ! [X0_29] :
      ( ( addition(c(X0_29),X0_29) = one )
      | ~ test(X0_29) ),
    inference(resolution,[status(thm)],[c_42,c_269]) ).

tff(c_278,plain,
    ! [X0_29] :
      ( ( addition(X0_29,c(X0_29)) = one )
      | ~ test(X0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_275]) ).

tff(c_8,plain,
    ! [A_7] : ( addition(A_7,A_7) = A_7 ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_386,plain,
    ! [A_65,B_66,C_67] : ( addition(addition(A_65,B_66),C_67) = addition(A_65,addition(B_66,C_67)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_696,plain,
    ! [A_75,C_76] : ( addition(A_75,addition(A_75,C_76)) = addition(A_75,C_76) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_386]) ).

tff(c_1694,plain,
    ! [X0_95] :
      ( ( addition(X0_95,c(X0_95)) = addition(X0_95,one) )
      | ~ test(X0_95) ),
    inference(superposition,[status(thm),theory(equality)],[c_278,c_696]) ).

tff(c_1828,plain,
    ! [X0_97] :
      ( ( addition(X0_97,one) = one )
      | ~ test(X0_97)
      | ~ test(X0_97) ),
    inference(superposition,[status(thm),theory(equality)],[c_1694,c_278]) ).

tff(c_1836,plain,
    ( ( addition('#skF_3',one) = one )
    | ~ test('#skF_3') ),
    inference(resolution,[status(thm)],[c_56,c_1828]) ).

tff(c_1845,plain,
    addition('#skF_3',one) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_1836]) ).

tff(c_503,plain,
    ! [A_69,B_70,C_71] : ( multiplication(multiplication(A_69,B_70),C_71) = multiplication(A_69,multiplication(B_70,C_71)) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_52,plain,
    multiplication(multiplication('#skF_3','#skF_2'),'#skF_4') = multiplication('#skF_3','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_180]) ).

tff(c_520,plain,
    multiplication('#skF_3',multiplication('#skF_2','#skF_4')) = multiplication('#skF_3','#skF_2'),
    inference(superposition,[status(thm),theory(equality)],[c_503,c_52]) ).

tff(c_773,plain,
    ! [A_77,C_78,B_79] : ( addition(multiplication(A_77,C_78),multiplication(B_79,C_78)) = multiplication(addition(A_77,B_79),C_78) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_4221,plain,
    ! [B_127,A_128] : ( multiplication(addition(one,B_127),A_128) = addition(A_128,multiplication(B_127,A_128)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_773]) ).

tff(c_4390,plain,
    multiplication(addition(one,'#skF_3'),multiplication('#skF_2','#skF_4')) = addition(multiplication('#skF_2','#skF_4'),multiplication('#skF_3','#skF_2')),
    inference(superposition,[status(thm),theory(equality)],[c_520,c_4221]) ).

tff(c_4487,plain,
    addition(multiplication('#skF_3','#skF_2'),multiplication('#skF_2','#skF_4')) = multiplication('#skF_2','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_1845,c_2,c_2,c_4390]) ).

tff(c_4489,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_283,c_4487]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : KLE026+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % 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
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 23:22:52 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 6.17/2.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/2.50  
% 6.17/2.50  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.17/2.53  
% 6.17/2.53  Inference rules
% 6.17/2.53  ----------------------
% 6.17/2.53  #Ref     : 0
% 6.17/2.53  #Sup     : 1060
% 6.17/2.53  #Fact    : 0
% 6.17/2.53  #Define  : 0
% 6.17/2.53  #Split   : 2
% 6.17/2.53  #Chain   : 0
% 6.17/2.53  #Close   : 0
% 6.17/2.53  
% 6.17/2.53  Ordering : KBO
% 6.17/2.53  
% 6.17/2.53  Simplification rules
% 6.17/2.53  ----------------------
% 6.17/2.53  #Subsume      : 167
% 6.17/2.53  #Demod        : 1093
% 6.17/2.53  #Tautology    : 507
% 6.17/2.53  #SimpNegUnit  : 4
% 6.17/2.53  #BackRed      : 0
% 6.17/2.53  
% 6.17/2.53  #Partial instantiations: 0
% 6.17/2.53  #Strategies tried      : 1
% 6.17/2.53  
% 6.17/2.53  Timing (in seconds)
% 6.17/2.53  ----------------------
% 6.17/2.53  Preprocessing        : 0.52
% 6.17/2.53  Parsing              : 0.28
% 6.17/2.53  CNF conversion       : 0.03
% 6.17/2.53  Main loop            : 0.94
% 6.17/2.53  Inferencing          : 0.31
% 6.17/2.53  Reduction            : 0.38
% 6.17/2.53  Demodulation         : 0.31
% 6.17/2.53  BG Simplification    : 0.04
% 6.17/2.53  Subsumption          : 0.15
% 6.17/2.53  Abstraction          : 0.04
% 6.17/2.53  MUC search           : 0.00
% 6.17/2.53  Cooper               : 0.00
% 6.17/2.53  Total                : 1.51
% 6.17/2.53  Index Insertion      : 0.00
% 6.17/2.53  Index Deletion       : 0.00
% 6.17/2.53  Index Matching       : 0.00
% 6.17/2.53  BG Taut test         : 0.00
%------------------------------------------------------------------------------