TSTP Solution File: KLE009+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE009+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 : n011.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 10:44:39 EDT 2023

% Result   : Theorem 3.86s 1.99s
% Output   : CNFRefutation 3.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   39 (  19 unt;  11 typ;   0 def)
%            Number of atoms       :   41 (  25 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   27 (  14   ~;   6   |;   3   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    6 (   2 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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   36 (;  36   !;   0   ?;   0   :)

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

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

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

tff(f_177,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( test(X1)
          & test(X0) )
       => ( one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(f_51,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

tff(f_126,axiom,
    ! [X0,X1] :
      ( test(X0)
     => ( ( c(X0) = X1 )
      <=> complement(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

tff(f_120,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_64,axiom,
    ! [A] : ( multiplication(one,A) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

tff(f_69,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(f_67,axiom,
    ! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

tff(f_53,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(c_54,plain,
    test('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_2,plain,
    ! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_42,plain,
    ! [X0_29] :
      ( complement(X0_29,c(X0_29))
      | ~ test(X0_29) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_266,plain,
    ! [X0_51,X1_52] :
      ( ( addition(X0_51,X1_52) = one )
      | ~ complement(X1_52,X0_51) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_269,plain,
    ! [X0_29] :
      ( ( addition(c(X0_29),X0_29) = one )
      | ~ test(X0_29) ),
    inference(resolution,[status(thm)],[c_42,c_266]) ).

tff(c_274,plain,
    ! [X0_29] :
      ( ( addition(X0_29,c(X0_29)) = one )
      | ~ test(X0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_269]) ).

tff(c_52,plain,
    test('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_14,plain,
    ! [A_12] : ( multiplication(one,A_12) = A_12 ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_483,plain,
    ! [X0_69] :
      ( ( addition(X0_69,c(X0_69)) = one )
      | ~ test(X0_69) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_269]) ).

tff(c_18,plain,
    ! [A_16,C_18,B_17] : ( addition(multiplication(A_16,C_18),multiplication(B_17,C_18)) = multiplication(addition(A_16,B_17),C_18) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_16,plain,
    ! [A_13,B_14,C_15] : ( addition(multiplication(A_13,B_14),multiplication(A_13,C_15)) = multiplication(A_13,addition(B_14,C_15)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_4,plain,
    ! [A_5,B_4,C_3] : ( addition(addition(A_5,B_4),C_3) = addition(A_5,addition(B_4,C_3)) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_50,plain,
    addition(addition(addition(multiplication('#skF_2','#skF_3'),multiplication('#skF_2',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))) != one,
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_55,plain,
    addition(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))) != one,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_50]) ).

tff(c_56,plain,
    addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),addition(multiplication(c('#skF_2'),'#skF_3'),multiplication(c('#skF_2'),c('#skF_3')))) != one,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_55]) ).

tff(c_57,plain,
    multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3'))) != one,
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_16,c_56]) ).

tff(c_500,plain,
    ( ( multiplication(one,addition('#skF_3',c('#skF_3'))) != one )
    | ~ test('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_483,c_57]) ).

tff(c_520,plain,
    addition('#skF_3',c('#skF_3')) != one,
    inference(demodulation,[status(thm),theory(equality)],[c_52,c_14,c_500]) ).

tff(c_636,plain,
    ~ test('#skF_3'),
    inference(superposition,[status(thm),theory(equality)],[c_274,c_520]) ).

tff(c_640,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_636]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KLE009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % 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
% 0.14/0.37  % Computer : n011.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Thu Aug  3 23:30:06 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 3.86/1.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.86/1.99  
% 3.86/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.02  
% 3.86/2.02  Inference rules
% 3.86/2.02  ----------------------
% 3.86/2.02  #Ref     : 0
% 3.86/2.02  #Sup     : 135
% 3.86/2.02  #Fact    : 0
% 3.86/2.02  #Define  : 0
% 3.86/2.02  #Split   : 2
% 3.86/2.02  #Chain   : 0
% 3.86/2.02  #Close   : 0
% 3.86/2.02  
% 3.86/2.02  Ordering : KBO
% 3.86/2.02  
% 3.86/2.02  Simplification rules
% 3.86/2.02  ----------------------
% 3.86/2.02  #Subsume      : 15
% 3.86/2.02  #Demod        : 58
% 3.86/2.02  #Tautology    : 84
% 3.86/2.02  #SimpNegUnit  : 1
% 3.86/2.02  #BackRed      : 0
% 3.86/2.02  
% 3.86/2.02  #Partial instantiations: 0
% 3.86/2.02  #Strategies tried      : 1
% 3.86/2.02  
% 3.86/2.02  Timing (in seconds)
% 3.86/2.02  ----------------------
% 3.86/2.02  Preprocessing        : 0.53
% 3.86/2.02  Parsing              : 0.28
% 3.86/2.02  CNF conversion       : 0.03
% 3.86/2.02  Main loop            : 0.39
% 3.86/2.02  Inferencing          : 0.15
% 3.86/2.02  Reduction            : 0.13
% 3.86/2.02  Demodulation         : 0.09
% 3.86/2.02  BG Simplification    : 0.02
% 3.86/2.02  Subsumption          : 0.08
% 3.86/2.02  Abstraction          : 0.02
% 3.86/2.02  MUC search           : 0.00
% 3.86/2.02  Cooper               : 0.00
% 3.86/2.02  Total                : 0.97
% 3.86/2.02  Index Insertion      : 0.00
% 3.86/2.02  Index Deletion       : 0.00
% 3.86/2.02  Index Matching       : 0.00
% 3.86/2.02  BG Taut test         : 0.00
%------------------------------------------------------------------------------