TSTP Solution File: KLE025+2 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE025+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 : 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 10:44:42 EDT 2023

% Result   : Theorem 5.01s 2.38s
% Output   : CNFRefutation 5.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   48 (  24 unt;  12 typ;   0 def)
%            Number of atoms       :   54 (  36 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  13   ~;  10   |;   3   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   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   :   47 (;  47   !;   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_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_180,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( test(X1)
          & test(X2) )
       => ( ( multiplication(multiplication(X1,X0),c(X2)) = zero )
         => ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(f_63,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_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_56,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

tff(f_68,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(c_10,plain,
    ! [A_8,B_9,C_10] : ( multiplication(multiplication(A_8,B_9),C_10) = multiplication(A_8,multiplication(B_9,C_10)) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

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

tff(c_57,plain,
    multiplication('#skF_3',multiplication('#skF_2','#skF_4')) != multiplication('#skF_3','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_50]) ).

tff(c_54,plain,
    test('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_180]) ).

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

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_271,plain,
    ! [X0_53,X1_54] :
      ( ( addition(X0_53,X1_54) = one )
      | ~ complement(X1_54,X0_53) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_277,plain,
    ! [X0_29] :
      ( ( addition(c(X0_29),X0_29) = one )
      | ~ test(X0_29) ),
    inference(resolution,[status(thm)],[c_42,c_271]) ).

tff(c_280,plain,
    ! [X0_29] :
      ( ( addition(X0_29,c(X0_29)) = one )
      | ~ test(X0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_277]) ).

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

tff(c_346,plain,
    ! [A_64,B_65,C_66] : ( addition(addition(A_64,B_65),C_66) = addition(A_64,addition(B_65,C_66)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_704,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_346]) ).

tff(c_1236,plain,
    ! [X0_88] :
      ( ( addition(X0_88,c(X0_88)) = addition(X0_88,one) )
      | ~ test(X0_88) ),
    inference(superposition,[status(thm),theory(equality)],[c_280,c_704]) ).

tff(c_1296,plain,
    ! [X0_89] :
      ( ( addition(X0_89,one) = one )
      | ~ test(X0_89)
      | ~ test(X0_89) ),
    inference(superposition,[status(thm),theory(equality)],[c_1236,c_280]) ).

tff(c_1302,plain,
    ( ( addition('#skF_4',one) = one )
    | ~ test('#skF_4') ),
    inference(resolution,[status(thm)],[c_54,c_1296]) ).

tff(c_1310,plain,
    addition('#skF_4',one) = one,
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_1302]) ).

tff(c_730,plain,
    ! [X0_29] :
      ( ( addition(X0_29,c(X0_29)) = addition(X0_29,one) )
      | ~ test(X0_29) ),
    inference(superposition,[status(thm),theory(equality)],[c_280,c_704]) ).

tff(c_6,plain,
    ! [A_6] : ( addition(A_6,zero) = A_6 ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

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

tff(c_1314,plain,
    ! [A_90,B_91,C_92] : ( addition(multiplication(A_90,B_91),multiplication(A_90,C_92)) = multiplication(A_90,addition(B_91,C_92)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_1423,plain,
    ! [B_91] : ( multiplication(multiplication('#skF_3','#skF_2'),addition(B_91,c('#skF_4'))) = addition(multiplication(multiplication('#skF_3','#skF_2'),B_91),zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_52,c_1314]) ).

tff(c_2492,plain,
    ! [B_107] : ( multiplication(multiplication('#skF_3','#skF_2'),addition(B_107,c('#skF_4'))) = multiplication('#skF_3',multiplication('#skF_2',B_107)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_6,c_1423]) ).

tff(c_2535,plain,
    ( ( multiplication(multiplication('#skF_3','#skF_2'),addition('#skF_4',one)) = multiplication('#skF_3',multiplication('#skF_2','#skF_4')) )
    | ~ test('#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_730,c_2492]) ).

tff(c_2573,plain,
    multiplication('#skF_3',multiplication('#skF_2','#skF_4')) = multiplication('#skF_3','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_12,c_1310,c_10,c_2535]) ).

tff(c_2575,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_57,c_2573]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % 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
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 23:47:15 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 5.01/2.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/2.39  
% 5.44/2.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.53/2.42  
% 5.53/2.42  Inference rules
% 5.53/2.42  ----------------------
% 5.53/2.42  #Ref     : 0
% 5.53/2.42  #Sup     : 602
% 5.53/2.42  #Fact    : 0
% 5.53/2.42  #Define  : 0
% 5.53/2.42  #Split   : 2
% 5.53/2.42  #Chain   : 0
% 5.53/2.42  #Close   : 0
% 5.53/2.42  
% 5.53/2.42  Ordering : KBO
% 5.53/2.42  
% 5.53/2.42  Simplification rules
% 5.53/2.42  ----------------------
% 5.53/2.42  #Subsume      : 56
% 5.53/2.42  #Demod        : 588
% 5.53/2.42  #Tautology    : 318
% 5.53/2.42  #SimpNegUnit  : 2
% 5.53/2.42  #BackRed      : 0
% 5.53/2.42  
% 5.53/2.42  #Partial instantiations: 0
% 5.53/2.42  #Strategies tried      : 1
% 5.53/2.42  
% 5.53/2.42  Timing (in seconds)
% 5.53/2.42  ----------------------
% 5.53/2.42  Preprocessing        : 0.52
% 5.53/2.42  Parsing              : 0.28
% 5.53/2.42  CNF conversion       : 0.03
% 5.53/2.42  Main loop            : 0.73
% 5.53/2.42  Inferencing          : 0.25
% 5.53/2.42  Reduction            : 0.28
% 5.53/2.42  Demodulation         : 0.22
% 5.53/2.42  BG Simplification    : 0.03
% 5.53/2.42  Subsumption          : 0.12
% 5.53/2.42  Abstraction          : 0.03
% 5.53/2.42  MUC search           : 0.00
% 5.53/2.42  Cooper               : 0.00
% 5.53/2.42  Total                : 1.30
% 5.53/2.42  Index Insertion      : 0.00
% 5.53/2.42  Index Deletion       : 0.00
% 5.53/2.42  Index Matching       : 0.00
% 5.53/2.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------