TSTP Solution File: KLE142+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE142+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 : n024.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 10:44:55 EDT 2023

% Result   : Theorem 12.00s 4.06s
% Output   : CNFRefutation 12.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   53 (  35 unt;   8 typ;   0 def)
%            Number of atoms       :   55 (  33 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   20 (  10   ~;   8   |;   0   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   69 (;  69   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > strong_iteration > star > zero > one > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

tff(addition,type,
    addition: ( $i * $i ) > $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_63,axiom,
    ! [A] : ( multiplication(A,one) = A ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

tff(f_58,axiom,
    ! [A] : ( addition(A,A) = A ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).

tff(f_54,axiom,
    ! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).

tff(f_100,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> ( addition(A,B) = B ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).

tff(f_65,axiom,
    ! [A] : ( multiplication(one,A) = A ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).

tff(f_93,axiom,
    ! [A,B,C] :
      ( leq(C,addition(multiplication(A,C),B))
     => leq(C,multiplication(strong_iteration(A),B)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).

tff(f_52,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

tff(f_56,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

tff(f_95,axiom,
    ! [A] : ( strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).

tff(f_105,negated_conjecture,
    ~ ! [X0] : ( strong_iteration(strong_iteration(X0)) = strong_iteration(one) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

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

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

tff(c_343,plain,
    ! [A_51,B_52,C_53] : ( addition(addition(A_51,B_52),C_53) = addition(A_51,addition(B_52,C_53)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_417,plain,
    ! [A_7,C_53] : ( addition(A_7,addition(A_7,C_53)) = addition(A_7,C_53) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_343]) ).

tff(c_38,plain,
    ! [A_33,B_34] :
      ( leq(A_33,B_34)
      | ( addition(A_33,B_34) != B_34 ) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

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

tff(c_1299,plain,
    ! [C_87,A_88,B_89] :
      ( leq(C_87,multiplication(strong_iteration(A_88),B_89))
      | ~ leq(C_87,addition(multiplication(A_88,C_87),B_89)) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_10048,plain,
    ! [A_188,B_189] :
      ( leq(A_188,multiplication(strong_iteration(one),B_189))
      | ~ leq(A_188,addition(A_188,B_189)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1299]) ).

tff(c_10144,plain,
    ! [A_33,B_189] :
      ( leq(A_33,multiplication(strong_iteration(one),B_189))
      | ( addition(A_33,addition(A_33,B_189)) != addition(A_33,B_189) ) ),
    inference(resolution,[status(thm)],[c_38,c_10048]) ).

tff(c_10173,plain,
    ! [A_190,B_191] : leq(A_190,multiplication(strong_iteration(one),B_191)),
    inference(demodulation,[status(thm),theory(equality)],[c_417,c_10144]) ).

tff(c_10204,plain,
    ! [A_192] : leq(A_192,strong_iteration(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_10173]) ).

tff(c_36,plain,
    ! [A_33,B_34] :
      ( ( addition(A_33,B_34) = B_34 )
      | ~ leq(A_33,B_34) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_10219,plain,
    ! [A_193] : ( addition(A_193,strong_iteration(one)) = strong_iteration(one) ),
    inference(resolution,[status(thm)],[c_10204,c_36]) ).

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_10377,plain,
    ! [A_193] : ( addition(strong_iteration(one),A_193) = strong_iteration(one) ),
    inference(superposition,[status(thm),theory(equality)],[c_10219,c_2]) ).

tff(c_10197,plain,
    ! [A_190] : leq(A_190,strong_iteration(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_10173]) ).

tff(c_32,plain,
    ! [C_31,A_29,B_30] :
      ( leq(C_31,multiplication(strong_iteration(A_29),B_30))
      | ~ leq(C_31,addition(multiplication(A_29,C_31),B_30)) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_10339,plain,
    ! [C_31,A_29] :
      ( leq(C_31,multiplication(strong_iteration(A_29),strong_iteration(one)))
      | ~ leq(C_31,strong_iteration(one)) ),
    inference(superposition,[status(thm),theory(equality)],[c_10219,c_32]) ).

tff(c_11417,plain,
    ! [C_203,A_204] : leq(C_203,multiplication(strong_iteration(A_204),strong_iteration(one))),
    inference(demodulation,[status(thm),theory(equality)],[c_10197,c_10339]) ).

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

tff(c_1338,plain,
    ! [C_87,A_88] :
      ( leq(C_87,multiplication(strong_iteration(A_88),zero))
      | ~ leq(C_87,multiplication(A_88,C_87)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1299]) ).

tff(c_17715,plain,
    ! [A_294] : leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A_294)),zero)),
    inference(resolution,[status(thm)],[c_11417,c_1338]) ).

tff(c_17718,plain,
    ! [A_294] : ( addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A_294)),zero)) = multiplication(strong_iteration(strong_iteration(A_294)),zero) ),
    inference(resolution,[status(thm)],[c_17715,c_36]) ).

tff(c_17909,plain,
    ! [A_298] : ( multiplication(strong_iteration(strong_iteration(A_298)),zero) = strong_iteration(one) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10377,c_17718]) ).

tff(c_114,plain,
    ! [B_40,A_41] : ( addition(B_40,A_41) = addition(A_41,B_40) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_130,plain,
    ! [A_41] : ( addition(zero,A_41) = A_41 ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_6]) ).

tff(c_34,plain,
    ! [A_32] : ( addition(star(A_32),multiplication(strong_iteration(A_32),zero)) = strong_iteration(A_32) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_2312,plain,
    ! [C_105,A_106,B_107] : ( addition(C_105,addition(A_106,B_107)) = addition(A_106,addition(B_107,C_105)) ),
    inference(superposition,[status(thm),theory(equality)],[c_343,c_2]) ).

tff(c_2735,plain,
    ! [A_108,C_109] : ( addition(zero,addition(A_108,C_109)) = addition(C_109,A_108) ),
    inference(superposition,[status(thm),theory(equality)],[c_130,c_2312]) ).

tff(c_2858,plain,
    ! [A_32] : ( addition(multiplication(strong_iteration(A_32),zero),star(A_32)) = addition(zero,strong_iteration(A_32)) ),
    inference(superposition,[status(thm),theory(equality)],[c_34,c_2735]) ).

tff(c_2921,plain,
    ! [A_32] : ( addition(multiplication(strong_iteration(A_32),zero),star(A_32)) = strong_iteration(A_32) ),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_2858]) ).

tff(c_17945,plain,
    ! [A_298] : ( addition(strong_iteration(one),star(strong_iteration(A_298))) = strong_iteration(strong_iteration(A_298)) ),
    inference(superposition,[status(thm),theory(equality)],[c_17909,c_2921]) ).

tff(c_18004,plain,
    ! [A_298] : ( strong_iteration(strong_iteration(A_298)) = strong_iteration(one) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10377,c_17945]) ).

tff(c_40,plain,
    strong_iteration(strong_iteration('#skF_1')) != strong_iteration(one),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_18025,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_18004,c_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KLE142+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % 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
% 0.14/0.36  % Computer : n024.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 23:29:15 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 12.00/4.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.00/4.07  
% 12.00/4.07  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.00/4.11  
% 12.00/4.11  Inference rules
% 12.00/4.11  ----------------------
% 12.00/4.11  #Ref     : 0
% 12.00/4.11  #Sup     : 4723
% 12.00/4.11  #Fact    : 0
% 12.00/4.11  #Define  : 0
% 12.00/4.11  #Split   : 3
% 12.00/4.11  #Chain   : 0
% 12.00/4.11  #Close   : 0
% 12.00/4.11  
% 12.00/4.11  Ordering : KBO
% 12.00/4.11  
% 12.00/4.11  Simplification rules
% 12.00/4.11  ----------------------
% 12.00/4.11  #Subsume      : 1206
% 12.00/4.11  #Demod        : 3923
% 12.00/4.11  #Tautology    : 1539
% 12.00/4.11  #SimpNegUnit  : 28
% 12.00/4.11  #BackRed      : 9
% 12.00/4.11  
% 12.00/4.11  #Partial instantiations: 0
% 12.00/4.11  #Strategies tried      : 1
% 12.00/4.11  
% 12.00/4.11  Timing (in seconds)
% 12.00/4.11  ----------------------
% 12.00/4.11  Preprocessing        : 0.48
% 12.00/4.11  Parsing              : 0.26
% 12.00/4.11  CNF conversion       : 0.03
% 12.00/4.11  Main loop            : 2.55
% 12.00/4.11  Inferencing          : 0.62
% 12.00/4.11  Reduction            : 1.24
% 12.00/4.11  Demodulation         : 1.05
% 12.00/4.11  BG Simplification    : 0.08
% 12.00/4.11  Subsumption          : 0.41
% 12.00/4.11  Abstraction          : 0.08
% 12.00/4.11  MUC search           : 0.00
% 12.00/4.11  Cooper               : 0.00
% 12.00/4.11  Total                : 3.09
% 12.00/4.11  Index Insertion      : 0.00
% 12.00/4.11  Index Deletion       : 0.00
% 12.00/4.11  Index Matching       : 0.00
% 12.00/4.11  BG Taut test         : 0.00
%------------------------------------------------------------------------------