TSTP Solution File: KLE137+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE137+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/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 : n007.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 10:44:54 EDT 2023

% Result   : Theorem 10.49s 3.52s
% Output   : CNFRefutation 10.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   28 (  14 unt;   8 typ;   0 def)
%            Number of atoms       :   26 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   12 (   6   ~;   4   |;   0   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 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   :   32 (;  32   !;   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/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

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

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

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

tff(f_105,negated_conjecture,
    ~ ! [X0] : leq(X0,strong_iteration(one)),
    file('/export/starexec/sandbox/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_371,plain,
    ! [A_52,B_53,C_54] : ( addition(addition(A_52,B_53),C_54) = addition(A_52,addition(B_53,C_54)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_448,plain,
    ! [A_7,C_54] : ( addition(A_7,addition(A_7,C_54)) = addition(A_7,C_54) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_371]) ).

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_1264,plain,
    ! [C_80,A_81,B_82] :
      ( leq(C_80,multiplication(strong_iteration(A_81),B_82))
      | ~ leq(C_80,addition(multiplication(A_81,C_80),B_82)) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_11851,plain,
    ! [A_203,B_204] :
      ( leq(A_203,multiplication(strong_iteration(one),B_204))
      | ~ leq(A_203,addition(A_203,B_204)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1264]) ).

tff(c_11952,plain,
    ! [A_33,B_204] :
      ( leq(A_33,multiplication(strong_iteration(one),B_204))
      | ( addition(A_33,addition(A_33,B_204)) != addition(A_33,B_204) ) ),
    inference(resolution,[status(thm)],[c_38,c_11851]) ).

tff(c_11987,plain,
    ! [A_205,B_206] : leq(A_205,multiplication(strong_iteration(one),B_206)),
    inference(demodulation,[status(thm),theory(equality)],[c_448,c_11952]) ).

tff(c_12022,plain,
    ! [A_205] : leq(A_205,strong_iteration(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_11987]) ).

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

tff(c_12038,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12022,c_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : KLE137+1 : 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
% 0.18/0.37  % Computer : n007.cluster.edu
% 0.18/0.37  % Model    : x86_64 x86_64
% 0.18/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37  % Memory   : 8042.1875MB
% 0.18/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37  % CPULimit : 300
% 0.18/0.37  % WCLimit  : 300
% 0.18/0.37  % DateTime : Thu Aug  3 23:08:24 EDT 2023
% 0.18/0.37  % CPUTime  : 
% 10.49/3.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.52/3.53  
% 10.52/3.53  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.52/3.58  
% 10.52/3.58  Inference rules
% 10.52/3.58  ----------------------
% 10.52/3.58  #Ref     : 0
% 10.52/3.58  #Sup     : 3126
% 10.52/3.58  #Fact    : 0
% 10.52/3.58  #Define  : 0
% 10.52/3.58  #Split   : 1
% 10.52/3.58  #Chain   : 0
% 10.52/3.58  #Close   : 0
% 10.52/3.58  
% 10.52/3.58  Ordering : KBO
% 10.52/3.58  
% 10.52/3.58  Simplification rules
% 10.52/3.58  ----------------------
% 10.52/3.58  #Subsume      : 414
% 10.52/3.58  #Demod        : 2817
% 10.52/3.58  #Tautology    : 1230
% 10.52/3.58  #SimpNegUnit  : 25
% 10.52/3.58  #BackRed      : 5
% 10.52/3.58  
% 10.52/3.58  #Partial instantiations: 0
% 10.52/3.58  #Strategies tried      : 1
% 10.52/3.58  
% 10.52/3.58  Timing (in seconds)
% 10.52/3.58  ----------------------
% 10.52/3.58  Preprocessing        : 0.50
% 10.52/3.58  Parsing              : 0.28
% 10.52/3.58  CNF conversion       : 0.03
% 10.52/3.58  Main loop            : 1.97
% 10.52/3.58  Inferencing          : 0.55
% 10.52/3.58  Reduction            : 0.92
% 10.52/3.58  Demodulation         : 0.77
% 10.52/3.58  BG Simplification    : 0.06
% 10.52/3.58  Subsumption          : 0.33
% 10.52/3.58  Abstraction          : 0.07
% 10.52/3.58  MUC search           : 0.00
% 10.52/3.58  Cooper               : 0.00
% 10.52/3.58  Total                : 2.55
% 10.52/3.58  Index Insertion      : 0.00
% 10.52/3.58  Index Deletion       : 0.00
% 10.52/3.58  Index Matching       : 0.00
% 10.52/3.58  BG Taut test         : 0.00
%------------------------------------------------------------------------------