TSTP Solution File: KLE144+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KLE144+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 : n015.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 13.91s 4.49s
% Output   : CNFRefutation 13.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   56 (  39 unt;   8 typ;   0 def)
%            Number of atoms       :   57 (  37 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   18 (   9   ~;   7   |;   0   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   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   :   76 (;  76   !;   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_52,axiom,
    ! [A,B] : ( addition(A,B) = addition(B,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

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_56,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

tff(f_76,axiom,
    ! [A] : ( addition(one,multiplication(A,star(A))) = star(A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).

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/KLE004+0.ax',distributivity2) ).

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

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_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_10731,plain,
    ! [A_195,B_196] :
      ( leq(A_195,multiplication(strong_iteration(one),B_196))
      | ~ leq(A_195,addition(A_195,B_196)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1299]) ).

tff(c_10827,plain,
    ! [A_33,B_196] :
      ( leq(A_33,multiplication(strong_iteration(one),B_196))
      | ( addition(A_33,addition(A_33,B_196)) != addition(A_33,B_196) ) ),
    inference(resolution,[status(thm)],[c_38,c_10731]) ).

tff(c_10856,plain,
    ! [A_197,B_198] : leq(A_197,multiplication(strong_iteration(one),B_198)),
    inference(demodulation,[status(thm),theory(equality)],[c_417,c_10827]) ).

tff(c_10887,plain,
    ! [A_199] : leq(A_199,strong_iteration(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_10856]) ).

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_10902,plain,
    ! [A_200] : ( addition(A_200,strong_iteration(one)) = strong_iteration(one) ),
    inference(resolution,[status(thm)],[c_10887,c_36]) ).

tff(c_11138,plain,
    ! [A_1] : ( addition(strong_iteration(one),A_1) = strong_iteration(one) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_10902]) ).

tff(c_10880,plain,
    ! [A_197] : leq(A_197,strong_iteration(one)),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_10856]) ).

tff(c_10901,plain,
    ! [A_199] : ( addition(A_199,strong_iteration(one)) = strong_iteration(one) ),
    inference(resolution,[status(thm)],[c_10887,c_36]) ).

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_6,plain,
    ! [A_6] : ( addition(A_6,zero) = A_6 ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

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

tff(c_22,plain,
    ! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = star(A_20) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_3677,plain,
    ! [B_126,A_127,B_128] : ( addition(B_126,addition(A_127,B_128)) = addition(A_127,addition(B_128,B_126)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_343]) ).

tff(c_4191,plain,
    ! [A_129,B_130] : ( addition(zero,addition(A_129,B_130)) = addition(B_130,A_129) ),
    inference(superposition,[status(thm),theory(equality)],[c_130,c_3677]) ).

tff(c_4341,plain,
    ! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = addition(zero,star(A_20)) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_4191]) ).

tff(c_4406,plain,
    ! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = star(A_20) ),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_4341]) ).

tff(c_648,plain,
    ! [A_62,C_63,B_64] : ( addition(multiplication(A_62,C_63),multiplication(B_64,C_63)) = multiplication(addition(A_62,B_64),C_63) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_694,plain,
    ! [A_62,A_12] : ( multiplication(addition(A_62,one),A_12) = addition(multiplication(A_62,A_12),A_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_648]) ).

tff(c_18341,plain,
    ! [A_301] : ( multiplication(addition(A_301,one),strong_iteration(one)) = strong_iteration(one) ),
    inference(superposition,[status(thm),theory(equality)],[c_694,c_10902]) ).

tff(c_18447,plain,
    ! [A_20] : ( multiplication(star(A_20),strong_iteration(one)) = strong_iteration(one) ),
    inference(superposition,[status(thm),theory(equality)],[c_4406,c_18341]) ).

tff(c_20482,plain,
    ! [C_319,A_320,A_321] :
      ( leq(C_319,multiplication(strong_iteration(A_320),A_321))
      | ~ leq(C_319,addition(A_321,multiplication(A_320,C_319))) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1299]) ).

tff(c_20494,plain,
    ! [A_20,A_321] :
      ( leq(strong_iteration(one),multiplication(strong_iteration(star(A_20)),A_321))
      | ~ leq(strong_iteration(one),addition(A_321,strong_iteration(one))) ),
    inference(superposition,[status(thm),theory(equality)],[c_18447,c_20482]) ).

tff(c_21852,plain,
    ! [A_331,A_332] : leq(strong_iteration(one),multiplication(strong_iteration(star(A_331)),A_332)),
    inference(demodulation,[status(thm),theory(equality)],[c_10880,c_10901,c_20494]) ).

tff(c_21892,plain,
    ! [A_333] : leq(strong_iteration(one),strong_iteration(star(A_333))),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_21852]) ).

tff(c_21895,plain,
    ! [A_333] : ( addition(strong_iteration(one),strong_iteration(star(A_333))) = strong_iteration(star(A_333)) ),
    inference(resolution,[status(thm)],[c_21892,c_36]) ).

tff(c_21905,plain,
    ! [A_333] : ( strong_iteration(star(A_333)) = strong_iteration(one) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11138,c_21895]) ).

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

tff(c_21918,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_21905,c_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KLE144+1 : 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
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 23:47:29 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 13.91/4.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.91/4.49  
% 13.91/4.49  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.91/4.53  
% 13.91/4.53  Inference rules
% 13.91/4.53  ----------------------
% 13.91/4.53  #Ref     : 0
% 13.91/4.53  #Sup     : 5724
% 13.91/4.53  #Fact    : 0
% 13.91/4.53  #Define  : 0
% 13.91/4.53  #Split   : 3
% 13.91/4.53  #Chain   : 0
% 13.91/4.53  #Close   : 0
% 13.91/4.53  
% 13.91/4.53  Ordering : KBO
% 13.91/4.53  
% 13.91/4.53  Simplification rules
% 13.91/4.53  ----------------------
% 13.91/4.53  #Subsume      : 1650
% 13.91/4.53  #Demod        : 4850
% 13.91/4.53  #Tautology    : 1836
% 13.91/4.53  #SimpNegUnit  : 43
% 13.91/4.53  #BackRed      : 16
% 13.91/4.53  
% 13.91/4.53  #Partial instantiations: 0
% 13.91/4.53  #Strategies tried      : 1
% 13.91/4.53  
% 13.91/4.53  Timing (in seconds)
% 13.91/4.53  ----------------------
% 13.91/4.53  Preprocessing        : 0.49
% 13.91/4.53  Parsing              : 0.26
% 13.91/4.53  CNF conversion       : 0.03
% 13.91/4.53  Main loop            : 2.96
% 13.91/4.53  Inferencing          : 0.71
% 13.91/4.53  Reduction            : 1.44
% 13.91/4.53  Demodulation         : 1.21
% 13.91/4.53  BG Simplification    : 0.07
% 13.91/4.53  Subsumption          : 0.52
% 13.91/4.53  Abstraction          : 0.10
% 13.91/4.53  MUC search           : 0.00
% 13.91/4.53  Cooper               : 0.00
% 13.91/4.53  Total                : 3.50
% 13.91/4.53  Index Insertion      : 0.00
% 13.91/4.53  Index Deletion       : 0.00
% 13.91/4.53  Index Matching       : 0.00
% 13.91/4.53  BG Taut test         : 0.00
%------------------------------------------------------------------------------