TSTP Solution File: KLE089+1 by Beagle---0.9.47

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.47
% Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xms512M -Xmx4G -Xss10M -XX:MaxPermSize=384M -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 : n093.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.75MB
% OS       : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Tue Jan 17 17:57:08 EST 2017

% Result   : Theorem 5.29s
% Output   : CNFRefutation 5.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   25 (  13 unt;  11 typ;   0 def)
%            Number of atoms       :   15 (  14 equ)
%            Maximal formula atoms :    2 (   0 avg)
%            Number of connectives :    3 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   7   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   16 (  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Beagle---0.9.47 format not known, defaulting to TPTP
%$ leq > multiplication > addition > #nlpp > domain > codomain > coantidomain > antidomain > zero > one > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

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

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

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

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

tff(f_133,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( multiplication(domain(X0),X1) = zero )
       <= ( addition(domain(X0),antidomain(X1)) = antidomain(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

tff(f_111,axiom,
    ! [X0] : ( multiplication(antidomain(X0),X0) = zero ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).

tff(f_56,axiom,
    ! [A] : ( addition(A,zero) = A ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

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/KLE001+0.ax',left_distributivity) ).

tff(c_44,plain,
    multiplication(domain('#skF_1'),'#skF_2') != zero,
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_28,plain,
    ! [X0_23] : ( multiplication(antidomain(X0_23),X0_23) = zero ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_46,plain,
    addition(domain('#skF_1'),antidomain('#skF_2')) = antidomain('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_133]) ).

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

tff(c_1446,plain,
    ! [A_79,C_80,B_81] : ( addition(multiplication(A_79,C_80),multiplication(B_81,C_80)) = multiplication(addition(A_79,B_81),C_80) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_1524,plain,
    ! [A_79,X0_23] : ( multiplication(addition(A_79,antidomain(X0_23)),X0_23) = addition(multiplication(A_79,X0_23),zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_1446]) ).

tff(c_5199,plain,
    ! [A_127,X0_128] : ( multiplication(addition(A_127,antidomain(X0_128)),X0_128) = multiplication(A_127,X0_128) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1524]) ).

tff(c_5284,plain,
    multiplication(domain('#skF_1'),'#skF_2') = multiplication(antidomain('#skF_2'),'#skF_2'),
    inference(superposition,[status(thm),theory(equality)],[c_46,c_5199]) ).

tff(c_5325,plain,
    multiplication(domain('#skF_1'),'#skF_2') = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_5284]) ).

tff(c_5327,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_44,c_5325]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : java -Xms512M -Xmx4G -Xss10M -XX:MaxPermSize=384M -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
% 0.03/0.23  % Computer : n093.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.75MB
% 0.03/0.23  % OS       : Linux 3.10.0-327.36.3.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Sat Jan 14 16:32:17 CST 2017
% 0.03/0.23  % CPUTime  : 
% 0.03/0.24  OpenJDK 64-Bit Server VM warning: ignoring option MaxPermSize=384M; support was removed in 8.0
% 5.29/2.32  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/2.33  
% 5.29/2.33  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.29/2.34  % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/2.34  
% 5.29/2.34  Inference rules
% 5.29/2.34  ----------------------
% 5.29/2.34  #Ref   : 0
% 5.29/2.34  #Sup   : 1329
% 5.29/2.34  #Fact  : 0
% 5.29/2.34  #Define: 0
% 5.29/2.34  #Split : 0
% 5.29/2.34  #Chain : 0
% 5.29/2.34  #Close : 0
% 5.29/2.34  
% 5.29/2.34  Ordering : KBO
% 5.29/2.34  
% 5.29/2.34  Simplification rules
% 5.29/2.34  ----------------------
% 5.29/2.34  #Subsume    : 0
% 5.29/2.34  #Demod      : 1889
% 5.29/2.34  #Tautology  : 895
% 5.29/2.34  #SimpNegUnit: 1
% 5.29/2.34  #BackRed    : 16
% 5.29/2.34  
% 5.29/2.34  #Partial instantiations: 0
% 5.29/2.34  #Strategies tried    : 1
% 5.29/2.34  
% 5.29/2.34  Timing (in seconds)
% 5.29/2.34  ----------------------
% 5.29/2.34  Preprocessing      : 0.39
% 5.29/2.34  Parsing            : 0.22
% 5.29/2.34  CNF conversion     : 0.02
% 5.29/2.34  Main loop          : 1.32
% 5.29/2.34  Inferencing        : 0.38
% 5.29/2.34  Reduction          : 0.63
% 5.29/2.34  Demodulation       : 0.53
% 5.29/2.34  BG Simplification  : 0.04
% 5.29/2.34  Subsumption        : 0.19
% 5.29/2.34  Abstraction        : 0.06
% 5.29/2.34  MUC search         : 0.00
% 5.29/2.34  Cooper             : 0.00
% 5.29/2.34  Total              : 1.74
% 5.29/2.34  Index Insertion    : 0.00
% 5.29/2.34  Index Deletion     : 0.00
% 5.29/2.34  Index Matching     : 0.00
% 5.29/2.34  BG Taut test       : 0.00
%------------------------------------------------------------------------------