TSTP Solution File: ARI673_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ARI673_1 : TPTP v8.1.2. Released v6.3.0.
% 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 : n013.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 10:34:13 EDT 2023

% Result   : Theorem 3.80s 2.11s
% Output   : CNFRefutation 3.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   47 (  30 unt;   2 typ;   0 def)
%            Number of atoms       :   65 (  62 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   39 (  19   ~;  18   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number arithmetic     :  150 (   0 atm;  73 fun;  55 num;  22 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   2 usr;   4 con; 0-2 aty)
%            Number of variables   :   22 (;  22   !;   0   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
%$ #nlpp

%Foreground sorts:

%Background operators:
tff('#skE_1',type,
    '#skE_1': $int ).

tff(a,type,
    a: $int ).

%Foreground operators:

tff(f_228,axiom,
    ! [C: $int,B: $int] :
      ( ( $product(C,B) = C )
    <=> ( ( C = 0 )
        | ( B = 1 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).

tff(f_212,axiom,
    ! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
    file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).

tff(f_220,axiom,
    ! [A: $int,B: $int] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
    file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',minus_mult_left) ).

tff(f_35,negated_conjecture,
    ~ ( ( $product(a,a) = 1 )
    <=> ( ( a = $uminus(1) )
        | ( a = 1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

tff(f_209,axiom,
    ! [M: $int,N: $int] : ( $product($sum(1,M),N) = $sum(N,$product(M,N)) ),
    file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_def_2) ).

tff(c_50,plain,
    ! [C_23: $int] : ( $product(C_23,1) = C_23 ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_57,plain,
    ! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_52,plain,
    ! [A_17: $int,B_18: $int,X_45: $int] :
      ( ( $uminus($product(A_17,B_18)) = $product(X_45,B_18) )
      | ( X_45 != $uminus(A_17) ) ),
    inference(cnfTransformation,[status(thm)],[f_220]) ).

tff(c_54,plain,
    ! [X_45: $int,B_18: $int,A_17: $int] :
      ( ( $uminus($product(X_45,B_18)) = $product(A_17,B_18) )
      | ( X_45 != $uminus(A_17) ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_52]) ).

tff(c_47,plain,
    ( ( $product(a,a) != 1 )
    | ( a != 1 ) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_69,plain,
    $product(a,a) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_47]) ).

tff(c_62,plain,
    ( ( $product(a,a) != 1 )
    | ( a != 1 ) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_76,plain,
    ( ( '#skE_1' != 1 )
    | ( a != 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_69,c_62]) ).

tff(c_78,plain,
    a != 1,
    inference(splitLeft,[status(thm)],[c_76]) ).

tff(c_80,plain,
    $product(a,a) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_47]) ).

tff(c_43,plain,
    ( ( $product(a,a) != 1 )
    | ( a != $uminus(1) ) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_226,plain,
    ( ( '#skE_1' != 1 )
    | ( a != $uminus(1) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_43]) ).

tff(c_228,plain,
    a != $uminus(1),
    inference(splitLeft,[status(thm)],[c_226]) ).

tff(c_34,plain,
    ( ( $product(a,a) = 1 )
    | ( a = $uminus(1) )
    | ( a = 1 ) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_229,plain,
    ( ( '#skE_1' = 1 )
    | ( a = $uminus(1) )
    | ( a = 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_34]) ).

tff(c_231,plain,
    '#skE_1' = 1,
    inference(negUnitSimplification,[status(thm)],[c_78,c_228,c_229]) ).

tff(c_81,plain,
    $product(a,a) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_47]) ).

tff(c_59,plain,
    ! [X_47: $int,N_4: $int,M_3: $int] :
      ( ( $product(X_47,N_4) = $sum(N_4,$product(M_3,N_4)) )
      | ( X_47 != $sum(1,M_3) ) ),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_161,plain,
    $product($sum(1,a),a) = $sum(a,'#skE_1'),
    inference(superposition,[status(thm),theory(equality)],[c_81,c_59]) ).

tff(c_164,plain,
    $product($sum(1,a),a) = $sum('#skE_1',a),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_161]) ).

tff(c_737,plain,
    $product($sum(1,a),a) = $sum(1,a),
    inference(demodulation,[status(thm),theory(equality)],[c_231,c_164]) ).

tff(c_51,plain,
    ! [C_21: $int,B_22: $int] :
      ( ( $product(C_21,B_22) != C_21 )
      | ( C_21 = 0 )
      | ( B_22 = 1 ) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_889,plain,
    ( ( $sum(1,a) = 0 )
    | ( a = 1 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_737,c_51]) ).

tff(c_891,plain,
    ( ( a = $uminus(1) )
    | ( a = 1 ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_889]) ).

tff(c_940,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_78,c_228,c_891]) ).

tff(c_944,plain,
    a = $uminus(1),
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_75,plain,
    $product(a,a) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_47]) ).

tff(c_949,plain,
    $product($uminus(1),$uminus(1)) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_944,c_944,c_75]) ).

tff(c_991,plain,
    $uminus($product($uminus($uminus(1)),$uminus(1))) = '#skE_1',
    inference(superposition,[status(thm),theory(equality)],[c_54,c_949]) ).

tff(c_1034,plain,
    $uminus($product($uminus(1),$uminus($uminus(1)))) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_57,c_991]) ).

tff(c_1036,plain,
    $product($uminus(1),1) = $uminus('#skE_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1034]) ).

tff(c_1045,plain,
    $uminus('#skE_1') = $uminus(1),
    inference(demodulation,[status(thm),theory(equality)],[c_50,c_1036]) ).

tff(c_1047,plain,
    '#skE_1' = 1,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1045]) ).

tff(c_943,plain,
    '#skE_1' != 1,
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_1054,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1047,c_943]) ).

tff(c_1057,plain,
    '#skE_1' != 1,
    inference(splitRight,[status(thm)],[c_76]) ).

tff(c_1058,plain,
    a = 1,
    inference(splitRight,[status(thm)],[c_76]) ).

tff(c_1060,plain,
    $product(1,1) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_1058,c_1058,c_75]) ).

tff(c_1090,plain,
    '#skE_1' = 1,
    inference(superposition,[status(thm),theory(equality)],[c_1060,c_50]) ).

tff(c_1139,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1057,c_1090]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ARI673_1 : TPTP v8.1.2. Released v6.3.0.
% 0.14/0.15  % 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
% 0.15/0.37  % Computer : n013.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Fri Aug  4 00:06:18 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 3.80/2.11  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.80/2.12  
% 3.80/2.12  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/2.15  
% 3.80/2.15  Inference rules
% 3.80/2.15  ----------------------
% 3.80/2.15  #Ref     : 0
% 3.80/2.15  #Sup     : 152
% 3.80/2.15  #Fact    : 0
% 3.80/2.15  #Define  : 1
% 3.80/2.15  #Split   : 3
% 3.80/2.15  #Chain   : 0
% 3.80/2.15  #Close   : 0
% 3.80/2.15  
% 3.80/2.15  Ordering : LPO
% 3.80/2.15  
% 3.80/2.15  Simplification rules
% 3.80/2.15  ----------------------
% 3.80/2.15  #Subsume      : 22
% 3.80/2.15  #Demod        : 56
% 3.80/2.15  #Tautology    : 47
% 3.80/2.15  #SimpNegUnit  : 5
% 3.80/2.15  #BackRed      : 4
% 3.80/2.15  
% 3.80/2.15  #Partial instantiations: 0
% 3.80/2.15  #Strategies tried      : 1
% 3.80/2.15  
% 3.80/2.15  Timing (in seconds)
% 3.80/2.15  ----------------------
% 3.80/2.15  Preprocessing        : 0.55
% 3.80/2.16  Parsing              : 0.29
% 3.80/2.16  CNF conversion       : 0.03
% 3.80/2.16  Main loop            : 0.45
% 3.80/2.16  Inferencing          : 0.10
% 3.80/2.16  Reduction            : 0.14
% 3.80/2.16  Demodulation         : 0.11
% 3.80/2.16  BG Simplification    : 0.08
% 3.80/2.16  Subsumption          : 0.09
% 3.80/2.16  Abstraction          : 0.03
% 3.80/2.16  MUC search           : 0.00
% 3.80/2.16  Cooper               : 0.02
% 3.80/2.16  Total                : 1.06
% 3.80/2.16  Index Insertion      : 0.00
% 3.80/2.16  Index Deletion       : 0.00
% 3.80/2.16  Index Matching       : 0.00
% 3.80/2.16  BG Taut test         : 0.00
%------------------------------------------------------------------------------