TSTP Solution File: ARI640_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ARI640_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/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 : n009.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 10:34:10 EDT 2023

% Result   : Theorem 6.32s 3.09s
% Output   : CNFRefutation 6.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   46 (  32 unt;   3 typ;   0 def)
%            Number of atoms       :   59 (  23 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   41 (  25   ~;  12   |;   0   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  113 (  31 atm;  39 fun;  27 num;  16 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   3 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;  16   :)

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

%Foreground sorts:

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

tff(x,type,
    x: $real ).

tff(y,type,
    y: $real ).

%Foreground operators:

tff(f_32,hypothesis,
    $greater($product(x,y),$sum(x,y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_03) ).

tff(f_74,axiom,
    ! [X: $real,Y: $real,Z: $real] :
      ( ( Y != 0 )
     => ( ( Z = $quotient(X,Y) )
      <=> ( X = $product(Y,Z) ) ) ),
    file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas_real.p',nonzero_eq_divide_eq) ).

tff(f_94,axiom,
    ! [A: $real,B: $real] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
    file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas_real.p',minus_mult_left) ).

tff(f_161,axiom,
    ! [A: $real,B: $real] :
      ( $less(0,A)
     => ( $lesseq(1,$quotient(B,A))
      <=> $lesseq(A,B) ) ),
    file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas_real.p',le_divide_eq_1_pos) ).

tff(f_30,hypothesis,
    $greater(y,0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).

tff(f_31,hypothesis,
    $less(y,1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_02) ).

tff(f_29,hypothesis,
    $greater(x,0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).

tff(c_8,plain,
    $greater($product(x,y),$sum(x,y)),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_87,plain,
    ~ $lesseq($product(x,y),$sum(x,y)),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).

tff(c_119,plain,
    $product(x,y) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_87]) ).

tff(c_19,plain,
    ! [Y_10: $real,Z_11: $real] :
      ( ( $quotient($product(Y_10,Z_11),Y_10) = Z_11 )
      | ( Y_10 = 0 ) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_207,plain,
    ( ( $quotient('#skE_1',x) = y )
    | ( x = 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_119,c_19]) ).

tff(c_669,plain,
    x = 0,
    inference(splitLeft,[status(thm)],[c_207]) ).

tff(c_92,plain,
    ! [A_32: $real,B_33: $real,X_106: $real] :
      ( ( $uminus($product(A_32,B_33)) = $product(X_106,B_33) )
      | ( X_106 != $uminus(A_32) ) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_415,plain,
    $product($uminus(x),y) = $uminus('#skE_1'),
    inference(superposition,[status(thm),theory(equality)],[c_119,c_92]) ).

tff(c_116,plain,
    $product(x,y) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_87]) ).

tff(c_514,plain,
    ( ( $uminus('#skE_1') = '#skE_1' )
    | ( $uminus(x) != x ) ),
    inference(superposition,[status(thm),theory(equality)],[c_415,c_116]) ).

tff(c_515,plain,
    ( ( $uminus('#skE_1') = '#skE_1' )
    | ( $uminus(x) != x ) ),
    inference(backgroundSimplification,[status(thm),theory('LFA')],[c_514]) ).

tff(c_663,plain,
    $uminus(x) != x,
    inference(splitLeft,[status(thm)],[c_515]) ).

tff(c_752,plain,
    $uminus(0) != 0,
    inference(demodulation,[status(thm),theory(equality)],[c_669,c_669,c_663]) ).

tff(c_778,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LFA')],[c_752]) ).

tff(c_785,plain,
    $quotient('#skE_1',x) = y,
    inference(splitRight,[status(thm)],[c_207]) ).

tff(c_73,plain,
    ! [B_86: $real,A_85: $real] :
      ( $lesseq(1,$quotient(B_86,A_85))
      | ~ $less(0,A_85)
      | ~ $lesseq(A_85,B_86) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_75,plain,
    ! [B_87: $real,A_88: $real] :
      ( ~ $less($quotient(B_87,A_88),1)
      | ~ $less(0,A_88)
      | ~ $lesseq(A_88,B_87) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_73]) ).

tff(c_871,plain,
    ( ~ $less(y,1)
    | ~ $less(0,x)
    | ~ $lesseq(x,'#skE_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_785,c_75]) ).

tff(c_883,plain,
    ~ $lesseq(x,'#skE_1'),
    inference(splitLeft,[status(thm)],[c_871]) ).

tff(c_111,plain,
    $product(x,y) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_87]) ).

tff(c_95,plain,
    ~ $lesseq($product(x,y),$sum(x,y)),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).

tff(c_113,plain,
    ~ $lesseq('#skE_1',$sum(x,y)),
    inference(demodulation,[status(thm),theory(equality)],[c_111,c_95]) ).

tff(c_3,plain,
    $greater(y,0),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_4,plain,
    ~ $lesseq(y,0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).

tff(c_884,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_883,c_113,c_4]) ).

tff(c_885,plain,
    ( ~ $less(0,x)
    | ~ $less(y,1) ),
    inference(splitRight,[status(thm)],[c_871]) ).

tff(c_1081,plain,
    ~ $less(y,1),
    inference(splitLeft,[status(thm)],[c_885]) ).

tff(c_5,plain,
    $less(y,1),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_6,plain,
    ~ $lesseq(1,y),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).

tff(c_1082,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_1081,c_6]) ).

tff(c_1083,plain,
    ~ $less(0,x),
    inference(splitRight,[status(thm)],[c_885]) ).

tff(c_1,plain,
    $greater(x,0),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_2,plain,
    ~ $lesseq(x,0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).

tff(c_1087,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_1083,c_2]) ).

tff(c_1088,plain,
    $uminus('#skE_1') = '#skE_1',
    inference(splitRight,[status(thm)],[c_515]) ).

tff(c_1096,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_1088,c_113,c_4,c_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ARI640_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.13  % 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
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Aug  4 00:08:08 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.32/3.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.32/3.11  
% 6.32/3.11  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.48/3.14  
% 6.48/3.14  Inference rules
% 6.48/3.14  ----------------------
% 6.48/3.14  #Ref     : 0
% 6.48/3.14  #Sup     : 158
% 6.48/3.14  #Fact    : 0
% 6.48/3.14  #Define  : 1
% 6.48/3.14  #Split   : 12
% 6.48/3.14  #Chain   : 0
% 6.48/3.14  #Close   : 5
% 6.48/3.14  
% 6.48/3.14  Ordering : LPO
% 6.48/3.14  
% 6.48/3.14  Simplification rules
% 6.48/3.14  ----------------------
% 6.48/3.14  #Subsume      : 11
% 6.48/3.14  #Demod        : 56
% 6.48/3.14  #Tautology    : 36
% 6.48/3.14  #SimpNegUnit  : 2
% 6.48/3.14  #BackRed      : 13
% 6.48/3.14  
% 6.48/3.14  #Partial instantiations: 0
% 6.48/3.14  #Strategies tried      : 1
% 6.48/3.14  
% 6.48/3.14  Timing (in seconds)
% 6.48/3.14  ----------------------
% 6.48/3.14  Preprocessing        : 0.85
% 6.48/3.14  Parsing              : 0.40
% 6.48/3.14  CNF conversion       : 0.04
% 6.48/3.14  Main loop            : 1.19
% 6.48/3.14  Inferencing          : 0.15
% 6.48/3.14  Reduction            : 0.21
% 6.48/3.14  Demodulation         : 0.16
% 6.48/3.14  BG Simplification    : 0.07
% 6.48/3.14  Subsumption          : 0.11
% 6.48/3.14  Abstraction          : 0.05
% 6.48/3.15  MUC search           : 0.39
% 6.48/3.15  Cooper               : 0.00
% 6.48/3.15  Total                : 2.12
% 6.48/3.15  Index Insertion      : 0.00
% 6.48/3.15  Index Deletion       : 0.00
% 6.48/3.15  Index Matching       : 0.00
% 6.48/3.15  BG Taut test         : 0.00
%------------------------------------------------------------------------------