TSTP Solution File: ARI670_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ARI670_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 : 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 10:34:13 EDT 2023

% Result   : Theorem 7.15s 2.82s
% Output   : CNFRefutation 7.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  35 unt;   4 typ;   0 def)
%            Number of atoms       :   74 (  34 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   49 (  26   ~;  20   |;   1   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  178 (  35 atm;  67 fun;  46 num;  30 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   4 usr;   6 con; 0-2 aty)
%            Number of variables   :   30 (;  30   !;   0   ?;  30   :)

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

%Foreground sorts:

%Background operators:
tff(c,type,
    c: $int ).

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

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

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

%Foreground operators:

tff(f_67,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_59,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_31,negated_conjecture,
    ~ $lesseq(a,$product(a,a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

tff(f_84,axiom,
    ! [A: $int,B: $int] :
      ( ( $less(0,A)
        & $less(0,B) )
     => $less(0,$product(A,B)) ),
    file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_nonneg_nonneg) ).

tff(f_75,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_56,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_35,plain,
    ! [A_17: $int,B_18: $int,X_35: $int] :
      ( ( $uminus($product(A_17,B_18)) = $product(X_35,B_18) )
      | ( X_35 != $uminus(A_17) ) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_37,plain,
    ! [X_35: $int,B_18: $int,A_17: $int] :
      ( ( $uminus($product(X_35,B_18)) = $product(A_17,B_18) )
      | ( X_35 != $uminus(A_17) ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_35]) ).

tff(c_40,plain,
    ! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_2,plain,
    ~ $lesseq(a,$product(a,a)),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_30,plain,
    $less($product(a,a),a),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).

tff(c_58,plain,
    $product(a,a) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_30]) ).

tff(c_90,plain,
    $uminus($product($uminus(a),a)) = '#skE_1',
    inference(superposition,[status(thm),theory(equality)],[c_58,c_37]) ).

tff(c_164,plain,
    $uminus($product(a,$uminus(a))) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_90]) ).

tff(c_212,plain,
    $product(a,$uminus(a)) = $uminus('#skE_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_164]) ).

tff(c_361,plain,
    $uminus($product($uminus(a),$uminus(a))) = $uminus('#skE_1'),
    inference(superposition,[status(thm),theory(equality)],[c_37,c_212]) ).

tff(c_558,plain,
    $product($uminus(a),$uminus(a)) = '#skE_1',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_361]) ).

tff(c_31,plain,
    ! [A_27: $int,B_28: $int] :
      ( $less(0,$product(A_27,B_28))
      | ~ $less(0,A_27)
      | ~ $less(0,B_28) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_707,plain,
    ( $less(0,'#skE_1')
    | ~ $less(0,$uminus(a)) ),
    inference(superposition,[status(thm),theory(equality)],[c_558,c_31]) ).

tff(c_709,plain,
    ( $less(0,'#skE_1')
    | ~ $less(a,0) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_707]) ).

tff(c_1424,plain,
    ~ $less(a,0),
    inference(splitLeft,[status(thm)],[c_709]) ).

tff(c_175,plain,
    ( $less(0,'#skE_1')
    | ~ $less(0,a) ),
    inference(superposition,[status(thm),theory(equality)],[c_58,c_31]) ).

tff(c_207,plain,
    ~ $less(0,a),
    inference(splitLeft,[status(thm)],[c_175]) ).

tff(c_32,plain,
    ! [B_24: $int] : ( $product(0,B_24) = 0 ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_173,plain,
    ( ( '#skE_1' = 0 )
    | ( a != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_58,c_32]) ).

tff(c_205,plain,
    a != 0,
    inference(splitLeft,[status(thm)],[c_173]) ).

tff(c_1425,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_1424,c_207,c_205]) ).

tff(c_1428,plain,
    $less(0,'#skE_1'),
    inference(splitRight,[status(thm)],[c_709]) ).

tff(c_48,plain,
    $product(a,a) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_30]) ).

tff(c_43,plain,
    $less($product(a,a),a),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).

tff(c_55,plain,
    $less('#skE_1',a),
    inference(demodulation,[status(thm),theory(equality)],[c_48,c_43]) ).

tff(c_1430,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_1428,c_207,c_55]) ).

tff(c_1434,plain,
    $less(0,a),
    inference(splitRight,[status(thm)],[c_175]) ).

tff(c_42,plain,
    ! [X_37: $int,N_4: $int,M_3: $int] :
      ( ( $product(X_37,N_4) = $sum(N_4,$product(M_3,N_4)) )
      | ( X_37 != $sum(1,M_3) ) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_134,plain,
    ! [M_3: $int] :
      ( ( $sum(a,$product(M_3,a)) = '#skE_1' )
      | ( a != $sum(1,M_3) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_58,c_42]) ).

tff(c_2219,plain,
    ! [M_428: $int] :
      ( ( $product(M_428,a) = $sum($uminus(a),'#skE_1') )
      | ( a != $sum(1,M_428) ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_134]) ).

tff(c_2284,plain,
    ! [M_428: $int] :
      ( $less(0,$sum($uminus(a),'#skE_1'))
      | ~ $less(0,M_428)
      | ~ $less(0,a)
      | ( a != $sum(1,M_428) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2219,c_31]) ).

tff(c_2393,plain,
    ! [M_428: $int] :
      ( $less(0,$sum($uminus(a),'#skE_1'))
      | ~ $less(0,M_428)
      | ( a != $sum(1,M_428) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1434,c_2284]) ).

tff(c_2395,plain,
    ! [M_428: $int] :
      ( $less(a,'#skE_1')
      | ~ $less(0,M_428)
      | ( a != $sum(1,M_428) ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2393]) ).

tff(c_9516,plain,
    ! [M_428: $int] :
      ( ~ $less(0,M_428)
      | ( a != $sum(1,M_428) ) ),
    inference(splitLeft,[status(thm)],[c_2395]) ).

tff(c_9517,plain,
    $lesseq(a,1),
    inference(quantifierElimination,[status(thm),theory('LIA')],[c_9516]) ).

tff(c_9519,plain,
    ~ $less(1,a),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9517]) ).

tff(c_1433,plain,
    $less(0,'#skE_1'),
    inference(splitRight,[status(thm)],[c_175]) ).

tff(c_9520,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_9519,c_1433,c_55]) ).

tff(c_9522,plain,
    $less(a,'#skE_1'),
    inference(splitRight,[status(thm)],[c_2395]) ).

tff(c_9523,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_9522,c_55]) ).

tff(c_9527,plain,
    a = 0,
    inference(splitRight,[status(thm)],[c_173]) ).

tff(c_9526,plain,
    '#skE_1' = 0,
    inference(splitRight,[status(thm)],[c_173]) ).

tff(c_9538,plain,
    $less(0,a),
    inference(demodulation,[status(thm),theory(equality)],[c_9526,c_55]) ).

tff(c_9539,plain,
    $less(0,0),
    inference(demodulation,[status(thm),theory(equality)],[c_9527,c_9538]) ).

tff(c_9543,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9539]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ARI670_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.14  % 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
% 0.13/0.35  % Computer : n015.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 00:27:59 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.15/2.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.15/2.83  
% 7.15/2.83  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.15/2.87  
% 7.15/2.87  Inference rules
% 7.15/2.87  ----------------------
% 7.15/2.87  #Ref     : 0
% 7.15/2.87  #Sup     : 1413
% 7.15/2.87  #Fact    : 0
% 7.15/2.87  #Define  : 1
% 7.15/2.87  #Split   : 25
% 7.15/2.87  #Chain   : 0
% 7.15/2.87  #Close   : 5
% 7.15/2.87  
% 7.15/2.87  Ordering : LPO
% 7.15/2.87  
% 7.15/2.87  Simplification rules
% 7.15/2.87  ----------------------
% 7.15/2.87  #Subsume      : 311
% 7.15/2.87  #Demod        : 340
% 7.15/2.87  #Tautology    : 641
% 7.15/2.87  #SimpNegUnit  : 16
% 7.15/2.87  #BackRed      : 3
% 7.15/2.87  
% 7.15/2.87  #Partial instantiations: 0
% 7.15/2.87  #Strategies tried      : 1
% 7.15/2.87  
% 7.15/2.87  Timing (in seconds)
% 7.15/2.87  ----------------------
% 7.36/2.92  Preprocessing        : 0.51
% 7.36/2.92  Parsing              : 0.27
% 7.36/2.92  CNF conversion       : 0.03
% 7.36/2.92  Main loop            : 1.26
% 7.36/2.92  Inferencing          : 0.25
% 7.36/2.92  Reduction            : 0.40
% 7.36/2.92  Demodulation         : 0.31
% 7.36/2.92  BG Simplification    : 0.17
% 7.36/2.92  Subsumption          : 0.22
% 7.36/2.92  Abstraction          : 0.07
% 7.36/2.92  MUC search           : 0.05
% 7.36/2.92  Cooper               : 0.10
% 7.36/2.92  Total                : 1.83
% 7.36/2.92  Index Insertion      : 0.00
% 7.36/2.92  Index Deletion       : 0.00
% 7.36/2.92  Index Matching       : 0.00
% 7.36/2.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------