TSTP Solution File: ALG020+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG020+1 : TPTP v8.1.2. Released v2.7.0.
% 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 : n002.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 10:30:53 EDT 2023

% Result   : Theorem 5.90s 2.38s
% Output   : CNFRefutation 6.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   97 (  72 unt;  12 typ;   0 def)
%            Number of atoms       :  212 ( 202 equ)
%            Maximal formula atoms :   72 (   2 avg)
%            Number of connectives :  140 (  13   ~;  45   |;  81   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   43 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ op2 > op1 > #nlpp > j > h > e23 > e22 > e21 > e20 > e13 > e12 > e11 > e10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(e21,type,
    e21: $i ).

tff(e20,type,
    e20: $i ).

tff(e13,type,
    e13: $i ).

tff(e22,type,
    e22: $i ).

tff(op2,type,
    op2: ( $i * $i ) > $i ).

tff(op1,type,
    op1: ( $i * $i ) > $i ).

tff(e10,type,
    e10: $i ).

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

tff(e23,type,
    e23: $i ).

tff(e12,type,
    e12: $i ).

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

tff(e11,type,
    e11: $i ).

tff(f_59,axiom,
    ( ( e20 != e21 )
    & ( e20 != e22 )
    & ( e20 != e23 )
    & ( e21 != e22 )
    & ( e21 != e23 )
    & ( e22 != e23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(f_168,axiom,
    ( ( op2(e20,e20) = e20 )
    & ( op2(e20,e21) = e21 )
    & ( op2(e20,e22) = e22 )
    & ( op2(e20,e23) = e23 )
    & ( op2(e21,e20) = e21 )
    & ( op2(e21,e21) = e23 )
    & ( op2(e21,e22) = e20 )
    & ( op2(e21,e23) = e22 )
    & ( op2(e22,e20) = e22 )
    & ( op2(e22,e21) = e20 )
    & ( op2(e22,e22) = e23 )
    & ( op2(e22,e23) = e21 )
    & ( op2(e23,e20) = e23 )
    & ( op2(e23,e21) = e22 )
    & ( op2(e23,e22) = e21 )
    & ( op2(e23,e23) = e20 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f_313,negated_conjecture,
    ~ ( ( ( ( h(e10) = e20 )
          | ( h(e10) = e21 )
          | ( h(e10) = e22 )
          | ( h(e10) = e23 ) )
        & ( ( h(e11) = e20 )
          | ( h(e11) = e21 )
          | ( h(e11) = e22 )
          | ( h(e11) = e23 ) )
        & ( ( h(e12) = e20 )
          | ( h(e12) = e21 )
          | ( h(e12) = e22 )
          | ( h(e12) = e23 ) )
        & ( ( h(e13) = e20 )
          | ( h(e13) = e21 )
          | ( h(e13) = e22 )
          | ( h(e13) = e23 ) )
        & ( ( j(e20) = e10 )
          | ( j(e20) = e11 )
          | ( j(e20) = e12 )
          | ( j(e20) = e13 ) )
        & ( ( j(e21) = e10 )
          | ( j(e21) = e11 )
          | ( j(e21) = e12 )
          | ( j(e21) = e13 ) )
        & ( ( j(e22) = e10 )
          | ( j(e22) = e11 )
          | ( j(e22) = e12 )
          | ( j(e22) = e13 ) )
        & ( ( j(e23) = e10 )
          | ( j(e23) = e11 )
          | ( j(e23) = e12 )
          | ( j(e23) = e13 ) ) )
     => ~ ( ( h(op1(e10,e10)) = op2(h(e10),h(e10)) )
          & ( h(op1(e10,e11)) = op2(h(e10),h(e11)) )
          & ( h(op1(e10,e12)) = op2(h(e10),h(e12)) )
          & ( h(op1(e10,e13)) = op2(h(e10),h(e13)) )
          & ( h(op1(e11,e10)) = op2(h(e11),h(e10)) )
          & ( h(op1(e11,e11)) = op2(h(e11),h(e11)) )
          & ( h(op1(e11,e12)) = op2(h(e11),h(e12)) )
          & ( h(op1(e11,e13)) = op2(h(e11),h(e13)) )
          & ( h(op1(e12,e10)) = op2(h(e12),h(e10)) )
          & ( h(op1(e12,e11)) = op2(h(e12),h(e11)) )
          & ( h(op1(e12,e12)) = op2(h(e12),h(e12)) )
          & ( h(op1(e12,e13)) = op2(h(e12),h(e13)) )
          & ( h(op1(e13,e10)) = op2(h(e13),h(e10)) )
          & ( h(op1(e13,e11)) = op2(h(e13),h(e11)) )
          & ( h(op1(e13,e12)) = op2(h(e13),h(e12)) )
          & ( h(op1(e13,e13)) = op2(h(e13),h(e13)) )
          & ( j(op2(e20,e20)) = op1(j(e20),j(e20)) )
          & ( j(op2(e20,e21)) = op1(j(e20),j(e21)) )
          & ( j(op2(e20,e22)) = op1(j(e20),j(e22)) )
          & ( j(op2(e20,e23)) = op1(j(e20),j(e23)) )
          & ( j(op2(e21,e20)) = op1(j(e21),j(e20)) )
          & ( j(op2(e21,e21)) = op1(j(e21),j(e21)) )
          & ( j(op2(e21,e22)) = op1(j(e21),j(e22)) )
          & ( j(op2(e21,e23)) = op1(j(e21),j(e23)) )
          & ( j(op2(e22,e20)) = op1(j(e22),j(e20)) )
          & ( j(op2(e22,e21)) = op1(j(e22),j(e21)) )
          & ( j(op2(e22,e22)) = op1(j(e22),j(e22)) )
          & ( j(op2(e22,e23)) = op1(j(e22),j(e23)) )
          & ( j(op2(e23,e20)) = op1(j(e23),j(e20)) )
          & ( j(op2(e23,e21)) = op1(j(e23),j(e21)) )
          & ( j(op2(e23,e22)) = op1(j(e23),j(e22)) )
          & ( j(op2(e23,e23)) = op1(j(e23),j(e23)) )
          & ( h(j(e20)) = e20 )
          & ( h(j(e21)) = e21 )
          & ( h(j(e22)) = e22 )
          & ( h(j(e23)) = e23 )
          & ( j(h(e10)) = e10 )
          & ( j(h(e11)) = e11 )
          & ( j(h(e12)) = e12 )
          & ( j(h(e13)) = e13 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_137,axiom,
    ( ( op1(e10,e10) = e10 )
    & ( op1(e10,e11) = e11 )
    & ( op1(e10,e12) = e12 )
    & ( op1(e10,e13) = e13 )
    & ( op1(e11,e10) = e11 )
    & ( op1(e11,e11) = e10 )
    & ( op1(e11,e12) = e13 )
    & ( op1(e11,e13) = e12 )
    & ( op1(e12,e10) = e12 )
    & ( op1(e12,e11) = e13 )
    & ( op1(e12,e12) = e10 )
    & ( op1(e12,e13) = e11 )
    & ( op1(e13,e10) = e13 )
    & ( op1(e13,e11) = e12 )
    & ( op1(e13,e12) = e11 )
    & ( op1(e13,e13) = e10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(c_20,plain,
    e23 != e20,
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_90,plain,
    op2(e23,e23) = e20,
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_100,plain,
    op2(e22,e22) = e23,
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_110,plain,
    op2(e21,e21) = e23,
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_208,plain,
    ( ( j(e20) = e13 )
    | ( j(e20) = e12 )
    | ( j(e20) = e11 )
    | ( j(e20) = e10 ) ),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_413,plain,
    j(e20) = e10,
    inference(splitLeft,[status(thm)],[c_208]) ).

tff(c_136,plain,
    h(j(e20)) = e20,
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_414,plain,
    h(e10) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_413,c_136]) ).

tff(c_68,plain,
    op1(e12,e12) = e10,
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_202,plain,
    ( ( j(e23) = e13 )
    | ( j(e23) = e12 )
    | ( j(e23) = e11 )
    | ( j(e23) = e10 ) ),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_637,plain,
    j(e23) = e10,
    inference(splitLeft,[status(thm)],[c_202]) ).

tff(c_130,plain,
    h(j(e23)) = e23,
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_661,plain,
    h(e10) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_637,c_130]) ).

tff(c_665,plain,
    e23 = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_661]) ).

tff(c_667,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_665]) ).

tff(c_669,plain,
    j(e23) != e10,
    inference(splitRight,[status(thm)],[c_202]) ).

tff(c_78,plain,
    op1(e11,e11) = e10,
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_58,plain,
    op1(e13,e13) = e10,
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_24,plain,
    e21 != e20,
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_206,plain,
    ( ( j(e21) = e13 )
    | ( j(e21) = e12 )
    | ( j(e21) = e11 )
    | ( j(e21) = e10 ) ),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_580,plain,
    j(e21) = e10,
    inference(splitLeft,[status(thm)],[c_206]) ).

tff(c_134,plain,
    h(j(e21)) = e21,
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_588,plain,
    h(e10) = e21,
    inference(demodulation,[status(thm),theory(equality)],[c_580,c_134]) ).

tff(c_590,plain,
    e21 = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_588]) ).

tff(c_592,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24,c_590]) ).

tff(c_593,plain,
    ( ( j(e21) = e11 )
    | ( j(e21) = e12 )
    | ( j(e21) = e13 ) ),
    inference(splitRight,[status(thm)],[c_206]) ).

tff(c_604,plain,
    j(e21) = e13,
    inference(splitLeft,[status(thm)],[c_593]) ).

tff(c_158,plain,
    op1(j(e21),j(e21)) = j(op2(e21,e21)),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_222,plain,
    op1(j(e21),j(e21)) = j(e23),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_158]) ).

tff(c_606,plain,
    op1(e13,e13) = j(e23),
    inference(demodulation,[status(thm),theory(equality)],[c_604,c_604,c_222]) ).

tff(c_617,plain,
    j(e23) = e10,
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_606]) ).

tff(c_627,plain,
    h(e10) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_617,c_130]) ).

tff(c_631,plain,
    e23 = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_627]) ).

tff(c_633,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_631]) ).

tff(c_634,plain,
    ( ( j(e21) = e12 )
    | ( j(e21) = e11 ) ),
    inference(splitRight,[status(thm)],[c_593]) ).

tff(c_636,plain,
    j(e21) = e11,
    inference(splitLeft,[status(thm)],[c_634]) ).

tff(c_672,plain,
    op1(e11,e11) = j(e23),
    inference(demodulation,[status(thm),theory(equality)],[c_636,c_636,c_222]) ).

tff(c_683,plain,
    j(e23) = e10,
    inference(demodulation,[status(thm),theory(equality)],[c_78,c_672]) ).

tff(c_689,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_669,c_683]) ).

tff(c_690,plain,
    j(e21) = e12,
    inference(splitRight,[status(thm)],[c_634]) ).

tff(c_694,plain,
    op1(e12,e12) = j(e23),
    inference(demodulation,[status(thm),theory(equality)],[c_690,c_690,c_222]) ).

tff(c_705,plain,
    j(e23) = e10,
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_694]) ).

tff(c_716,plain,
    h(e10) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_705,c_130]) ).

tff(c_720,plain,
    e23 = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_716]) ).

tff(c_722,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_720]) ).

tff(c_724,plain,
    j(e20) != e10,
    inference(splitRight,[status(thm)],[c_208]) ).

tff(c_216,plain,
    ( ( h(e10) = e23 )
    | ( h(e10) = e22 )
    | ( h(e10) = e21 )
    | ( h(e10) = e20 ) ),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_1021,plain,
    h(e10) = e20,
    inference(splitLeft,[status(thm)],[c_216]) ).

tff(c_128,plain,
    j(h(e10)) = e10,
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_1029,plain,
    j(e20) = e10,
    inference(demodulation,[status(thm),theory(equality)],[c_1021,c_128]) ).

tff(c_1032,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_724,c_1029]) ).

tff(c_1034,plain,
    h(e10) != e20,
    inference(splitRight,[status(thm)],[c_216]) ).

tff(c_120,plain,
    op2(e20,e20) = e20,
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_212,plain,
    ( ( h(e12) = e23 )
    | ( h(e12) = e22 )
    | ( h(e12) = e21 )
    | ( h(e12) = e20 ) ),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_1063,plain,
    h(e12) = e20,
    inference(splitLeft,[status(thm)],[c_212]) ).

tff(c_180,plain,
    op2(h(e12),h(e12)) = h(op1(e12,e12)),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_243,plain,
    op2(h(e12),h(e12)) = h(e10),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_180]) ).

tff(c_1072,plain,
    op2(e20,e20) = h(e10),
    inference(demodulation,[status(thm),theory(equality)],[c_1063,c_1063,c_243]) ).

tff(c_1074,plain,
    h(e10) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_120,c_1072]) ).

tff(c_1076,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1034,c_1074]) ).

tff(c_1077,plain,
    ( ( h(e12) = e21 )
    | ( h(e12) = e22 )
    | ( h(e12) = e23 ) ),
    inference(splitRight,[status(thm)],[c_212]) ).

tff(c_1083,plain,
    h(e12) = e23,
    inference(splitLeft,[status(thm)],[c_1077]) ).

tff(c_1093,plain,
    op2(e23,e23) = h(e10),
    inference(demodulation,[status(thm),theory(equality)],[c_1083,c_1083,c_243]) ).

tff(c_1095,plain,
    h(e10) = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_90,c_1093]) ).

tff(c_1097,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1034,c_1095]) ).

tff(c_1098,plain,
    ( ( h(e12) = e22 )
    | ( h(e12) = e21 ) ),
    inference(splitRight,[status(thm)],[c_1077]) ).

tff(c_1100,plain,
    h(e12) = e21,
    inference(splitLeft,[status(thm)],[c_1098]) ).

tff(c_1111,plain,
    op2(e21,e21) = h(e10),
    inference(demodulation,[status(thm),theory(equality)],[c_1100,c_1100,c_243]) ).

tff(c_1113,plain,
    h(e10) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_1111]) ).

tff(c_88,plain,
    op1(e10,e10) = e10,
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_200,plain,
    op2(h(e10),h(e10)) = h(op1(e10,e10)),
    inference(cnfTransformation,[status(thm)],[f_313]) ).

tff(c_233,plain,
    op2(h(e10),h(e10)) = h(e10),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_200]) ).

tff(c_1123,plain,
    op2(e23,e23) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_1113,c_1113,c_1113,c_233]) ).

tff(c_1127,plain,
    e23 = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_90,c_1123]) ).

tff(c_1129,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_1127]) ).

tff(c_1130,plain,
    h(e12) = e22,
    inference(splitRight,[status(thm)],[c_1098]) ).

tff(c_1144,plain,
    op2(e22,e22) = h(e10),
    inference(demodulation,[status(thm),theory(equality)],[c_1130,c_1130,c_243]) ).

tff(c_1146,plain,
    h(e10) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_1144]) ).

tff(c_1156,plain,
    op2(e23,e23) = e23,
    inference(demodulation,[status(thm),theory(equality)],[c_1146,c_1146,c_1146,c_233]) ).

tff(c_1160,plain,
    e23 = e20,
    inference(demodulation,[status(thm),theory(equality)],[c_90,c_1156]) ).

tff(c_1162,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_1160]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG020+1 : TPTP v8.1.2. Released v2.7.0.
% 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
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 20:40:01 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 5.90/2.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.90/2.39  
% 5.90/2.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.33/2.43  
% 6.33/2.43  Inference rules
% 6.33/2.43  ----------------------
% 6.33/2.43  #Ref     : 0
% 6.33/2.43  #Sup     : 280
% 6.33/2.43  #Fact    : 0
% 6.33/2.43  #Define  : 0
% 6.33/2.43  #Split   : 17
% 6.33/2.43  #Chain   : 0
% 6.33/2.43  #Close   : 0
% 6.33/2.43  
% 6.33/2.43  Ordering : KBO
% 6.33/2.43  
% 6.33/2.43  Simplification rules
% 6.33/2.43  ----------------------
% 6.33/2.43  #Subsume      : 16
% 6.33/2.43  #Demod        : 380
% 6.33/2.43  #Tautology    : 311
% 6.33/2.43  #SimpNegUnit  : 20
% 6.33/2.43  #BackRed      : 193
% 6.33/2.43  
% 6.33/2.43  #Partial instantiations: 0
% 6.33/2.43  #Strategies tried      : 1
% 6.33/2.43  
% 6.33/2.43  Timing (in seconds)
% 6.33/2.43  ----------------------
% 6.33/2.43  Preprocessing        : 0.59
% 6.33/2.43  Parsing              : 0.31
% 6.33/2.43  CNF conversion       : 0.03
% 6.33/2.43  Main loop            : 0.75
% 6.33/2.43  Inferencing          : 0.18
% 6.33/2.43  Reduction            : 0.30
% 6.33/2.43  Demodulation         : 0.21
% 6.33/2.43  BG Simplification    : 0.03
% 6.33/2.43  Subsumption          : 0.15
% 6.33/2.43  Abstraction          : 0.02
% 6.33/2.43  MUC search           : 0.00
% 6.33/2.43  Cooper               : 0.00
% 6.33/2.43  Total                : 1.40
% 6.33/2.43  Index Insertion      : 0.00
% 6.33/2.43  Index Deletion       : 0.00
% 6.33/2.43  Index Matching       : 0.00
% 6.33/2.43  BG Taut test         : 0.00
%------------------------------------------------------------------------------