TSTP Solution File: ALG029+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG029+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/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 : n021.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 10:30:56 EDT 2023

% Result   : Theorem 5.88s 2.60s
% Output   : CNFRefutation 5.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   32 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   80 (  21 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :   97 (  41   ~;  37   |;   4   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   6   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   41 (;  41   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sorti2 > sorti1 > op2 > op1 > #nlpp > j > h > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

tff(sorti2,type,
    sorti2: $i > $o ).

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

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

tff(sorti1,type,
    sorti1: $i > $o ).

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

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

tff(f_54,axiom,
    ~ ! [U] :
        ( sorti2(U)
       => ! [V] :
            ( sorti2(V)
           => ( op2(U,V) = op2(V,U) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

tff(f_39,axiom,
    ! [U] :
      ( sorti2(U)
     => ! [V] :
          ( sorti2(V)
         => sorti2(op2(U,V)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

tff(f_91,negated_conjecture,
    ~ ( ( ! [U] :
            ( sorti1(U)
           => sorti2(h(U)) )
        & ! [V] :
            ( sorti2(V)
           => sorti1(j(V)) ) )
     => ~ ( ! [W] :
              ( sorti1(W)
             => ! [X] :
                  ( sorti1(X)
                 => ( h(op1(W,X)) = op2(h(W),h(X)) ) ) )
          & ! [Y] :
              ( sorti2(Y)
             => ! [Z] :
                  ( sorti2(Z)
                 => ( j(op2(Y,Z)) = op1(j(Y),j(Z)) ) ) )
          & ! [X1] :
              ( sorti2(X1)
             => ( h(j(X1)) = X1 ) )
          & ! [X2] :
              ( sorti1(X2)
             => ( j(h(X2)) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f_46,axiom,
    ! [U] :
      ( sorti1(U)
     => ! [V] :
          ( sorti1(V)
         => ( op1(U,V) = op1(V,U) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(c_8,plain,
    op2('#skF_2','#skF_1') != op2('#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_12,plain,
    sorti2('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_10,plain,
    sorti2('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_4,plain,
    ! [U_4,V_6] :
      ( sorti2(op2(U_4,V_6))
      | ~ sorti2(V_6)
      | ~ sorti2(U_4) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_22,plain,
    ! [V_12] :
      ( sorti1(j(V_12))
      | ~ sorti2(V_12) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_18,plain,
    ! [Y_16,Z_18] :
      ( ( op1(j(Y_16),j(Z_18)) = j(op2(Y_16,Z_18)) )
      | ~ sorti2(Z_18)
      | ~ sorti2(Y_16) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_135,plain,
    ! [Y_35,Z_36] :
      ( ( op1(j(Y_35),j(Z_36)) = j(op2(Y_35,Z_36)) )
      | ~ sorti2(Z_36)
      | ~ sorti2(Y_35) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_79,plain,
    ! [V_31,U_32] :
      ( ( op1(V_31,U_32) = op1(U_32,V_31) )
      | ~ sorti1(V_31)
      | ~ sorti1(U_32) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_85,plain,
    ! [V_12,U_32] :
      ( ( op1(j(V_12),U_32) = op1(U_32,j(V_12)) )
      | ~ sorti1(U_32)
      | ~ sorti2(V_12) ),
    inference(resolution,[status(thm)],[c_22,c_79]) ).

tff(c_812,plain,
    ! [Z_70,Y_71] :
      ( ( op1(j(Z_70),j(Y_71)) = j(op2(Y_71,Z_70)) )
      | ~ sorti1(j(Z_70))
      | ~ sorti2(Y_71)
      | ~ sorti2(Z_70)
      | ~ sorti2(Y_71) ),
    inference(superposition,[status(thm),theory(equality)],[c_135,c_85]) ).

tff(c_2691,plain,
    ! [Z_118,Y_119] :
      ( ( j(op2(Z_118,Y_119)) = j(op2(Y_119,Z_118)) )
      | ~ sorti1(j(Y_119))
      | ~ sorti2(Z_118)
      | ~ sorti2(Y_119)
      | ~ sorti2(Z_118)
      | ~ sorti2(Z_118)
      | ~ sorti2(Y_119) ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_812]) ).

tff(c_2717,plain,
    ! [Z_120,V_121] :
      ( ( j(op2(Z_120,V_121)) = j(op2(V_121,Z_120)) )
      | ~ sorti2(Z_120)
      | ~ sorti2(V_121) ),
    inference(resolution,[status(thm)],[c_22,c_2691]) ).

tff(c_16,plain,
    ! [X1_19] :
      ( ( h(j(X1_19)) = X1_19 )
      | ~ sorti2(X1_19) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_2984,plain,
    ! [Z_124,V_125] :
      ( ( h(j(op2(Z_124,V_125))) = op2(V_125,Z_124) )
      | ~ sorti2(op2(V_125,Z_124))
      | ~ sorti2(Z_124)
      | ~ sorti2(V_125) ),
    inference(superposition,[status(thm),theory(equality)],[c_2717,c_16]) ).

tff(c_3241,plain,
    ! [Z_128,V_129] :
      ( ( op2(Z_128,V_129) = op2(V_129,Z_128) )
      | ~ sorti2(op2(Z_128,V_129))
      | ~ sorti2(op2(V_129,Z_128))
      | ~ sorti2(Z_128)
      | ~ sorti2(V_129) ),
    inference(superposition,[status(thm),theory(equality)],[c_2984,c_16]) ).

tff(c_3258,plain,
    ! [V_130,U_131] :
      ( ( op2(V_130,U_131) = op2(U_131,V_130) )
      | ~ sorti2(op2(V_130,U_131))
      | ~ sorti2(V_130)
      | ~ sorti2(U_131) ),
    inference(resolution,[status(thm)],[c_4,c_3241]) ).

tff(c_3281,plain,
    ! [V_132,U_133] :
      ( ( op2(V_132,U_133) = op2(U_133,V_132) )
      | ~ sorti2(V_132)
      | ~ sorti2(U_133) ),
    inference(resolution,[status(thm)],[c_4,c_3258]) ).

tff(c_3527,plain,
    ! [U_136] :
      ( ( op2(U_136,'#skF_2') = op2('#skF_2',U_136) )
      | ~ sorti2(U_136) ),
    inference(resolution,[status(thm)],[c_10,c_3281]) ).

tff(c_3551,plain,
    op2('#skF_2','#skF_1') = op2('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_12,c_3527]) ).

tff(c_3563,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_3551]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG029+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % 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
% 0.13/0.36  % Computer : n021.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 20:28:51 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 5.88/2.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.88/2.61  
% 5.88/2.61  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.88/2.67  
% 5.88/2.67  Inference rules
% 5.88/2.67  ----------------------
% 5.88/2.67  #Ref     : 0
% 5.88/2.67  #Sup     : 1043
% 5.88/2.67  #Fact    : 0
% 5.88/2.67  #Define  : 0
% 5.88/2.67  #Split   : 0
% 5.88/2.67  #Chain   : 0
% 5.88/2.67  #Close   : 0
% 5.88/2.67  
% 5.88/2.67  Ordering : KBO
% 5.88/2.67  
% 5.88/2.67  Simplification rules
% 5.88/2.67  ----------------------
% 5.88/2.67  #Subsume      : 231
% 5.88/2.67  #Demod        : 0
% 5.88/2.67  #Tautology    : 113
% 5.88/2.67  #SimpNegUnit  : 1
% 5.88/2.67  #BackRed      : 0
% 5.88/2.67  
% 5.88/2.67  #Partial instantiations: 0
% 5.88/2.67  #Strategies tried      : 1
% 5.88/2.67  
% 5.88/2.67  Timing (in seconds)
% 5.88/2.67  ----------------------
% 5.88/2.68  Preprocessing        : 0.45
% 5.88/2.68  Parsing              : 0.25
% 5.88/2.68  CNF conversion       : 0.03
% 5.88/2.68  Main loop            : 0.95
% 5.88/2.68  Inferencing          : 0.37
% 5.88/2.68  Reduction            : 0.22
% 5.88/2.68  Demodulation         : 0.15
% 5.88/2.68  BG Simplification    : 0.07
% 5.88/2.68  Subsumption          : 0.23
% 5.88/2.68  Abstraction          : 0.05
% 5.88/2.68  MUC search           : 0.00
% 5.88/2.68  Cooper               : 0.00
% 5.88/2.68  Total                : 1.48
% 5.88/2.68  Index Insertion      : 0.00
% 5.88/2.68  Index Deletion       : 0.00
% 5.88/2.68  Index Matching       : 0.00
% 5.88/2.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------