TSTP Solution File: ALG017+1 by CSE---1.6

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE---1.6
% Problem  : ALG017+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d

% Computer : n025.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 : Wed Aug 30 15:58:35 EDT 2023

% Result   : Theorem 0.20s 0.68s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ALG017+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35  % Computer : n025.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   : Mon Aug 28 05:32:09 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.57  start to proof:theBenchmark
% 0.20/0.66  %-------------------------------------------
% 0.20/0.66  % File        :CSE---1.6
% 0.20/0.66  % Problem     :theBenchmark
% 0.20/0.66  % Transform   :cnf
% 0.20/0.66  % Format      :tptp:raw
% 0.20/0.66  % Command     :java -jar mcs_scs.jar %d %s
% 0.20/0.66  
% 0.20/0.66  % Result      :Theorem 0.010000s
% 0.20/0.66  % Output      :CNFRefutation 0.010000s
% 0.20/0.66  %-------------------------------------------
% 0.20/0.66  %--------------------------------------------------------------------------
% 0.20/0.66  % File     : ALG017+1 : TPTP v8.1.2. Released v2.7.0.
% 0.20/0.66  % Domain   : General Algebra
% 0.20/0.66  % Problem  : Groups 4: CPROPS-PAIRWISE-EXCLUSIVE-PROBLEM-1
% 0.20/0.66  % Version  : Especial.
% 0.20/0.66  % English  :
% 0.20/0.66  
% 0.20/0.66  % Refs     : [Mei03] Meier (2003), Email to G.Sutcliffe
% 0.20/0.66  %          : [CM+04] Colton et al. (2004), Automatic Generation of Classifi
% 0.20/0.66  % Source   : [Mei03]
% 0.20/0.66  % Names    :
% 0.20/0.66  
% 0.20/0.66  % Status   : Theorem
% 0.20/0.66  % Rating   : 0.08 v8.1.0, 0.04 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.2.0, 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v3.7.0, 0.14 v3.5.0, 0.11 v3.4.0, 0.08 v3.3.0, 0.11 v2.7.0
% 0.20/0.66  % Syntax   : Number of formulae    :   12 (   1 unt;   0 def)
% 0.20/0.66  %            Number of atoms       :  295 ( 295 equ)
% 0.20/0.66  %            Maximal formula atoms :   64 (  24 avg)
% 0.20/0.66  %            Number of connectives :  345 (  62   ~;  69   |; 198   &)
% 0.20/0.66  %                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
% 0.20/0.66  %            Maximal formula depth :   64 (  17 avg)
% 0.20/0.66  %            Maximal term depth    :    3 (   1 avg)
% 0.20/0.66  %            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
% 0.20/0.66  %            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
% 0.20/0.66  %            Number of variables   :    0 (   0   !;   0   ?)
% 0.20/0.66  % SPC      : FOF_THM_RFO_PEQ
% 0.20/0.66  
% 0.20/0.66  % Comments :
% 0.20/0.66  %--------------------------------------------------------------------------
% 0.20/0.66  fof(ax1,axiom,
% 0.20/0.66      ( ( op(e0,e0) = e0
% 0.20/0.66        | op(e0,e0) = e1
% 0.20/0.66        | op(e0,e0) = e2
% 0.20/0.66        | op(e0,e0) = e3 )
% 0.20/0.66      & ( op(e0,e1) = e0
% 0.20/0.66        | op(e0,e1) = e1
% 0.20/0.66        | op(e0,e1) = e2
% 0.20/0.66        | op(e0,e1) = e3 )
% 0.20/0.66      & ( op(e0,e2) = e0
% 0.20/0.66        | op(e0,e2) = e1
% 0.20/0.66        | op(e0,e2) = e2
% 0.20/0.66        | op(e0,e2) = e3 )
% 0.20/0.67      & ( op(e0,e3) = e0
% 0.20/0.67        | op(e0,e3) = e1
% 0.20/0.67        | op(e0,e3) = e2
% 0.20/0.67        | op(e0,e3) = e3 )
% 0.20/0.67      & ( op(e1,e0) = e0
% 0.20/0.67        | op(e1,e0) = e1
% 0.20/0.67        | op(e1,e0) = e2
% 0.20/0.67        | op(e1,e0) = e3 )
% 0.20/0.67      & ( op(e1,e1) = e0
% 0.20/0.67        | op(e1,e1) = e1
% 0.20/0.67        | op(e1,e1) = e2
% 0.20/0.67        | op(e1,e1) = e3 )
% 0.20/0.67      & ( op(e1,e2) = e0
% 0.20/0.67        | op(e1,e2) = e1
% 0.20/0.67        | op(e1,e2) = e2
% 0.20/0.67        | op(e1,e2) = e3 )
% 0.20/0.67      & ( op(e1,e3) = e0
% 0.20/0.67        | op(e1,e3) = e1
% 0.20/0.67        | op(e1,e3) = e2
% 0.20/0.67        | op(e1,e3) = e3 )
% 0.20/0.67      & ( op(e2,e0) = e0
% 0.20/0.67        | op(e2,e0) = e1
% 0.20/0.67        | op(e2,e0) = e2
% 0.20/0.67        | op(e2,e0) = e3 )
% 0.20/0.67      & ( op(e2,e1) = e0
% 0.20/0.67        | op(e2,e1) = e1
% 0.20/0.67        | op(e2,e1) = e2
% 0.20/0.67        | op(e2,e1) = e3 )
% 0.20/0.67      & ( op(e2,e2) = e0
% 0.20/0.67        | op(e2,e2) = e1
% 0.20/0.67        | op(e2,e2) = e2
% 0.20/0.67        | op(e2,e2) = e3 )
% 0.20/0.67      & ( op(e2,e3) = e0
% 0.20/0.67        | op(e2,e3) = e1
% 0.20/0.67        | op(e2,e3) = e2
% 0.20/0.67        | op(e2,e3) = e3 )
% 0.20/0.67      & ( op(e3,e0) = e0
% 0.20/0.67        | op(e3,e0) = e1
% 0.20/0.67        | op(e3,e0) = e2
% 0.20/0.67        | op(e3,e0) = e3 )
% 0.20/0.67      & ( op(e3,e1) = e0
% 0.20/0.67        | op(e3,e1) = e1
% 0.20/0.67        | op(e3,e1) = e2
% 0.20/0.67        | op(e3,e1) = e3 )
% 0.20/0.67      & ( op(e3,e2) = e0
% 0.20/0.67        | op(e3,e2) = e1
% 0.20/0.67        | op(e3,e2) = e2
% 0.20/0.67        | op(e3,e2) = e3 )
% 0.20/0.67      & ( op(e3,e3) = e0
% 0.20/0.67        | op(e3,e3) = e1
% 0.20/0.67        | op(e3,e3) = e2
% 0.20/0.67        | op(e3,e3) = e3 ) ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax2,axiom,
% 0.20/0.67      ( op(op(e0,e0),e0) = op(e0,op(e0,e0))
% 0.20/0.67      & op(op(e0,e0),e1) = op(e0,op(e0,e1))
% 0.20/0.67      & op(op(e0,e0),e2) = op(e0,op(e0,e2))
% 0.20/0.67      & op(op(e0,e0),e3) = op(e0,op(e0,e3))
% 0.20/0.67      & op(op(e0,e1),e0) = op(e0,op(e1,e0))
% 0.20/0.67      & op(op(e0,e1),e1) = op(e0,op(e1,e1))
% 0.20/0.67      & op(op(e0,e1),e2) = op(e0,op(e1,e2))
% 0.20/0.67      & op(op(e0,e1),e3) = op(e0,op(e1,e3))
% 0.20/0.67      & op(op(e0,e2),e0) = op(e0,op(e2,e0))
% 0.20/0.67      & op(op(e0,e2),e1) = op(e0,op(e2,e1))
% 0.20/0.67      & op(op(e0,e2),e2) = op(e0,op(e2,e2))
% 0.20/0.67      & op(op(e0,e2),e3) = op(e0,op(e2,e3))
% 0.20/0.67      & op(op(e0,e3),e0) = op(e0,op(e3,e0))
% 0.20/0.67      & op(op(e0,e3),e1) = op(e0,op(e3,e1))
% 0.20/0.67      & op(op(e0,e3),e2) = op(e0,op(e3,e2))
% 0.20/0.67      & op(op(e0,e3),e3) = op(e0,op(e3,e3))
% 0.20/0.67      & op(op(e1,e0),e0) = op(e1,op(e0,e0))
% 0.20/0.67      & op(op(e1,e0),e1) = op(e1,op(e0,e1))
% 0.20/0.67      & op(op(e1,e0),e2) = op(e1,op(e0,e2))
% 0.20/0.67      & op(op(e1,e0),e3) = op(e1,op(e0,e3))
% 0.20/0.67      & op(op(e1,e1),e0) = op(e1,op(e1,e0))
% 0.20/0.67      & op(op(e1,e1),e1) = op(e1,op(e1,e1))
% 0.20/0.67      & op(op(e1,e1),e2) = op(e1,op(e1,e2))
% 0.20/0.67      & op(op(e1,e1),e3) = op(e1,op(e1,e3))
% 0.20/0.67      & op(op(e1,e2),e0) = op(e1,op(e2,e0))
% 0.20/0.67      & op(op(e1,e2),e1) = op(e1,op(e2,e1))
% 0.20/0.67      & op(op(e1,e2),e2) = op(e1,op(e2,e2))
% 0.20/0.67      & op(op(e1,e2),e3) = op(e1,op(e2,e3))
% 0.20/0.67      & op(op(e1,e3),e0) = op(e1,op(e3,e0))
% 0.20/0.67      & op(op(e1,e3),e1) = op(e1,op(e3,e1))
% 0.20/0.67      & op(op(e1,e3),e2) = op(e1,op(e3,e2))
% 0.20/0.67      & op(op(e1,e3),e3) = op(e1,op(e3,e3))
% 0.20/0.67      & op(op(e2,e0),e0) = op(e2,op(e0,e0))
% 0.20/0.67      & op(op(e2,e0),e1) = op(e2,op(e0,e1))
% 0.20/0.67      & op(op(e2,e0),e2) = op(e2,op(e0,e2))
% 0.20/0.67      & op(op(e2,e0),e3) = op(e2,op(e0,e3))
% 0.20/0.67      & op(op(e2,e1),e0) = op(e2,op(e1,e0))
% 0.20/0.67      & op(op(e2,e1),e1) = op(e2,op(e1,e1))
% 0.20/0.67      & op(op(e2,e1),e2) = op(e2,op(e1,e2))
% 0.20/0.67      & op(op(e2,e1),e3) = op(e2,op(e1,e3))
% 0.20/0.67      & op(op(e2,e2),e0) = op(e2,op(e2,e0))
% 0.20/0.67      & op(op(e2,e2),e1) = op(e2,op(e2,e1))
% 0.20/0.67      & op(op(e2,e2),e2) = op(e2,op(e2,e2))
% 0.20/0.67      & op(op(e2,e2),e3) = op(e2,op(e2,e3))
% 0.20/0.67      & op(op(e2,e3),e0) = op(e2,op(e3,e0))
% 0.20/0.67      & op(op(e2,e3),e1) = op(e2,op(e3,e1))
% 0.20/0.67      & op(op(e2,e3),e2) = op(e2,op(e3,e2))
% 0.20/0.67      & op(op(e2,e3),e3) = op(e2,op(e3,e3))
% 0.20/0.67      & op(op(e3,e0),e0) = op(e3,op(e0,e0))
% 0.20/0.67      & op(op(e3,e0),e1) = op(e3,op(e0,e1))
% 0.20/0.67      & op(op(e3,e0),e2) = op(e3,op(e0,e2))
% 0.20/0.67      & op(op(e3,e0),e3) = op(e3,op(e0,e3))
% 0.20/0.67      & op(op(e3,e1),e0) = op(e3,op(e1,e0))
% 0.20/0.67      & op(op(e3,e1),e1) = op(e3,op(e1,e1))
% 0.20/0.67      & op(op(e3,e1),e2) = op(e3,op(e1,e2))
% 0.20/0.67      & op(op(e3,e1),e3) = op(e3,op(e1,e3))
% 0.20/0.67      & op(op(e3,e2),e0) = op(e3,op(e2,e0))
% 0.20/0.67      & op(op(e3,e2),e1) = op(e3,op(e2,e1))
% 0.20/0.67      & op(op(e3,e2),e2) = op(e3,op(e2,e2))
% 0.20/0.67      & op(op(e3,e2),e3) = op(e3,op(e2,e3))
% 0.20/0.67      & op(op(e3,e3),e0) = op(e3,op(e3,e0))
% 0.20/0.67      & op(op(e3,e3),e1) = op(e3,op(e3,e1))
% 0.20/0.67      & op(op(e3,e3),e2) = op(e3,op(e3,e2))
% 0.20/0.67      & op(op(e3,e3),e3) = op(e3,op(e3,e3)) ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax3,axiom,
% 0.20/0.67      ( op(unit,e0) = e0
% 0.20/0.67      & op(e0,unit) = e0
% 0.20/0.67      & op(unit,e1) = e1
% 0.20/0.67      & op(e1,unit) = e1
% 0.20/0.67      & op(unit,e2) = e2
% 0.20/0.67      & op(e2,unit) = e2
% 0.20/0.67      & op(unit,e3) = e3
% 0.20/0.67      & op(e3,unit) = e3
% 0.20/0.67      & ( unit = e0
% 0.20/0.67        | unit = e1
% 0.20/0.67        | unit = e2
% 0.20/0.67        | unit = e3 ) ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax4,axiom,
% 0.20/0.67      ( op(e0,inv(e0)) = unit
% 0.20/0.67      & op(inv(e0),e0) = unit
% 0.20/0.67      & op(e1,inv(e1)) = unit
% 0.20/0.67      & op(inv(e1),e1) = unit
% 0.20/0.67      & op(e2,inv(e2)) = unit
% 0.20/0.67      & op(inv(e2),e2) = unit
% 0.20/0.67      & op(e3,inv(e3)) = unit
% 0.20/0.67      & op(inv(e3),e3) = unit
% 0.20/0.67      & ( inv(e0) = e0
% 0.20/0.67        | inv(e0) = e1
% 0.20/0.67        | inv(e0) = e2
% 0.20/0.67        | inv(e0) = e3 )
% 0.20/0.67      & ( inv(e1) = e0
% 0.20/0.67        | inv(e1) = e1
% 0.20/0.67        | inv(e1) = e2
% 0.20/0.67        | inv(e1) = e3 )
% 0.20/0.67      & ( inv(e2) = e0
% 0.20/0.67        | inv(e2) = e1
% 0.20/0.67        | inv(e2) = e2
% 0.20/0.67        | inv(e2) = e3 )
% 0.20/0.67      & ( inv(e3) = e0
% 0.20/0.67        | inv(e3) = e1
% 0.20/0.67        | inv(e3) = e2
% 0.20/0.67        | inv(e3) = e3 ) ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax5,axiom,
% 0.20/0.67      inv(unit) = unit ).
% 0.20/0.67  
% 0.20/0.67  fof(ax6,axiom,
% 0.20/0.67      ( inv(inv(e0)) = e0
% 0.20/0.67      & inv(inv(e1)) = e1
% 0.20/0.67      & inv(inv(e2)) = e2
% 0.20/0.67      & inv(inv(e3)) = e3 ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax7,axiom,
% 0.20/0.67      ( ( inv(e0) = e0
% 0.20/0.67       => inv(e0) = e0 )
% 0.20/0.67      & ( inv(e0) = e1
% 0.20/0.67       => inv(e1) = e0 )
% 0.20/0.67      & ( inv(e0) = e2
% 0.20/0.67       => inv(e2) = e0 )
% 0.20/0.67      & ( inv(e0) = e3
% 0.20/0.67       => inv(e3) = e0 )
% 0.20/0.67      & ( inv(e1) = e0
% 0.20/0.67       => inv(e0) = e1 )
% 0.20/0.67      & ( inv(e1) = e1
% 0.20/0.67       => inv(e1) = e1 )
% 0.20/0.67      & ( inv(e1) = e2
% 0.20/0.67       => inv(e2) = e1 )
% 0.20/0.67      & ( inv(e1) = e3
% 0.20/0.67       => inv(e3) = e1 )
% 0.20/0.67      & ( inv(e2) = e0
% 0.20/0.67       => inv(e0) = e2 )
% 0.20/0.67      & ( inv(e2) = e1
% 0.20/0.67       => inv(e1) = e2 )
% 0.20/0.67      & ( inv(e2) = e2
% 0.20/0.67       => inv(e2) = e2 )
% 0.20/0.67      & ( inv(e2) = e3
% 0.20/0.67       => inv(e3) = e2 )
% 0.20/0.67      & ( inv(e3) = e0
% 0.20/0.67       => inv(e0) = e3 )
% 0.20/0.67      & ( inv(e3) = e1
% 0.20/0.67       => inv(e1) = e3 )
% 0.20/0.67      & ( inv(e3) = e2
% 0.20/0.67       => inv(e2) = e3 )
% 0.20/0.67      & ( inv(e3) = e3
% 0.20/0.67       => inv(e3) = e3 ) ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax8,axiom,
% 0.20/0.67      ( inv(e0) != inv(e1)
% 0.20/0.67      & inv(e0) != inv(e2)
% 0.20/0.67      & inv(e0) != inv(e3)
% 0.20/0.67      & inv(e1) != inv(e2)
% 0.20/0.67      & inv(e1) != inv(e3)
% 0.20/0.67      & inv(e2) != inv(e3) ) ).
% 0.20/0.67  
% 0.20/0.67  fof(ax9,axiom,
% 0.20/0.67      ( op(e0,e0) != op(e1,e0)
% 0.20/0.67      & op(e0,e0) != op(e2,e0)
% 0.20/0.67      & op(e0,e0) != op(e3,e0)
% 0.20/0.67      & op(e1,e0) != op(e2,e0)
% 0.20/0.67      & op(e1,e0) != op(e3,e0)
% 0.20/0.67      & op(e2,e0) != op(e3,e0)
% 0.20/0.67      & op(e0,e1) != op(e1,e1)
% 0.20/0.67      & op(e0,e1) != op(e2,e1)
% 0.20/0.67      & op(e0,e1) != op(e3,e1)
% 0.20/0.67      & op(e1,e1) != op(e2,e1)
% 0.20/0.67      & op(e1,e1) != op(e3,e1)
% 0.20/0.67      & op(e2,e1) != op(e3,e1)
% 0.20/0.67      & op(e0,e2) != op(e1,e2)
% 0.20/0.67      & op(e0,e2) != op(e2,e2)
% 0.20/0.67      & op(e0,e2) != op(e3,e2)
% 0.20/0.67      & op(e1,e2) != op(e2,e2)
% 0.20/0.67      & op(e1,e2) != op(e3,e2)
% 0.20/0.67      & op(e2,e2) != op(e3,e2)
% 0.20/0.67      & op(e0,e3) != op(e1,e3)
% 0.20/0.67      & op(e0,e3) != op(e2,e3)
% 0.20/0.67      & op(e0,e3) != op(e3,e3)
% 0.20/0.67      & op(e1,e3) != op(e2,e3)
% 0.20/0.68      & op(e1,e3) != op(e3,e3)
% 0.20/0.68      & op(e2,e3) != op(e3,e3)
% 0.20/0.68      & op(e0,e0) != op(e0,e1)
% 0.20/0.68      & op(e0,e0) != op(e0,e2)
% 0.20/0.68      & op(e0,e0) != op(e0,e3)
% 0.20/0.68      & op(e0,e1) != op(e0,e2)
% 0.20/0.68      & op(e0,e1) != op(e0,e3)
% 0.20/0.68      & op(e0,e2) != op(e0,e3)
% 0.20/0.68      & op(e1,e0) != op(e1,e1)
% 0.20/0.68      & op(e1,e0) != op(e1,e2)
% 0.20/0.68      & op(e1,e0) != op(e1,e3)
% 0.20/0.68      & op(e1,e1) != op(e1,e2)
% 0.20/0.68      & op(e1,e1) != op(e1,e3)
% 0.20/0.68      & op(e1,e2) != op(e1,e3)
% 0.20/0.68      & op(e2,e0) != op(e2,e1)
% 0.20/0.68      & op(e2,e0) != op(e2,e2)
% 0.20/0.68      & op(e2,e0) != op(e2,e3)
% 0.20/0.68      & op(e2,e1) != op(e2,e2)
% 0.20/0.68      & op(e2,e1) != op(e2,e3)
% 0.20/0.68      & op(e2,e2) != op(e2,e3)
% 0.20/0.68      & op(e3,e0) != op(e3,e1)
% 0.20/0.68      & op(e3,e0) != op(e3,e2)
% 0.20/0.68      & op(e3,e0) != op(e3,e3)
% 0.20/0.68      & op(e3,e1) != op(e3,e2)
% 0.20/0.68      & op(e3,e1) != op(e3,e3)
% 0.20/0.68      & op(e3,e2) != op(e3,e3) ) ).
% 0.20/0.68  
% 0.20/0.68  fof(ax10,axiom,
% 0.20/0.68      ( e0 != e1
% 0.20/0.68      & e0 != e2
% 0.20/0.68      & e0 != e3
% 0.20/0.68      & e1 != e2
% 0.20/0.68      & e1 != e3
% 0.20/0.68      & e2 != e3 ) ).
% 0.20/0.68  
% 0.20/0.68  fof(ax11,axiom,
% 0.20/0.68      ( e0 = op(e3,e3)
% 0.20/0.68      & e1 = op(e2,e3) ) ).
% 0.20/0.68  
% 0.20/0.68  fof(co1,conjecture,
% 0.20/0.68      ~ ( ( ( op(e0,e0) = e0
% 0.20/0.68            & op(e1,e1) = e0
% 0.20/0.68            & op(e2,e2) = e0
% 0.20/0.68            & op(e3,e3) = e0 )
% 0.20/0.68          | ( op(e0,e0) = e1
% 0.20/0.68            & op(e1,e1) = e1
% 0.20/0.68            & op(e2,e2) = e1
% 0.20/0.68            & op(e3,e3) = e1 )
% 0.20/0.68          | ( op(e0,e0) = e2
% 0.20/0.68            & op(e1,e1) = e2
% 0.20/0.68            & op(e2,e2) = e2
% 0.20/0.68            & op(e3,e3) = e2 )
% 0.20/0.68          | ( op(e0,e0) = e3
% 0.20/0.68            & op(e1,e1) = e3
% 0.20/0.68            & op(e2,e2) = e3
% 0.20/0.68            & op(e3,e3) = e3 ) )
% 0.20/0.68        & ~ ( ( op(e0,e0) = e0
% 0.20/0.68              & op(e1,e1) = e0
% 0.20/0.68              & op(e2,e2) = e0
% 0.20/0.68              & op(e3,e3) = e0 )
% 0.20/0.68            | ( op(e0,e0) = e1
% 0.20/0.68              & op(e1,e1) = e1
% 0.20/0.68              & op(e2,e2) = e1
% 0.20/0.68              & op(e3,e3) = e1 )
% 0.20/0.68            | ( op(e0,e0) = e2
% 0.20/0.68              & op(e1,e1) = e2
% 0.20/0.68              & op(e2,e2) = e2
% 0.20/0.68              & op(e3,e3) = e2 )
% 0.20/0.68            | ( op(e0,e0) = e3
% 0.20/0.68              & op(e1,e1) = e3
% 0.20/0.68              & op(e2,e2) = e3
% 0.20/0.68              & op(e3,e3) = e3 ) ) ) ).
% 0.20/0.68  
% 0.20/0.68  %--------------------------------------------------------------------------
% 0.20/0.68  %-------------------------------------------
% 0.20/0.68  % Proof found
% 0.20/0.68  % SZS status Theorem for theBenchmark
% 0.20/0.68  % SZS output start Proof
% 0.20/0.68  %ClaNum:260(EqnAxiom:7)
% 0.20/0.68  %VarNum:0(SingletonVarNum:0)
% 0.20/0.68  %MaxLitNum:5
% 0.20/0.68  %MaxfuncDepth:2
% 0.20/0.68  %SharedTerms:392
% 0.20/0.68  %goalClause: 101 169 170 171 172 257
% 0.20/0.68  %singleGoalClaCount:1
% 0.20/0.68  [95]~E(a4,a3)
% 0.20/0.68  [96]~E(a5,a3)
% 0.20/0.68  [97]~E(a5,a4)
% 0.20/0.68  [98]~E(a6,a3)
% 0.20/0.68  [99]~E(a4,a6)
% 0.20/0.68  [100]~E(a5,a6)
% 0.20/0.68  [101]~P1(a500)
% 0.20/0.68  [8]E(f2(a1),a1)
% 0.20/0.68  [13]E(f7(a6,a6),a3)
% 0.20/0.68  [14]E(f7(a5,a6),a4)
% 0.20/0.68  [15]E(f7(a3,a1),a3)
% 0.20/0.68  [16]E(f7(a4,a1),a4)
% 0.20/0.68  [17]E(f7(a5,a1),a5)
% 0.20/0.68  [18]E(f7(a6,a1),a6)
% 0.20/0.68  [19]E(f7(a1,a3),a3)
% 0.20/0.68  [20]E(f7(a1,a4),a4)
% 0.20/0.68  [21]E(f7(a1,a5),a5)
% 0.20/0.68  [22]E(f7(a1,a6),a6)
% 0.20/0.68  [102]~E(f2(a4),f2(a3))
% 0.20/0.68  [103]~E(f2(a5),f2(a3))
% 0.20/0.68  [104]~E(f2(a5),f2(a4))
% 0.20/0.68  [105]~E(f2(a6),f2(a3))
% 0.20/0.68  [106]~E(f2(a4),f2(a6))
% 0.20/0.68  [107]~E(f2(a5),f2(a6))
% 0.20/0.68  [108]~E(f7(a3,a4),f7(a3,a3))
% 0.20/0.68  [109]~E(f7(a3,a5),f7(a3,a3))
% 0.20/0.68  [110]~E(f7(a3,a5),f7(a3,a4))
% 0.20/0.68  [111]~E(f7(a3,a6),f7(a3,a3))
% 0.20/0.68  [112]~E(f7(a3,a4),f7(a3,a6))
% 0.20/0.68  [113]~E(f7(a3,a5),f7(a3,a6))
% 0.20/0.68  [114]~E(f7(a4,a3),f7(a3,a3))
% 0.20/0.68  [115]~E(f7(a4,a4),f7(a3,a4))
% 0.20/0.68  [116]~E(f7(a4,a4),f7(a4,a3))
% 0.20/0.68  [117]~E(f7(a4,a5),f7(a3,a5))
% 0.20/0.68  [118]~E(f7(a4,a5),f7(a4,a3))
% 0.20/0.68  [119]~E(f7(a4,a5),f7(a4,a4))
% 0.20/0.68  [120]~E(f7(a4,a6),f7(a3,a6))
% 0.20/0.68  [121]~E(f7(a4,a6),f7(a4,a3))
% 0.20/0.68  [122]~E(f7(a4,a4),f7(a4,a6))
% 0.20/0.68  [123]~E(f7(a4,a5),f7(a4,a6))
% 0.20/0.68  [124]~E(f7(a5,a3),f7(a3,a3))
% 0.20/0.68  [125]~E(f7(a5,a3),f7(a4,a3))
% 0.20/0.68  [126]~E(f7(a5,a4),f7(a3,a4))
% 0.20/0.68  [127]~E(f7(a5,a4),f7(a4,a4))
% 0.20/0.68  [128]~E(f7(a5,a4),f7(a5,a3))
% 0.20/0.68  [129]~E(f7(a5,a5),f7(a3,a5))
% 0.20/0.68  [130]~E(f7(a5,a5),f7(a4,a5))
% 0.20/0.68  [131]~E(f7(a5,a5),f7(a5,a3))
% 0.20/0.68  [132]~E(f7(a5,a5),f7(a5,a4))
% 0.20/0.68  [133]~E(f7(a5,a6),f7(a3,a6))
% 0.20/0.68  [134]~E(f7(a5,a6),f7(a4,a6))
% 0.20/0.68  [135]~E(f7(a5,a6),f7(a5,a3))
% 0.20/0.68  [136]~E(f7(a5,a4),f7(a5,a6))
% 0.20/0.68  [137]~E(f7(a5,a5),f7(a5,a6))
% 0.20/0.68  [138]~E(f7(a6,a3),f7(a3,a3))
% 0.20/0.68  [139]~E(f7(a4,a3),f7(a6,a3))
% 0.20/0.68  [140]~E(f7(a5,a3),f7(a6,a3))
% 0.20/0.68  [141]~E(f7(a6,a4),f7(a3,a4))
% 0.20/0.68  [142]~E(f7(a4,a4),f7(a6,a4))
% 0.20/0.68  [143]~E(f7(a5,a4),f7(a6,a4))
% 0.20/0.68  [144]~E(f7(a6,a4),f7(a6,a3))
% 0.20/0.68  [145]~E(f7(a6,a5),f7(a3,a5))
% 0.20/0.68  [146]~E(f7(a4,a5),f7(a6,a5))
% 0.20/0.68  [147]~E(f7(a5,a5),f7(a6,a5))
% 0.20/0.68  [148]~E(f7(a6,a5),f7(a6,a3))
% 0.20/0.68  [149]~E(f7(a6,a5),f7(a6,a4))
% 0.20/0.68  [150]~E(f7(a6,a6),f7(a3,a6))
% 0.20/0.68  [151]~E(f7(a4,a6),f7(a6,a6))
% 0.20/0.68  [152]~E(f7(a5,a6),f7(a6,a6))
% 0.20/0.68  [153]~E(f7(a6,a6),f7(a6,a3))
% 0.20/0.68  [154]~E(f7(a6,a4),f7(a6,a6))
% 0.20/0.68  [155]~E(f7(a6,a5),f7(a6,a6))
% 0.20/0.68  [9]E(f2(f2(a3)),a3)
% 0.20/0.68  [10]E(f2(f2(a4)),a4)
% 0.20/0.68  [11]E(f2(f2(a5)),a5)
% 0.20/0.68  [12]E(f2(f2(a6)),a6)
% 0.20/0.68  [23]E(f7(a3,f2(a3)),a1)
% 0.20/0.68  [24]E(f7(a4,f2(a4)),a1)
% 0.20/0.68  [25]E(f7(a5,f2(a5)),a1)
% 0.20/0.68  [26]E(f7(a6,f2(a6)),a1)
% 0.20/0.68  [27]E(f7(f2(a3),a3),a1)
% 0.20/0.68  [28]E(f7(f2(a4),a4),a1)
% 0.20/0.68  [29]E(f7(f2(a5),a5),a1)
% 0.20/0.68  [30]E(f7(f2(a6),a6),a1)
% 0.20/0.68  [31]E(f7(f7(a3,a3),a3),f7(a3,f7(a3,a3)))
% 0.20/0.68  [32]E(f7(f7(a3,a3),a4),f7(a3,f7(a3,a4)))
% 0.20/0.68  [33]E(f7(f7(a3,a3),a5),f7(a3,f7(a3,a5)))
% 0.20/0.68  [34]E(f7(f7(a3,a3),a6),f7(a3,f7(a3,a6)))
% 0.20/0.68  [35]E(f7(f7(a3,a4),a3),f7(a3,f7(a4,a3)))
% 0.20/0.68  [36]E(f7(f7(a3,a4),a4),f7(a3,f7(a4,a4)))
% 0.20/0.68  [37]E(f7(f7(a3,a4),a5),f7(a3,f7(a4,a5)))
% 0.20/0.68  [38]E(f7(f7(a3,a4),a6),f7(a3,f7(a4,a6)))
% 0.20/0.68  [39]E(f7(f7(a3,a5),a3),f7(a3,f7(a5,a3)))
% 0.20/0.68  [40]E(f7(f7(a3,a5),a4),f7(a3,f7(a5,a4)))
% 0.20/0.68  [41]E(f7(f7(a3,a5),a5),f7(a3,f7(a5,a5)))
% 0.20/0.68  [42]E(f7(f7(a3,a5),a6),f7(a3,f7(a5,a6)))
% 0.20/0.68  [43]E(f7(f7(a3,a6),a3),f7(a3,f7(a6,a3)))
% 0.20/0.68  [44]E(f7(f7(a3,a6),a4),f7(a3,f7(a6,a4)))
% 0.20/0.68  [45]E(f7(f7(a3,a6),a5),f7(a3,f7(a6,a5)))
% 0.20/0.68  [46]E(f7(f7(a3,a6),a6),f7(a3,f7(a6,a6)))
% 0.20/0.68  [47]E(f7(f7(a4,a3),a3),f7(a4,f7(a3,a3)))
% 0.20/0.68  [48]E(f7(f7(a4,a3),a4),f7(a4,f7(a3,a4)))
% 0.20/0.68  [49]E(f7(f7(a4,a3),a5),f7(a4,f7(a3,a5)))
% 0.20/0.68  [50]E(f7(f7(a4,a3),a6),f7(a4,f7(a3,a6)))
% 0.20/0.68  [51]E(f7(f7(a4,a4),a3),f7(a4,f7(a4,a3)))
% 0.20/0.68  [52]E(f7(f7(a4,a4),a4),f7(a4,f7(a4,a4)))
% 0.20/0.68  [53]E(f7(f7(a4,a4),a5),f7(a4,f7(a4,a5)))
% 0.20/0.68  [54]E(f7(f7(a4,a4),a6),f7(a4,f7(a4,a6)))
% 0.20/0.68  [55]E(f7(f7(a4,a5),a3),f7(a4,f7(a5,a3)))
% 0.20/0.68  [56]E(f7(f7(a4,a5),a4),f7(a4,f7(a5,a4)))
% 0.20/0.68  [57]E(f7(f7(a4,a5),a5),f7(a4,f7(a5,a5)))
% 0.20/0.68  [58]E(f7(f7(a4,a5),a6),f7(a4,f7(a5,a6)))
% 0.20/0.68  [59]E(f7(f7(a4,a6),a3),f7(a4,f7(a6,a3)))
% 0.20/0.68  [60]E(f7(f7(a4,a6),a4),f7(a4,f7(a6,a4)))
% 0.20/0.68  [61]E(f7(f7(a4,a6),a5),f7(a4,f7(a6,a5)))
% 0.20/0.68  [62]E(f7(f7(a4,a6),a6),f7(a4,f7(a6,a6)))
% 0.20/0.68  [63]E(f7(f7(a5,a3),a3),f7(a5,f7(a3,a3)))
% 0.20/0.68  [64]E(f7(f7(a5,a3),a4),f7(a5,f7(a3,a4)))
% 0.20/0.68  [65]E(f7(f7(a5,a3),a5),f7(a5,f7(a3,a5)))
% 0.20/0.68  [66]E(f7(f7(a5,a3),a6),f7(a5,f7(a3,a6)))
% 0.20/0.68  [67]E(f7(f7(a5,a4),a3),f7(a5,f7(a4,a3)))
% 0.20/0.68  [68]E(f7(f7(a5,a4),a4),f7(a5,f7(a4,a4)))
% 0.20/0.68  [69]E(f7(f7(a5,a4),a5),f7(a5,f7(a4,a5)))
% 0.20/0.68  [70]E(f7(f7(a5,a4),a6),f7(a5,f7(a4,a6)))
% 0.20/0.68  [71]E(f7(f7(a5,a5),a3),f7(a5,f7(a5,a3)))
% 0.20/0.68  [72]E(f7(f7(a5,a5),a4),f7(a5,f7(a5,a4)))
% 0.20/0.68  [73]E(f7(f7(a5,a5),a5),f7(a5,f7(a5,a5)))
% 0.20/0.68  [74]E(f7(f7(a5,a5),a6),f7(a5,f7(a5,a6)))
% 0.20/0.68  [75]E(f7(f7(a5,a6),a3),f7(a5,f7(a6,a3)))
% 0.20/0.68  [76]E(f7(f7(a5,a6),a4),f7(a5,f7(a6,a4)))
% 0.20/0.68  [77]E(f7(f7(a5,a6),a5),f7(a5,f7(a6,a5)))
% 0.20/0.68  [78]E(f7(f7(a5,a6),a6),f7(a5,f7(a6,a6)))
% 0.20/0.68  [79]E(f7(f7(a6,a3),a3),f7(a6,f7(a3,a3)))
% 0.20/0.68  [80]E(f7(f7(a6,a3),a4),f7(a6,f7(a3,a4)))
% 0.20/0.68  [81]E(f7(f7(a6,a3),a5),f7(a6,f7(a3,a5)))
% 0.20/0.68  [82]E(f7(f7(a6,a3),a6),f7(a6,f7(a3,a6)))
% 0.20/0.68  [83]E(f7(f7(a6,a4),a3),f7(a6,f7(a4,a3)))
% 0.20/0.68  [84]E(f7(f7(a6,a4),a4),f7(a6,f7(a4,a4)))
% 0.20/0.68  [85]E(f7(f7(a6,a4),a5),f7(a6,f7(a4,a5)))
% 0.20/0.68  [86]E(f7(f7(a6,a4),a6),f7(a6,f7(a4,a6)))
% 0.20/0.68  [87]E(f7(f7(a6,a5),a3),f7(a6,f7(a5,a3)))
% 0.20/0.68  [88]E(f7(f7(a6,a5),a4),f7(a6,f7(a5,a4)))
% 0.20/0.68  [89]E(f7(f7(a6,a5),a5),f7(a6,f7(a5,a5)))
% 0.20/0.68  [90]E(f7(f7(a6,a5),a6),f7(a6,f7(a5,a6)))
% 0.20/0.68  [91]E(f7(f7(a6,a6),a3),f7(a6,f7(a6,a3)))
% 0.20/0.68  [92]E(f7(f7(a6,a6),a4),f7(a6,f7(a6,a4)))
% 0.20/0.68  [93]E(f7(f7(a6,a6),a5),f7(a6,f7(a6,a5)))
% 0.20/0.68  [94]E(f7(f7(a6,a6),a6),f7(a6,f7(a6,a6)))
% 0.20/0.68  [157]E(f2(a3),a4)+~E(f2(a4),a3)
% 0.20/0.68  [158]E(f2(a3),a5)+~E(f2(a5),a3)
% 0.20/0.68  [159]E(f2(a3),a6)+~E(f2(a6),a3)
% 0.20/0.68  [160]E(f2(a4),a3)+~E(f2(a3),a4)
% 0.20/0.68  [161]E(f2(a4),a5)+~E(f2(a5),a4)
% 0.20/0.68  [162]E(f2(a4),a6)+~E(f2(a6),a4)
% 0.20/0.68  [163]E(f2(a5),a3)+~E(f2(a3),a5)
% 0.20/0.68  [164]E(f2(a5),a4)+~E(f2(a4),a5)
% 0.20/0.68  [165]E(f2(a5),a6)+~E(f2(a6),a5)
% 0.20/0.68  [166]E(f2(a6),a3)+~E(f2(a3),a6)
% 0.20/0.68  [167]E(f2(a6),a4)+~E(f2(a4),a6)
% 0.20/0.68  [168]E(f2(a6),a5)+~E(f2(a5),a6)
% 0.20/0.68  [169]P1(a500)+E(f7(a3,a3),a6)
% 0.20/0.68  [170]P1(a500)+E(f7(a4,a4),a6)
% 0.20/0.68  [171]P1(a500)+E(f7(a5,a5),a6)
% 0.20/0.68  [172]P1(a500)+E(f7(a6,a6),a6)
% 0.20/0.68  [156]E(a3,a1)+E(a4,a1)+E(a5,a1)+E(a6,a1)
% 0.20/0.68  [173]E(f2(a3),a4)+E(f2(a3),a5)+E(f2(a3),a6)+E(f2(a3),a3)
% 0.20/0.68  [174]E(f2(a4),a3)+E(f2(a4),a5)+E(f2(a4),a6)+E(f2(a4),a4)
% 0.20/0.68  [175]E(f2(a5),a3)+E(f2(a5),a4)+E(f2(a5),a6)+E(f2(a5),a5)
% 0.20/0.68  [176]E(f2(a6),a3)+E(f2(a6),a4)+E(f2(a6),a5)+E(f2(a6),a6)
% 0.20/0.68  [241]E(f7(a3,a3),a3)+E(f7(a3,a3),a4)+E(f7(a3,a3),a5)+E(f7(a3,a3),a6)
% 0.20/0.68  [242]E(f7(a3,a4),a6)+E(f7(a3,a4),a5)+E(f7(a3,a4),a4)+E(f7(a3,a4),a3)
% 0.20/0.68  [243]E(f7(a3,a5),a6)+E(f7(a3,a5),a5)+E(f7(a3,a5),a4)+E(f7(a3,a5),a3)
% 0.20/0.68  [244]E(f7(a3,a6),a6)+E(f7(a3,a6),a5)+E(f7(a3,a6),a4)+E(f7(a3,a6),a3)
% 0.20/0.68  [245]E(f7(a4,a3),a6)+E(f7(a4,a3),a5)+E(f7(a4,a3),a4)+E(f7(a4,a3),a3)
% 0.20/0.68  [246]E(f7(a4,a4),a3)+E(f7(a4,a4),a4)+E(f7(a4,a4),a5)+E(f7(a4,a4),a6)
% 0.20/0.68  [247]E(f7(a4,a5),a6)+E(f7(a4,a5),a5)+E(f7(a4,a5),a4)+E(f7(a4,a5),a3)
% 0.20/0.68  [248]E(f7(a4,a6),a6)+E(f7(a4,a6),a5)+E(f7(a4,a6),a4)+E(f7(a4,a6),a3)
% 0.20/0.68  [249]E(f7(a5,a3),a6)+E(f7(a5,a3),a5)+E(f7(a5,a3),a4)+E(f7(a5,a3),a3)
% 0.20/0.68  [250]E(f7(a5,a4),a6)+E(f7(a5,a4),a5)+E(f7(a5,a4),a4)+E(f7(a5,a4),a3)
% 0.20/0.68  [251]E(f7(a5,a5),a3)+E(f7(a5,a5),a4)+E(f7(a5,a5),a5)+E(f7(a5,a5),a6)
% 0.20/0.68  [253]E(f7(a6,a3),a6)+E(f7(a6,a3),a5)+E(f7(a6,a3),a4)+E(f7(a6,a3),a3)
% 0.20/0.68  [254]E(f7(a6,a4),a6)+E(f7(a6,a4),a5)+E(f7(a6,a4),a4)+E(f7(a6,a4),a3)
% 0.20/0.68  [255]E(f7(a6,a5),a6)+E(f7(a6,a5),a5)+E(f7(a6,a5),a4)+E(f7(a6,a5),a3)
% 0.20/0.68  [257]~E(f7(a3,a3),a6)+~E(f7(a4,a4),a6)+~E(f7(a5,a5),a6)+~E(f7(a6,a6),a6)
% 0.20/0.68  [258]P1(a500)+~E(f7(a3,a3),a3)+~E(f7(a4,a4),a3)+~E(f7(a5,a5),a3)+~E(f7(a6,a6),a3)
% 0.20/0.68  [259]P1(a500)+~E(f7(a3,a3),a4)+~E(f7(a4,a4),a4)+~E(f7(a5,a5),a4)+~E(f7(a6,a6),a4)
% 0.20/0.68  [260]P1(a500)+~E(f7(a3,a3),a5)+~E(f7(a4,a4),a5)+~E(f7(a5,a5),a5)+~E(f7(a6,a6),a5)
% 0.20/0.68  %EqnAxiom
% 0.20/0.68  [1]E(x11,x11)
% 0.20/0.68  [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.68  [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.68  [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.20/0.68  [5]~E(x51,x52)+E(f7(x51,x53),f7(x52,x53))
% 0.20/0.68  [6]~E(x61,x62)+E(f7(x63,x61),f7(x63,x62))
% 0.20/0.68  [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.20/0.68  
% 0.20/0.68  %-------------------------------------------
% 0.20/0.68  cnf(270,plain,
% 0.20/0.68     ($false),
% 0.20/0.68     inference(scs_inference,[],[101,95,8,13,2,3,172,171,170,169,6,5,4,257]),
% 0.20/0.68     ['proof']).
% 0.20/0.68  % SZS output end Proof
% 0.20/0.68  % Total time :0.010000s
%------------------------------------------------------------------------------