TSTP Solution File: ALG014+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ALG014+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 : n005.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 0.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG014+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
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:02:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.000000s
% 0.20/0.65 % Output :CNFRefutation 0.000000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 % File : ALG014+1 : TPTP v8.1.2. Released v2.7.0.
% 0.20/0.65 % Domain : General Algebra
% 0.20/0.65 % Problem : Groups 4: CPROPS-COVERING-PROBLEM-1
% 0.20/0.65 % Version : Especial.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [Mei03] Meier (2003), Email to G.Sutcliffe
% 0.20/0.65 % : [CM+04] Colton et al. (2004), Automatic Generation of Classifi
% 0.20/0.65 % Source : [Mei03]
% 0.20/0.65 % Names :
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % 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, 0.00 v3.2.0, 0.11 v2.7.0
% 0.20/0.65 % Syntax : Number of formulae : 12 ( 2 unt; 0 def)
% 0.20/0.65 % Number of atoms : 294 ( 294 equ)
% 0.20/0.65 % Maximal formula atoms : 64 ( 24 avg)
% 0.20/0.65 % Number of connectives : 343 ( 61 ~; 70 |; 196 &)
% 0.20/0.65 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 64 ( 17 avg)
% 0.20/0.65 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.65 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.20/0.65 % Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% 0.20/0.65 % Number of variables : 0 ( 0 !; 0 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_PEQ
% 0.20/0.65
% 0.20/0.65 % Comments :
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 fof(ax1,axiom,
% 0.20/0.65 ( ( op(e0,e0) = e0
% 0.20/0.65 | op(e0,e0) = e1
% 0.20/0.65 | op(e0,e0) = e2
% 0.20/0.65 | op(e0,e0) = e3 )
% 0.20/0.65 & ( op(e0,e1) = e0
% 0.20/0.65 | op(e0,e1) = e1
% 0.20/0.65 | op(e0,e1) = e2
% 0.20/0.65 | op(e0,e1) = e3 )
% 0.20/0.65 & ( op(e0,e2) = e0
% 0.20/0.65 | op(e0,e2) = e1
% 0.20/0.65 | op(e0,e2) = e2
% 0.20/0.65 | op(e0,e2) = e3 )
% 0.20/0.65 & ( op(e0,e3) = e0
% 0.20/0.65 | op(e0,e3) = e1
% 0.20/0.65 | op(e0,e3) = e2
% 0.20/0.65 | op(e0,e3) = e3 )
% 0.20/0.65 & ( op(e1,e0) = e0
% 0.20/0.65 | op(e1,e0) = e1
% 0.20/0.65 | op(e1,e0) = e2
% 0.20/0.65 | op(e1,e0) = e3 )
% 0.20/0.65 & ( op(e1,e1) = e0
% 0.20/0.65 | op(e1,e1) = e1
% 0.20/0.65 | op(e1,e1) = e2
% 0.20/0.65 | op(e1,e1) = e3 )
% 0.20/0.65 & ( op(e1,e2) = e0
% 0.20/0.65 | op(e1,e2) = e1
% 0.20/0.65 | op(e1,e2) = e2
% 0.20/0.65 | op(e1,e2) = e3 )
% 0.20/0.65 & ( op(e1,e3) = e0
% 0.20/0.65 | op(e1,e3) = e1
% 0.20/0.65 | op(e1,e3) = e2
% 0.20/0.65 | op(e1,e3) = e3 )
% 0.20/0.65 & ( op(e2,e0) = e0
% 0.20/0.65 | op(e2,e0) = e1
% 0.20/0.65 | op(e2,e0) = e2
% 0.20/0.65 | op(e2,e0) = e3 )
% 0.20/0.65 & ( op(e2,e1) = e0
% 0.20/0.65 | op(e2,e1) = e1
% 0.20/0.65 | op(e2,e1) = e2
% 0.20/0.65 | op(e2,e1) = e3 )
% 0.20/0.65 & ( op(e2,e2) = e0
% 0.20/0.65 | op(e2,e2) = e1
% 0.20/0.65 | op(e2,e2) = e2
% 0.20/0.66 | op(e2,e2) = e3 )
% 0.20/0.66 & ( op(e2,e3) = e0
% 0.20/0.66 | op(e2,e3) = e1
% 0.20/0.66 | op(e2,e3) = e2
% 0.20/0.66 | op(e2,e3) = e3 )
% 0.20/0.66 & ( op(e3,e0) = e0
% 0.20/0.66 | op(e3,e0) = e1
% 0.20/0.66 | op(e3,e0) = e2
% 0.20/0.66 | op(e3,e0) = e3 )
% 0.20/0.66 & ( op(e3,e1) = e0
% 0.20/0.66 | op(e3,e1) = e1
% 0.20/0.66 | op(e3,e1) = e2
% 0.20/0.66 | op(e3,e1) = e3 )
% 0.20/0.66 & ( op(e3,e2) = e0
% 0.20/0.66 | op(e3,e2) = e1
% 0.20/0.66 | op(e3,e2) = e2
% 0.20/0.66 | op(e3,e2) = e3 )
% 0.20/0.66 & ( op(e3,e3) = e0
% 0.20/0.66 | op(e3,e3) = e1
% 0.20/0.66 | op(e3,e3) = e2
% 0.20/0.66 | op(e3,e3) = e3 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax2,axiom,
% 0.20/0.66 ( op(op(e0,e0),e0) = op(e0,op(e0,e0))
% 0.20/0.66 & op(op(e0,e0),e1) = op(e0,op(e0,e1))
% 0.20/0.66 & op(op(e0,e0),e2) = op(e0,op(e0,e2))
% 0.20/0.66 & op(op(e0,e0),e3) = op(e0,op(e0,e3))
% 0.20/0.66 & op(op(e0,e1),e0) = op(e0,op(e1,e0))
% 0.20/0.66 & op(op(e0,e1),e1) = op(e0,op(e1,e1))
% 0.20/0.66 & op(op(e0,e1),e2) = op(e0,op(e1,e2))
% 0.20/0.66 & op(op(e0,e1),e3) = op(e0,op(e1,e3))
% 0.20/0.66 & op(op(e0,e2),e0) = op(e0,op(e2,e0))
% 0.20/0.66 & op(op(e0,e2),e1) = op(e0,op(e2,e1))
% 0.20/0.66 & op(op(e0,e2),e2) = op(e0,op(e2,e2))
% 0.20/0.66 & op(op(e0,e2),e3) = op(e0,op(e2,e3))
% 0.20/0.66 & op(op(e0,e3),e0) = op(e0,op(e3,e0))
% 0.20/0.66 & op(op(e0,e3),e1) = op(e0,op(e3,e1))
% 0.20/0.66 & op(op(e0,e3),e2) = op(e0,op(e3,e2))
% 0.20/0.66 & op(op(e0,e3),e3) = op(e0,op(e3,e3))
% 0.20/0.66 & op(op(e1,e0),e0) = op(e1,op(e0,e0))
% 0.20/0.66 & op(op(e1,e0),e1) = op(e1,op(e0,e1))
% 0.20/0.66 & op(op(e1,e0),e2) = op(e1,op(e0,e2))
% 0.20/0.66 & op(op(e1,e0),e3) = op(e1,op(e0,e3))
% 0.20/0.66 & op(op(e1,e1),e0) = op(e1,op(e1,e0))
% 0.20/0.66 & op(op(e1,e1),e1) = op(e1,op(e1,e1))
% 0.20/0.66 & op(op(e1,e1),e2) = op(e1,op(e1,e2))
% 0.20/0.66 & op(op(e1,e1),e3) = op(e1,op(e1,e3))
% 0.20/0.66 & op(op(e1,e2),e0) = op(e1,op(e2,e0))
% 0.20/0.66 & op(op(e1,e2),e1) = op(e1,op(e2,e1))
% 0.20/0.66 & op(op(e1,e2),e2) = op(e1,op(e2,e2))
% 0.20/0.66 & op(op(e1,e2),e3) = op(e1,op(e2,e3))
% 0.20/0.66 & op(op(e1,e3),e0) = op(e1,op(e3,e0))
% 0.20/0.66 & op(op(e1,e3),e1) = op(e1,op(e3,e1))
% 0.20/0.66 & op(op(e1,e3),e2) = op(e1,op(e3,e2))
% 0.20/0.66 & op(op(e1,e3),e3) = op(e1,op(e3,e3))
% 0.20/0.66 & op(op(e2,e0),e0) = op(e2,op(e0,e0))
% 0.20/0.66 & op(op(e2,e0),e1) = op(e2,op(e0,e1))
% 0.20/0.66 & op(op(e2,e0),e2) = op(e2,op(e0,e2))
% 0.20/0.66 & op(op(e2,e0),e3) = op(e2,op(e0,e3))
% 0.20/0.66 & op(op(e2,e1),e0) = op(e2,op(e1,e0))
% 0.20/0.66 & op(op(e2,e1),e1) = op(e2,op(e1,e1))
% 0.20/0.66 & op(op(e2,e1),e2) = op(e2,op(e1,e2))
% 0.20/0.66 & op(op(e2,e1),e3) = op(e2,op(e1,e3))
% 0.20/0.66 & op(op(e2,e2),e0) = op(e2,op(e2,e0))
% 0.20/0.66 & op(op(e2,e2),e1) = op(e2,op(e2,e1))
% 0.20/0.66 & op(op(e2,e2),e2) = op(e2,op(e2,e2))
% 0.20/0.66 & op(op(e2,e2),e3) = op(e2,op(e2,e3))
% 0.20/0.66 & op(op(e2,e3),e0) = op(e2,op(e3,e0))
% 0.20/0.66 & op(op(e2,e3),e1) = op(e2,op(e3,e1))
% 0.20/0.66 & op(op(e2,e3),e2) = op(e2,op(e3,e2))
% 0.20/0.66 & op(op(e2,e3),e3) = op(e2,op(e3,e3))
% 0.20/0.66 & op(op(e3,e0),e0) = op(e3,op(e0,e0))
% 0.20/0.66 & op(op(e3,e0),e1) = op(e3,op(e0,e1))
% 0.20/0.66 & op(op(e3,e0),e2) = op(e3,op(e0,e2))
% 0.20/0.66 & op(op(e3,e0),e3) = op(e3,op(e0,e3))
% 0.20/0.66 & op(op(e3,e1),e0) = op(e3,op(e1,e0))
% 0.20/0.66 & op(op(e3,e1),e1) = op(e3,op(e1,e1))
% 0.20/0.66 & op(op(e3,e1),e2) = op(e3,op(e1,e2))
% 0.20/0.66 & op(op(e3,e1),e3) = op(e3,op(e1,e3))
% 0.20/0.66 & op(op(e3,e2),e0) = op(e3,op(e2,e0))
% 0.20/0.66 & op(op(e3,e2),e1) = op(e3,op(e2,e1))
% 0.20/0.66 & op(op(e3,e2),e2) = op(e3,op(e2,e2))
% 0.20/0.66 & op(op(e3,e2),e3) = op(e3,op(e2,e3))
% 0.20/0.66 & op(op(e3,e3),e0) = op(e3,op(e3,e0))
% 0.20/0.66 & op(op(e3,e3),e1) = op(e3,op(e3,e1))
% 0.20/0.66 & op(op(e3,e3),e2) = op(e3,op(e3,e2))
% 0.20/0.66 & op(op(e3,e3),e3) = op(e3,op(e3,e3)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax3,axiom,
% 0.20/0.66 ( op(unit,e0) = e0
% 0.20/0.66 & op(e0,unit) = e0
% 0.20/0.66 & op(unit,e1) = e1
% 0.20/0.66 & op(e1,unit) = e1
% 0.20/0.66 & op(unit,e2) = e2
% 0.20/0.66 & op(e2,unit) = e2
% 0.20/0.66 & op(unit,e3) = e3
% 0.20/0.66 & op(e3,unit) = e3
% 0.20/0.66 & ( unit = e0
% 0.20/0.66 | unit = e1
% 0.20/0.66 | unit = e2
% 0.20/0.66 | unit = e3 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax4,axiom,
% 0.20/0.66 ( op(e0,inv(e0)) = unit
% 0.20/0.66 & op(inv(e0),e0) = unit
% 0.20/0.66 & op(e1,inv(e1)) = unit
% 0.20/0.66 & op(inv(e1),e1) = unit
% 0.20/0.66 & op(e2,inv(e2)) = unit
% 0.20/0.66 & op(inv(e2),e2) = unit
% 0.20/0.66 & op(e3,inv(e3)) = unit
% 0.20/0.66 & op(inv(e3),e3) = unit
% 0.20/0.66 & ( inv(e0) = e0
% 0.20/0.66 | inv(e0) = e1
% 0.20/0.66 | inv(e0) = e2
% 0.20/0.66 | inv(e0) = e3 )
% 0.20/0.66 & ( inv(e1) = e0
% 0.20/0.66 | inv(e1) = e1
% 0.20/0.66 | inv(e1) = e2
% 0.20/0.66 | inv(e1) = e3 )
% 0.20/0.66 & ( inv(e2) = e0
% 0.20/0.66 | inv(e2) = e1
% 0.20/0.66 | inv(e2) = e2
% 0.20/0.66 | inv(e2) = e3 )
% 0.20/0.66 & ( inv(e3) = e0
% 0.20/0.66 | inv(e3) = e1
% 0.20/0.66 | inv(e3) = e2
% 0.20/0.66 | inv(e3) = e3 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax5,axiom,
% 0.20/0.66 unit = e0 ).
% 0.20/0.66
% 0.20/0.66 fof(ax6,axiom,
% 0.20/0.66 inv(unit) = unit ).
% 0.20/0.66
% 0.20/0.66 fof(ax7,axiom,
% 0.20/0.66 ( inv(inv(e0)) = e0
% 0.20/0.66 & inv(inv(e1)) = e1
% 0.20/0.66 & inv(inv(e2)) = e2
% 0.20/0.66 & inv(inv(e3)) = e3 ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax8,axiom,
% 0.20/0.66 ( ( inv(e0) = e0
% 0.20/0.66 => inv(e0) = e0 )
% 0.20/0.66 & ( inv(e0) = e1
% 0.20/0.66 => inv(e1) = e0 )
% 0.20/0.66 & ( inv(e0) = e2
% 0.20/0.66 => inv(e2) = e0 )
% 0.20/0.66 & ( inv(e0) = e3
% 0.20/0.66 => inv(e3) = e0 )
% 0.20/0.66 & ( inv(e1) = e0
% 0.20/0.66 => inv(e0) = e1 )
% 0.20/0.66 & ( inv(e1) = e1
% 0.20/0.66 => inv(e1) = e1 )
% 0.20/0.66 & ( inv(e1) = e2
% 0.20/0.66 => inv(e2) = e1 )
% 0.20/0.66 & ( inv(e1) = e3
% 0.20/0.66 => inv(e3) = e1 )
% 0.20/0.66 & ( inv(e2) = e0
% 0.20/0.66 => inv(e0) = e2 )
% 0.20/0.66 & ( inv(e2) = e1
% 0.20/0.66 => inv(e1) = e2 )
% 0.20/0.66 & ( inv(e2) = e2
% 0.20/0.66 => inv(e2) = e2 )
% 0.20/0.66 & ( inv(e2) = e3
% 0.20/0.66 => inv(e3) = e2 )
% 0.20/0.66 & ( inv(e3) = e0
% 0.20/0.66 => inv(e0) = e3 )
% 0.20/0.66 & ( inv(e3) = e1
% 0.20/0.66 => inv(e1) = e3 )
% 0.20/0.66 & ( inv(e3) = e2
% 0.20/0.66 => inv(e2) = e3 )
% 0.20/0.66 & ( inv(e3) = e3
% 0.20/0.66 => inv(e3) = e3 ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax9,axiom,
% 0.20/0.66 ( inv(e0) != inv(e1)
% 0.20/0.66 & inv(e0) != inv(e2)
% 0.20/0.66 & inv(e0) != inv(e3)
% 0.20/0.66 & inv(e1) != inv(e2)
% 0.20/0.66 & inv(e1) != inv(e3)
% 0.20/0.66 & inv(e2) != inv(e3) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax10,axiom,
% 0.20/0.66 ( op(e0,e0) != op(e1,e0)
% 0.20/0.66 & op(e0,e0) != op(e2,e0)
% 0.20/0.66 & op(e0,e0) != op(e3,e0)
% 0.20/0.66 & op(e1,e0) != op(e2,e0)
% 0.20/0.66 & op(e1,e0) != op(e3,e0)
% 0.20/0.66 & op(e2,e0) != op(e3,e0)
% 0.20/0.66 & op(e0,e1) != op(e1,e1)
% 0.20/0.66 & op(e0,e1) != op(e2,e1)
% 0.20/0.66 & op(e0,e1) != op(e3,e1)
% 0.20/0.66 & op(e1,e1) != op(e2,e1)
% 0.20/0.66 & op(e1,e1) != op(e3,e1)
% 0.20/0.66 & op(e2,e1) != op(e3,e1)
% 0.20/0.66 & op(e0,e2) != op(e1,e2)
% 0.20/0.66 & op(e0,e2) != op(e2,e2)
% 0.20/0.66 & op(e0,e2) != op(e3,e2)
% 0.20/0.66 & op(e1,e2) != op(e2,e2)
% 0.20/0.66 & op(e1,e2) != op(e3,e2)
% 0.20/0.66 & op(e2,e2) != op(e3,e2)
% 0.20/0.66 & op(e0,e3) != op(e1,e3)
% 0.20/0.66 & op(e0,e3) != op(e2,e3)
% 0.20/0.66 & op(e0,e3) != op(e3,e3)
% 0.20/0.66 & op(e1,e3) != op(e2,e3)
% 0.20/0.66 & op(e1,e3) != op(e3,e3)
% 0.20/0.66 & op(e2,e3) != op(e3,e3)
% 0.20/0.66 & op(e0,e0) != op(e0,e1)
% 0.20/0.66 & op(e0,e0) != op(e0,e2)
% 0.20/0.66 & op(e0,e0) != op(e0,e3)
% 0.20/0.66 & op(e0,e1) != op(e0,e2)
% 0.20/0.66 & op(e0,e1) != op(e0,e3)
% 0.20/0.66 & op(e0,e2) != op(e0,e3)
% 0.20/0.66 & op(e1,e0) != op(e1,e1)
% 0.20/0.66 & op(e1,e0) != op(e1,e2)
% 0.20/0.66 & op(e1,e0) != op(e1,e3)
% 0.20/0.66 & op(e1,e1) != op(e1,e2)
% 0.20/0.66 & op(e1,e1) != op(e1,e3)
% 0.20/0.66 & op(e1,e2) != op(e1,e3)
% 0.20/0.66 & op(e2,e0) != op(e2,e1)
% 0.20/0.66 & op(e2,e0) != op(e2,e2)
% 0.20/0.66 & op(e2,e0) != op(e2,e3)
% 0.20/0.66 & op(e2,e1) != op(e2,e2)
% 0.20/0.66 & op(e2,e1) != op(e2,e3)
% 0.20/0.66 & op(e2,e2) != op(e2,e3)
% 0.20/0.66 & op(e3,e0) != op(e3,e1)
% 0.20/0.66 & op(e3,e0) != op(e3,e2)
% 0.20/0.66 & op(e3,e0) != op(e3,e3)
% 0.20/0.66 & op(e3,e1) != op(e3,e2)
% 0.20/0.66 & op(e3,e1) != op(e3,e3)
% 0.20/0.66 & op(e3,e2) != op(e3,e3) ) ).
% 0.20/0.66
% 0.20/0.66 fof(ax11,axiom,
% 0.20/0.66 ( e0 != e1
% 0.20/0.66 & e0 != e2
% 0.20/0.66 & e0 != e3
% 0.20/0.66 & e1 != e2
% 0.20/0.66 & e1 != e3
% 0.20/0.67 & e2 != e3 ) ).
% 0.20/0.67
% 0.20/0.67 fof(co1,conjecture,
% 0.20/0.67 ( ( op(e0,e0) = e0
% 0.20/0.67 & op(e1,e1) = e0
% 0.20/0.67 & op(e2,e2) = e0
% 0.20/0.67 & op(e3,e3) = e0 )
% 0.20/0.67 | ( op(e0,e0) = e1
% 0.20/0.67 & op(e1,e1) = e1
% 0.20/0.67 & op(e2,e2) = e1
% 0.20/0.67 & op(e3,e3) = e1 )
% 0.20/0.67 | ( op(e0,e0) = e2
% 0.20/0.67 & op(e1,e1) = e2
% 0.20/0.67 & op(e2,e2) = e2
% 0.20/0.67 & op(e3,e3) = e2 )
% 0.20/0.67 | ( op(e0,e0) = e3
% 0.20/0.67 & op(e1,e1) = e3
% 0.20/0.67 & op(e2,e2) = e3
% 0.20/0.67 & op(e3,e3) = e3 )
% 0.20/0.67 | ~ ( ( op(e0,e0) = e0
% 0.20/0.67 & op(e1,e1) = e0
% 0.20/0.67 & op(e2,e2) = e0
% 0.20/0.67 & op(e3,e3) = e0 )
% 0.20/0.67 | ( op(e0,e0) = e1
% 0.20/0.67 & op(e1,e1) = e1
% 0.20/0.67 & op(e2,e2) = e1
% 0.20/0.67 & op(e3,e3) = e1 )
% 0.20/0.67 | ( op(e0,e0) = e2
% 0.20/0.67 & op(e1,e1) = e2
% 0.20/0.67 & op(e2,e2) = e2
% 0.20/0.67 & op(e3,e3) = e2 )
% 0.20/0.67 | ( op(e0,e0) = e3
% 0.20/0.67 & op(e1,e1) = e3
% 0.20/0.67 & op(e2,e2) = e3
% 0.20/0.67 & op(e3,e3) = e3 ) ) ) ).
% 0.20/0.67
% 0.20/0.67 %--------------------------------------------------------------------------
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 % Proof found
% 0.20/0.67 % SZS status Theorem for theBenchmark
% 0.20/0.67 % SZS output start Proof
% 0.20/0.67 %ClaNum:259(EqnAxiom:7)
% 0.20/0.67 %VarNum:0(SingletonVarNum:0)
% 0.20/0.67 %MaxLitNum:5
% 0.20/0.67 %MaxfuncDepth:2
% 0.20/0.67 %SharedTerms:402
% 0.20/0.67 %goalClause: 100 168 169 170 171 256
% 0.20/0.67 %singleGoalClaCount:1
% 0.20/0.67 [8]E(a1,a2)
% 0.20/0.67 [94]~E(a4,a2)
% 0.20/0.67 [95]~E(a5,a2)
% 0.20/0.67 [96]~E(a5,a4)
% 0.20/0.67 [97]~E(a6,a2)
% 0.20/0.67 [98]~E(a6,a4)
% 0.20/0.67 [99]~E(a6,a5)
% 0.20/0.67 [100]~P1(a500)
% 0.20/0.67 [9]E(f3(a1),a1)
% 0.20/0.67 [14]E(f7(a2,a1),a2)
% 0.20/0.67 [15]E(f7(a4,a1),a4)
% 0.20/0.67 [16]E(f7(a5,a1),a5)
% 0.20/0.67 [17]E(f7(a6,a1),a6)
% 0.20/0.67 [18]E(f7(a1,a2),a2)
% 0.20/0.67 [19]E(f7(a1,a4),a4)
% 0.20/0.67 [20]E(f7(a1,a5),a5)
% 0.20/0.67 [21]E(f7(a1,a6),a6)
% 0.20/0.67 [101]~E(f3(a4),f3(a2))
% 0.20/0.67 [102]~E(f3(a5),f3(a2))
% 0.20/0.67 [103]~E(f3(a5),f3(a4))
% 0.20/0.67 [104]~E(f3(a6),f3(a2))
% 0.20/0.67 [105]~E(f3(a6),f3(a4))
% 0.20/0.67 [106]~E(f3(a6),f3(a5))
% 0.20/0.67 [107]~E(f7(a2,a4),f7(a2,a2))
% 0.20/0.67 [108]~E(f7(a2,a5),f7(a2,a2))
% 0.20/0.67 [109]~E(f7(a2,a5),f7(a2,a4))
% 0.20/0.67 [110]~E(f7(a2,a6),f7(a2,a2))
% 0.20/0.67 [111]~E(f7(a2,a6),f7(a2,a4))
% 0.20/0.67 [112]~E(f7(a2,a6),f7(a2,a5))
% 0.20/0.67 [113]~E(f7(a4,a2),f7(a2,a2))
% 0.20/0.67 [114]~E(f7(a4,a4),f7(a2,a4))
% 0.20/0.67 [115]~E(f7(a4,a4),f7(a4,a2))
% 0.20/0.67 [116]~E(f7(a4,a5),f7(a2,a5))
% 0.20/0.67 [117]~E(f7(a4,a5),f7(a4,a2))
% 0.20/0.67 [118]~E(f7(a4,a5),f7(a4,a4))
% 0.20/0.67 [119]~E(f7(a4,a6),f7(a2,a6))
% 0.20/0.67 [120]~E(f7(a4,a6),f7(a4,a2))
% 0.20/0.67 [121]~E(f7(a4,a6),f7(a4,a4))
% 0.20/0.67 [122]~E(f7(a4,a6),f7(a4,a5))
% 0.20/0.67 [123]~E(f7(a5,a2),f7(a2,a2))
% 0.20/0.67 [124]~E(f7(a5,a2),f7(a4,a2))
% 0.20/0.67 [125]~E(f7(a5,a4),f7(a2,a4))
% 0.20/0.67 [126]~E(f7(a5,a4),f7(a4,a4))
% 0.20/0.67 [127]~E(f7(a5,a4),f7(a5,a2))
% 0.20/0.67 [128]~E(f7(a5,a5),f7(a2,a5))
% 0.20/0.67 [129]~E(f7(a5,a5),f7(a4,a5))
% 0.20/0.67 [130]~E(f7(a5,a5),f7(a5,a2))
% 0.20/0.67 [131]~E(f7(a5,a5),f7(a5,a4))
% 0.20/0.67 [132]~E(f7(a5,a6),f7(a2,a6))
% 0.20/0.67 [133]~E(f7(a5,a6),f7(a4,a6))
% 0.20/0.67 [134]~E(f7(a5,a6),f7(a5,a2))
% 0.20/0.67 [135]~E(f7(a5,a6),f7(a5,a4))
% 0.20/0.67 [136]~E(f7(a5,a6),f7(a5,a5))
% 0.20/0.67 [137]~E(f7(a6,a2),f7(a2,a2))
% 0.20/0.67 [138]~E(f7(a6,a2),f7(a4,a2))
% 0.20/0.67 [139]~E(f7(a6,a2),f7(a5,a2))
% 0.20/0.67 [140]~E(f7(a6,a4),f7(a2,a4))
% 0.20/0.67 [141]~E(f7(a6,a4),f7(a4,a4))
% 0.20/0.67 [142]~E(f7(a6,a4),f7(a5,a4))
% 0.20/0.67 [143]~E(f7(a6,a4),f7(a6,a2))
% 0.20/0.67 [144]~E(f7(a6,a5),f7(a2,a5))
% 0.20/0.67 [145]~E(f7(a6,a5),f7(a4,a5))
% 0.20/0.67 [146]~E(f7(a6,a5),f7(a5,a5))
% 0.20/0.67 [147]~E(f7(a6,a5),f7(a6,a2))
% 0.20/0.67 [148]~E(f7(a6,a5),f7(a6,a4))
% 0.20/0.67 [149]~E(f7(a6,a6),f7(a2,a6))
% 0.20/0.67 [150]~E(f7(a6,a6),f7(a4,a6))
% 0.20/0.67 [151]~E(f7(a6,a6),f7(a5,a6))
% 0.20/0.67 [152]~E(f7(a6,a6),f7(a6,a2))
% 0.20/0.67 [153]~E(f7(a6,a6),f7(a6,a4))
% 0.20/0.67 [154]~E(f7(a6,a6),f7(a6,a5))
% 0.20/0.67 [10]E(f3(f3(a2)),a2)
% 0.20/0.67 [11]E(f3(f3(a4)),a4)
% 0.20/0.67 [12]E(f3(f3(a5)),a5)
% 0.20/0.67 [13]E(f3(f3(a6)),a6)
% 0.20/0.67 [22]E(f7(a2,f3(a2)),a1)
% 0.20/0.67 [23]E(f7(a4,f3(a4)),a1)
% 0.20/0.67 [24]E(f7(a5,f3(a5)),a1)
% 0.20/0.67 [25]E(f7(a6,f3(a6)),a1)
% 0.20/0.67 [26]E(f7(f3(a2),a2),a1)
% 0.20/0.67 [27]E(f7(f3(a4),a4),a1)
% 0.20/0.67 [28]E(f7(f3(a5),a5),a1)
% 0.20/0.67 [29]E(f7(f3(a6),a6),a1)
% 0.20/0.67 [30]E(f7(f7(a2,a2),a2),f7(a2,f7(a2,a2)))
% 0.20/0.67 [31]E(f7(f7(a2,a2),a4),f7(a2,f7(a2,a4)))
% 0.20/0.67 [32]E(f7(f7(a2,a2),a5),f7(a2,f7(a2,a5)))
% 0.20/0.67 [33]E(f7(f7(a2,a2),a6),f7(a2,f7(a2,a6)))
% 0.20/0.67 [34]E(f7(f7(a2,a4),a2),f7(a2,f7(a4,a2)))
% 0.20/0.67 [35]E(f7(f7(a2,a4),a4),f7(a2,f7(a4,a4)))
% 0.20/0.67 [36]E(f7(f7(a2,a4),a5),f7(a2,f7(a4,a5)))
% 0.20/0.67 [37]E(f7(f7(a2,a4),a6),f7(a2,f7(a4,a6)))
% 0.20/0.67 [38]E(f7(f7(a2,a5),a2),f7(a2,f7(a5,a2)))
% 0.20/0.67 [39]E(f7(f7(a2,a5),a4),f7(a2,f7(a5,a4)))
% 0.20/0.67 [40]E(f7(f7(a2,a5),a5),f7(a2,f7(a5,a5)))
% 0.20/0.67 [41]E(f7(f7(a2,a5),a6),f7(a2,f7(a5,a6)))
% 0.20/0.67 [42]E(f7(f7(a2,a6),a2),f7(a2,f7(a6,a2)))
% 0.20/0.67 [43]E(f7(f7(a2,a6),a4),f7(a2,f7(a6,a4)))
% 0.20/0.67 [44]E(f7(f7(a2,a6),a5),f7(a2,f7(a6,a5)))
% 0.20/0.67 [45]E(f7(f7(a2,a6),a6),f7(a2,f7(a6,a6)))
% 0.20/0.67 [46]E(f7(f7(a4,a2),a2),f7(a4,f7(a2,a2)))
% 0.20/0.67 [47]E(f7(f7(a4,a2),a4),f7(a4,f7(a2,a4)))
% 0.20/0.67 [48]E(f7(f7(a4,a2),a5),f7(a4,f7(a2,a5)))
% 0.20/0.67 [49]E(f7(f7(a4,a2),a6),f7(a4,f7(a2,a6)))
% 0.20/0.67 [50]E(f7(f7(a4,a4),a2),f7(a4,f7(a4,a2)))
% 0.20/0.67 [51]E(f7(f7(a4,a4),a4),f7(a4,f7(a4,a4)))
% 0.20/0.67 [52]E(f7(f7(a4,a4),a5),f7(a4,f7(a4,a5)))
% 0.20/0.67 [53]E(f7(f7(a4,a4),a6),f7(a4,f7(a4,a6)))
% 0.20/0.67 [54]E(f7(f7(a4,a5),a2),f7(a4,f7(a5,a2)))
% 0.20/0.67 [55]E(f7(f7(a4,a5),a4),f7(a4,f7(a5,a4)))
% 0.20/0.67 [56]E(f7(f7(a4,a5),a5),f7(a4,f7(a5,a5)))
% 0.20/0.67 [57]E(f7(f7(a4,a5),a6),f7(a4,f7(a5,a6)))
% 0.20/0.67 [58]E(f7(f7(a4,a6),a2),f7(a4,f7(a6,a2)))
% 0.20/0.67 [59]E(f7(f7(a4,a6),a4),f7(a4,f7(a6,a4)))
% 0.20/0.67 [60]E(f7(f7(a4,a6),a5),f7(a4,f7(a6,a5)))
% 0.20/0.67 [61]E(f7(f7(a4,a6),a6),f7(a4,f7(a6,a6)))
% 0.20/0.67 [62]E(f7(f7(a5,a2),a2),f7(a5,f7(a2,a2)))
% 0.20/0.67 [63]E(f7(f7(a5,a2),a4),f7(a5,f7(a2,a4)))
% 0.20/0.67 [64]E(f7(f7(a5,a2),a5),f7(a5,f7(a2,a5)))
% 0.20/0.67 [65]E(f7(f7(a5,a2),a6),f7(a5,f7(a2,a6)))
% 0.20/0.67 [66]E(f7(f7(a5,a4),a2),f7(a5,f7(a4,a2)))
% 0.20/0.67 [67]E(f7(f7(a5,a4),a4),f7(a5,f7(a4,a4)))
% 0.20/0.67 [68]E(f7(f7(a5,a4),a5),f7(a5,f7(a4,a5)))
% 0.20/0.67 [69]E(f7(f7(a5,a4),a6),f7(a5,f7(a4,a6)))
% 0.20/0.67 [70]E(f7(f7(a5,a5),a2),f7(a5,f7(a5,a2)))
% 0.20/0.67 [71]E(f7(f7(a5,a5),a4),f7(a5,f7(a5,a4)))
% 0.20/0.67 [72]E(f7(f7(a5,a5),a5),f7(a5,f7(a5,a5)))
% 0.20/0.67 [73]E(f7(f7(a5,a5),a6),f7(a5,f7(a5,a6)))
% 0.20/0.67 [74]E(f7(f7(a5,a6),a2),f7(a5,f7(a6,a2)))
% 0.20/0.67 [75]E(f7(f7(a5,a6),a4),f7(a5,f7(a6,a4)))
% 0.20/0.67 [76]E(f7(f7(a5,a6),a5),f7(a5,f7(a6,a5)))
% 0.20/0.67 [77]E(f7(f7(a5,a6),a6),f7(a5,f7(a6,a6)))
% 0.20/0.67 [78]E(f7(f7(a6,a2),a2),f7(a6,f7(a2,a2)))
% 0.20/0.67 [79]E(f7(f7(a6,a2),a4),f7(a6,f7(a2,a4)))
% 0.20/0.67 [80]E(f7(f7(a6,a2),a5),f7(a6,f7(a2,a5)))
% 0.20/0.67 [81]E(f7(f7(a6,a2),a6),f7(a6,f7(a2,a6)))
% 0.20/0.67 [82]E(f7(f7(a6,a4),a2),f7(a6,f7(a4,a2)))
% 0.20/0.67 [83]E(f7(f7(a6,a4),a4),f7(a6,f7(a4,a4)))
% 0.20/0.67 [84]E(f7(f7(a6,a4),a5),f7(a6,f7(a4,a5)))
% 0.20/0.67 [85]E(f7(f7(a6,a4),a6),f7(a6,f7(a4,a6)))
% 0.20/0.67 [86]E(f7(f7(a6,a5),a2),f7(a6,f7(a5,a2)))
% 0.20/0.67 [87]E(f7(f7(a6,a5),a4),f7(a6,f7(a5,a4)))
% 0.20/0.67 [88]E(f7(f7(a6,a5),a5),f7(a6,f7(a5,a5)))
% 0.20/0.67 [89]E(f7(f7(a6,a5),a6),f7(a6,f7(a5,a6)))
% 0.20/0.67 [90]E(f7(f7(a6,a6),a2),f7(a6,f7(a6,a2)))
% 0.20/0.67 [91]E(f7(f7(a6,a6),a4),f7(a6,f7(a6,a4)))
% 0.20/0.67 [92]E(f7(f7(a6,a6),a5),f7(a6,f7(a6,a5)))
% 0.20/0.67 [93]E(f7(f7(a6,a6),a6),f7(a6,f7(a6,a6)))
% 0.20/0.67 [156]E(f3(a2),a4)+~E(f3(a4),a2)
% 0.20/0.67 [157]E(f3(a2),a5)+~E(f3(a5),a2)
% 0.20/0.67 [158]E(f3(a2),a6)+~E(f3(a6),a2)
% 0.20/0.67 [159]E(f3(a4),a2)+~E(f3(a2),a4)
% 0.20/0.67 [160]E(f3(a4),a5)+~E(f3(a5),a4)
% 0.20/0.67 [161]E(f3(a4),a6)+~E(f3(a6),a4)
% 0.20/0.67 [162]E(f3(a5),a2)+~E(f3(a2),a5)
% 0.20/0.67 [163]E(f3(a5),a4)+~E(f3(a4),a5)
% 0.20/0.67 [164]E(f3(a5),a6)+~E(f3(a6),a5)
% 0.20/0.67 [165]E(f3(a6),a2)+~E(f3(a2),a6)
% 0.20/0.67 [166]E(f3(a6),a4)+~E(f3(a4),a6)
% 0.20/0.67 [167]E(f3(a6),a5)+~E(f3(a5),a6)
% 0.20/0.67 [168]P1(a500)+E(f7(a2,a2),a6)
% 0.20/0.67 [169]P1(a500)+E(f7(a4,a4),a6)
% 0.20/0.67 [170]P1(a500)+E(f7(a5,a5),a6)
% 0.20/0.67 [171]P1(a500)+E(f7(a6,a6),a6)
% 0.20/0.67 [172]E(f3(a2),a4)+E(f3(a2),a5)+E(f3(a2),a6)+E(f3(a2),a2)
% 0.20/0.67 [173]E(f3(a4),a2)+E(f3(a4),a5)+E(f3(a4),a6)+E(f3(a4),a4)
% 0.20/0.67 [174]E(f3(a5),a2)+E(f3(a5),a4)+E(f3(a5),a6)+E(f3(a5),a5)
% 0.20/0.67 [175]E(f3(a6),a2)+E(f3(a6),a4)+E(f3(a6),a5)+E(f3(a6),a6)
% 0.20/0.67 [240]E(f7(a2,a2),a2)+E(f7(a2,a2),a4)+E(f7(a2,a2),a5)+E(f7(a2,a2),a6)
% 0.20/0.67 [241]E(f7(a2,a4),a6)+E(f7(a2,a4),a5)+E(f7(a2,a4),a4)+E(f7(a2,a4),a2)
% 0.20/0.67 [242]E(f7(a2,a5),a6)+E(f7(a2,a5),a5)+E(f7(a2,a5),a4)+E(f7(a2,a5),a2)
% 0.20/0.67 [243]E(f7(a2,a6),a6)+E(f7(a2,a6),a5)+E(f7(a2,a6),a4)+E(f7(a2,a6),a2)
% 0.20/0.67 [244]E(f7(a4,a2),a6)+E(f7(a4,a2),a5)+E(f7(a4,a2),a4)+E(f7(a4,a2),a2)
% 0.20/0.67 [245]E(f7(a4,a4),a2)+E(f7(a4,a4),a4)+E(f7(a4,a4),a5)+E(f7(a4,a4),a6)
% 0.20/0.67 [246]E(f7(a4,a5),a6)+E(f7(a4,a5),a5)+E(f7(a4,a5),a4)+E(f7(a4,a5),a2)
% 0.20/0.67 [247]E(f7(a4,a6),a6)+E(f7(a4,a6),a5)+E(f7(a4,a6),a4)+E(f7(a4,a6),a2)
% 0.20/0.67 [248]E(f7(a5,a2),a6)+E(f7(a5,a2),a5)+E(f7(a5,a2),a4)+E(f7(a5,a2),a2)
% 0.20/0.67 [249]E(f7(a5,a4),a6)+E(f7(a5,a4),a5)+E(f7(a5,a4),a4)+E(f7(a5,a4),a2)
% 0.20/0.67 [250]E(f7(a5,a5),a2)+E(f7(a5,a5),a4)+E(f7(a5,a5),a5)+E(f7(a5,a5),a6)
% 0.20/0.67 [251]E(f7(a5,a6),a6)+E(f7(a5,a6),a5)+E(f7(a5,a6),a4)+E(f7(a5,a6),a2)
% 0.20/0.67 [252]E(f7(a6,a2),a6)+E(f7(a6,a2),a5)+E(f7(a6,a2),a4)+E(f7(a6,a2),a2)
% 0.20/0.67 [253]E(f7(a6,a4),a6)+E(f7(a6,a4),a5)+E(f7(a6,a4),a4)+E(f7(a6,a4),a2)
% 0.20/0.67 [254]E(f7(a6,a5),a6)+E(f7(a6,a5),a5)+E(f7(a6,a5),a4)+E(f7(a6,a5),a2)
% 0.20/0.67 [255]E(f7(a6,a6),a2)+E(f7(a6,a6),a4)+E(f7(a6,a6),a5)+E(f7(a6,a6),a6)
% 0.20/0.67 [256]~E(f7(a2,a2),a6)+~E(f7(a4,a4),a6)+~E(f7(a5,a5),a6)+~E(f7(a6,a6),a6)
% 0.20/0.67 [257]P1(a500)+~E(f7(a2,a2),a2)+~E(f7(a4,a4),a2)+~E(f7(a5,a5),a2)+~E(f7(a6,a6),a2)
% 0.20/0.67 [258]P1(a500)+~E(f7(a2,a2),a4)+~E(f7(a4,a4),a4)+~E(f7(a5,a5),a4)+~E(f7(a6,a6),a4)
% 0.20/0.67 [259]P1(a500)+~E(f7(a2,a2),a5)+~E(f7(a4,a4),a5)+~E(f7(a5,a5),a5)+~E(f7(a6,a6),a5)
% 0.20/0.67 %EqnAxiom
% 0.20/0.67 [1]E(x11,x11)
% 0.20/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.67 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.20/0.67 [5]~E(x51,x52)+E(f7(x51,x53),f7(x52,x53))
% 0.20/0.67 [6]~E(x61,x62)+E(f7(x63,x61),f7(x63,x62))
% 0.20/0.67 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.20/0.67
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 cnf(269,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[100,8,94,2,3,171,170,169,168,6,5,4,256]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------