TSTP Solution File: ALG045+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 : 600s
% DateTime : Thu Jul 14 17:32:38 EDT 2022
% Result : Unsatisfiable 2.87s 3.08s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 82
% Syntax : Number of formulae : 371 ( 73 unt; 3 def)
% Number of atoms : 1621 (1397 equ)
% Maximal formula atoms : 128 ( 4 avg)
% Number of connectives : 1714 ( 464 ~; 964 |; 279 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
( ( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 )
& ( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 )
& ( op(e0,e2) = e0
| op(e0,e2) = e1
| op(e0,e2) = e2
| op(e0,e2) = e3 )
& ( op(e0,e3) = e0
| op(e0,e3) = e1
| op(e0,e3) = e2
| op(e0,e3) = e3 )
& ( op(e1,e0) = e0
| op(e1,e0) = e1
| op(e1,e0) = e2
| op(e1,e0) = e3 )
& ( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 )
& ( op(e1,e2) = e0
| op(e1,e2) = e1
| op(e1,e2) = e2
| op(e1,e2) = e3 )
& ( op(e1,e3) = e0
| op(e1,e3) = e1
| op(e1,e3) = e2
| op(e1,e3) = e3 )
& ( op(e2,e0) = e0
| op(e2,e0) = e1
| op(e2,e0) = e2
| op(e2,e0) = e3 )
& ( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 )
& ( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 )
& ( op(e2,e3) = e0
| op(e2,e3) = e1
| op(e2,e3) = e2
| op(e2,e3) = e3 )
& ( op(e3,e0) = e0
| op(e3,e0) = e1
| op(e3,e0) = e2
| op(e3,e0) = e3 )
& ( op(e3,e1) = e0
| op(e3,e1) = e1
| op(e3,e1) = e2
| op(e3,e1) = e3 )
& ( op(e3,e2) = e0
| op(e3,e2) = e1
| op(e3,e2) = e2
| op(e3,e2) = e3 )
& ( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ) ) ).
fof(ax2,axiom,
( op(unit,e0) = e0
& op(e0,unit) = e0
& op(unit,e1) = e1
& op(e1,unit) = e1
& op(unit,e2) = e2
& op(e2,unit) = e2
& op(unit,e3) = e3
& op(e3,unit) = e3
& ( unit = e0
| unit = e1
| unit = e2
| unit = e3 ) ) ).
fof(ax3,axiom,
( ( op(e0,e0) = e0
| op(e0,e1) = e0
| op(e0,e2) = e0
| op(e0,e3) = e0 )
& ( op(e0,e0) = e0
| op(e1,e0) = e0
| op(e2,e0) = e0
| op(e3,e0) = e0 )
& ( op(e0,e0) = e1
| op(e0,e1) = e1
| op(e0,e2) = e1
| op(e0,e3) = e1 )
& ( op(e0,e0) = e1
| op(e1,e0) = e1
| op(e2,e0) = e1
| op(e3,e0) = e1 )
& ( op(e0,e0) = e2
| op(e0,e1) = e2
| op(e0,e2) = e2
| op(e0,e3) = e2 )
& ( op(e0,e0) = e2
| op(e1,e0) = e2
| op(e2,e0) = e2
| op(e3,e0) = e2 )
& ( op(e0,e0) = e3
| op(e0,e1) = e3
| op(e0,e2) = e3
| op(e0,e3) = e3 )
& ( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 )
& ( op(e1,e0) = e0
| op(e1,e1) = e0
| op(e1,e2) = e0
| op(e1,e3) = e0 )
& ( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 )
& ( op(e1,e0) = e1
| op(e1,e1) = e1
| op(e1,e2) = e1
| op(e1,e3) = e1 )
& ( op(e0,e1) = e1
| op(e1,e1) = e1
| op(e2,e1) = e1
| op(e3,e1) = e1 )
& ( op(e1,e0) = e2
| op(e1,e1) = e2
| op(e1,e2) = e2
| op(e1,e3) = e2 )
& ( op(e0,e1) = e2
| op(e1,e1) = e2
| op(e2,e1) = e2
| op(e3,e1) = e2 )
& ( op(e1,e0) = e3
| op(e1,e1) = e3
| op(e1,e2) = e3
| op(e1,e3) = e3 )
& ( op(e0,e1) = e3
| op(e1,e1) = e3
| op(e2,e1) = e3
| op(e3,e1) = e3 )
& ( op(e2,e0) = e0
| op(e2,e1) = e0
| op(e2,e2) = e0
| op(e2,e3) = e0 )
& ( op(e0,e2) = e0
| op(e1,e2) = e0
| op(e2,e2) = e0
| op(e3,e2) = e0 )
& ( op(e2,e0) = e1
| op(e2,e1) = e1
| op(e2,e2) = e1
| op(e2,e3) = e1 )
& ( op(e0,e2) = e1
| op(e1,e2) = e1
| op(e2,e2) = e1
| op(e3,e2) = e1 )
& ( op(e2,e0) = e2
| op(e2,e1) = e2
| op(e2,e2) = e2
| op(e2,e3) = e2 )
& ( op(e0,e2) = e2
| op(e1,e2) = e2
| op(e2,e2) = e2
| op(e3,e2) = e2 )
& ( op(e2,e0) = e3
| op(e2,e1) = e3
| op(e2,e2) = e3
| op(e2,e3) = e3 )
& ( op(e0,e2) = e3
| op(e1,e2) = e3
| op(e2,e2) = e3
| op(e3,e2) = e3 )
& ( op(e3,e0) = e0
| op(e3,e1) = e0
| op(e3,e2) = e0
| op(e3,e3) = e0 )
& ( op(e0,e3) = e0
| op(e1,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 )
& ( op(e3,e0) = e1
| op(e3,e1) = e1
| op(e3,e2) = e1
| op(e3,e3) = e1 )
& ( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 )
& ( op(e3,e0) = e2
| op(e3,e1) = e2
| op(e3,e2) = e2
| op(e3,e3) = e2 )
& ( op(e0,e3) = e2
| op(e1,e3) = e2
| op(e2,e3) = e2
| op(e3,e3) = e2 )
& ( op(e3,e0) = e3
| op(e3,e1) = e3
| op(e3,e2) = e3
| op(e3,e3) = e3 )
& ( op(e0,e3) = e3
| op(e1,e3) = e3
| op(e2,e3) = e3
| op(e3,e3) = e3 ) ) ).
fof(ax4,axiom,
( op(e0,e0) != op(e1,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e1,e0) != op(e3,e0)
& op(e2,e0) != op(e3,e0)
& op(e0,e1) != op(e1,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e1,e1) != op(e3,e1)
& op(e2,e1) != op(e3,e1)
& op(e0,e2) != op(e1,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e1,e2) != op(e3,e2)
& op(e2,e2) != op(e3,e2)
& op(e0,e3) != op(e1,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e1,e3) != op(e3,e3)
& op(e2,e3) != op(e3,e3)
& op(e0,e0) != op(e0,e1)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e1) != op(e0,e3)
& op(e0,e2) != op(e0,e3)
& op(e1,e0) != op(e1,e1)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e1) != op(e1,e3)
& op(e1,e2) != op(e1,e3)
& op(e2,e0) != op(e2,e1)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e1) != op(e2,e3)
& op(e2,e2) != op(e2,e3)
& op(e3,e0) != op(e3,e1)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e1) != op(e3,e3)
& op(e3,e2) != op(e3,e3) ) ).
fof(ax5,axiom,
( e0 != e1
& e0 != e2
& e0 != e3
& e1 != e2
& e1 != e3
& e2 != e3 ) ).
fof(ax6,axiom,
( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ).
fof(ax11,axiom,
~ ( e0 = op(e3,e3)
& e1 = op(e2,e3) ) ).
fof(ax14,axiom,
~ ( e1 = op(e0,e0)
& e3 = op(e2,e0) ) ).
fof(ax21,axiom,
~ ( e2 = op(e1,e1)
& e0 = op(e3,e1) ) ).
fof(ax27,axiom,
~ ( e3 = op(e1,e1)
& e0 = op(e2,e1) ) ).
fof(definition_0,definition,
( definitionFOFtoCNF_0
<=> ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 ) ) ) ).
fof(definition_1,definition,
( definitionFOFtoCNF_1
<=> ( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 ) ) ).
fof(definition_2,definition,
( definitionFOFtoCNF_2
<=> ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 ) ) ).
fof(normalize_0_0,plain,
( ( op(e0,e0) = e0
| op(e0,e1) = e0
| op(e0,e2) = e0
| op(e0,e3) = e0 )
& ( op(e0,e0) = e0
| op(e1,e0) = e0
| op(e2,e0) = e0
| op(e3,e0) = e0 )
& ( op(e0,e0) = e1
| op(e0,e1) = e1
| op(e0,e2) = e1
| op(e0,e3) = e1 )
& ( op(e0,e0) = e1
| op(e1,e0) = e1
| op(e2,e0) = e1
| op(e3,e0) = e1 )
& ( op(e0,e0) = e2
| op(e0,e1) = e2
| op(e0,e2) = e2
| op(e0,e3) = e2 )
& ( op(e0,e0) = e2
| op(e1,e0) = e2
| op(e2,e0) = e2
| op(e3,e0) = e2 )
& ( op(e0,e0) = e3
| op(e0,e1) = e3
| op(e0,e2) = e3
| op(e0,e3) = e3 )
& ( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 )
& ( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 )
& ( op(e0,e1) = e1
| op(e1,e1) = e1
| op(e2,e1) = e1
| op(e3,e1) = e1 )
& ( op(e0,e1) = e2
| op(e1,e1) = e2
| op(e2,e1) = e2
| op(e3,e1) = e2 )
& ( op(e0,e1) = e3
| op(e1,e1) = e3
| op(e2,e1) = e3
| op(e3,e1) = e3 )
& ( op(e0,e2) = e0
| op(e1,e2) = e0
| op(e2,e2) = e0
| op(e3,e2) = e0 )
& ( op(e0,e2) = e1
| op(e1,e2) = e1
| op(e2,e2) = e1
| op(e3,e2) = e1 )
& ( op(e0,e2) = e2
| op(e1,e2) = e2
| op(e2,e2) = e2
| op(e3,e2) = e2 )
& ( op(e0,e2) = e3
| op(e1,e2) = e3
| op(e2,e2) = e3
| op(e3,e2) = e3 )
& ( op(e0,e3) = e0
| op(e1,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 )
& ( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 )
& ( op(e0,e3) = e2
| op(e1,e3) = e2
| op(e2,e3) = e2
| op(e3,e3) = e2 )
& ( op(e0,e3) = e3
| op(e1,e3) = e3
| op(e2,e3) = e3
| op(e3,e3) = e3 )
& ( op(e1,e0) = e0
| op(e1,e1) = e0
| op(e1,e2) = e0
| op(e1,e3) = e0 )
& ( op(e1,e0) = e1
| op(e1,e1) = e1
| op(e1,e2) = e1
| op(e1,e3) = e1 )
& ( op(e1,e0) = e2
| op(e1,e1) = e2
| op(e1,e2) = e2
| op(e1,e3) = e2 )
& ( op(e1,e0) = e3
| op(e1,e1) = e3
| op(e1,e2) = e3
| op(e1,e3) = e3 )
& ( op(e2,e0) = e0
| op(e2,e1) = e0
| op(e2,e2) = e0
| op(e2,e3) = e0 )
& ( op(e2,e0) = e1
| op(e2,e1) = e1
| op(e2,e2) = e1
| op(e2,e3) = e1 )
& ( op(e2,e0) = e2
| op(e2,e1) = e2
| op(e2,e2) = e2
| op(e2,e3) = e2 )
& ( op(e2,e0) = e3
| op(e2,e1) = e3
| op(e2,e2) = e3
| op(e2,e3) = e3 )
& ( op(e3,e0) = e0
| op(e3,e1) = e0
| op(e3,e2) = e0
| op(e3,e3) = e0 )
& ( op(e3,e0) = e1
| op(e3,e1) = e1
| op(e3,e2) = e1
| op(e3,e3) = e1 )
& ( op(e3,e0) = e2
| op(e3,e1) = e2
| op(e3,e2) = e2
| op(e3,e3) = e2 )
& ( op(e3,e0) = e3
| op(e3,e1) = e3
| op(e3,e2) = e3
| op(e3,e3) = e3 ) ),
inference(canonicalize,[],[ax3]) ).
fof(normalize_0_1,plain,
( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ definitionFOFtoCNF_0
<=> ( ( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 )
& ( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_3,plain,
( ~ definitionFOFtoCNF_1
<=> ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 ) ),
inference(canonicalize,[],[definition_1]) ).
fof(normalize_0_4,plain,
( ~ definitionFOFtoCNF_0
<=> ( definitionFOFtoCNF_1
& ( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 ) ) ),
inference(simplify,[],[normalize_0_2,normalize_0_3]) ).
fof(normalize_0_5,plain,
( ( definitionFOFtoCNF_0
| definitionFOFtoCNF_1 )
& ( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e0,e0) = e1 )
& ( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e1,e1) = e1 )
& ( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e2,e2) = e1 )
& ( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e3,e3) = e1 )
& ( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1
| definitionFOFtoCNF_0 ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e0,e0) = e1 ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( op(e0,unit) = e0
& op(e1,unit) = e1
& op(e2,unit) = e2
& op(e3,unit) = e3
& op(unit,e0) = e0
& op(unit,e1) = e1
& op(unit,e2) = e2
& op(unit,e3) = e3
& ( unit = e0
| unit = e1
| unit = e2
| unit = e3 ) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_0_8,plain,
op(unit,e3) = e3,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ( op(e0,e0) = e0
| definitionFOFtoCNF_1 )
& ( op(e1,e1) = e0
| definitionFOFtoCNF_1 )
& ( op(e2,e2) = e0
| definitionFOFtoCNF_1 )
& ( op(e3,e3) = e0
| definitionFOFtoCNF_1 )
& ( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0
| ~ definitionFOFtoCNF_1 ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
( op(e3,e3) = e0
| definitionFOFtoCNF_1 ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( op(e0,e0) != op(e0,e1)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e3)
& op(e0,e0) != op(e1,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e3,e0)
& op(e0,e1) != op(e0,e2)
& op(e0,e1) != op(e0,e3)
& op(e0,e1) != op(e1,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e3,e1)
& op(e0,e2) != op(e0,e3)
& op(e0,e2) != op(e1,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e3,e2)
& op(e0,e3) != op(e1,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e3,e3)
& op(e1,e0) != op(e1,e1)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e3)
& op(e1,e0) != op(e2,e0)
& op(e1,e0) != op(e3,e0)
& op(e1,e1) != op(e1,e2)
& op(e1,e1) != op(e1,e3)
& op(e1,e1) != op(e2,e1)
& op(e1,e1) != op(e3,e1)
& op(e1,e2) != op(e1,e3)
& op(e1,e2) != op(e2,e2)
& op(e1,e2) != op(e3,e2)
& op(e1,e3) != op(e2,e3)
& op(e1,e3) != op(e3,e3)
& op(e2,e0) != op(e2,e1)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e3)
& op(e2,e0) != op(e3,e0)
& op(e2,e1) != op(e2,e2)
& op(e2,e1) != op(e2,e3)
& op(e2,e1) != op(e3,e1)
& op(e2,e2) != op(e2,e3)
& op(e2,e2) != op(e3,e2)
& op(e2,e3) != op(e3,e3)
& op(e3,e0) != op(e3,e1)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e1) != op(e3,e3)
& op(e3,e2) != op(e3,e3) ),
inference(canonicalize,[],[ax4]) ).
fof(normalize_0_12,plain,
op(e0,e0) != op(e1,e0),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
( op(e0,e0) = e0
| definitionFOFtoCNF_1 ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
op(unit,e0) = e0,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
( op(e2,e2) = e0
| definitionFOFtoCNF_1 ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,plain,
op(unit,e2) = e2,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_17,plain,
( unit = e0
| unit = e1
| unit = e2
| unit = e3 ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_18,plain,
( e0 != e1
& e0 != e2
& e0 != e3
& e1 != e2
& e1 != e3
& e2 != e3 ),
inference(canonicalize,[],[ax5]) ).
fof(normalize_0_19,plain,
e0 != e2,
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
e0 != e3,
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_21,plain,
op(e1,e0) != op(e1,e3),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_22,plain,
( e0 != op(e3,e3)
| e1 != op(e2,e3) ),
inference(canonicalize,[],[ax11]) ).
fof(normalize_0_23,plain,
( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_24,plain,
e0 != e1,
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_25,plain,
op(e1,unit) = e1,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_26,plain,
e1 != e3,
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_27,plain,
op(e0,e1) != op(e0,e2),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_28,plain,
op(e0,unit) = e0,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_29,plain,
( ~ definitionFOFtoCNF_2
<=> ( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2 ) ),
inference(canonicalize,[],[definition_2]) ).
fof(normalize_0_30,plain,
( ( ~ definitionFOFtoCNF_2
| op(e0,e0) = e2 )
& ( ~ definitionFOFtoCNF_2
| op(e1,e1) = e2 )
& ( ~ definitionFOFtoCNF_2
| op(e2,e2) = e2 )
& ( ~ definitionFOFtoCNF_2
| op(e3,e3) = e2 )
& ( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2
| definitionFOFtoCNF_2 ) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
( ~ definitionFOFtoCNF_2
| op(e3,e3) = e2 ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
( e0 != op(e2,e1)
| e3 != op(e1,e1) ),
inference(canonicalize,[],[ax27]) ).
fof(normalize_0_33,plain,
op(e2,e1) != op(e2,e3),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_34,plain,
op(e2,unit) = e2,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_35,plain,
( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_36,plain,
( definitionFOFtoCNF_0
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ),
inference(simplify,[],[normalize_0_35,normalize_0_4,normalize_0_3]) ).
fof(normalize_0_37,plain,
( definitionFOFtoCNF_0
| definitionFOFtoCNF_2
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ),
inference(simplify,[],[normalize_0_36,normalize_0_29]) ).
fof(normalize_0_38,plain,
( ( op(e0,e0) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 )
& ( op(e1,e1) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 )
& ( op(e2,e2) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 )
& ( op(e3,e3) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
( op(e0,e0) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
( op(e2,e2) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_41,plain,
e2 != e3,
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_42,plain,
( op(e1,e1) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_43,plain,
e1 != e2,
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_44,plain,
op(e2,e1) != op(e3,e1),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_45,plain,
op(unit,e1) = e1,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_46,plain,
op(e1,e1) != op(e2,e1),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_47,plain,
( ( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 )
& ( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 )
& ( op(e0,e2) = e0
| op(e0,e2) = e1
| op(e0,e2) = e2
| op(e0,e2) = e3 )
& ( op(e0,e3) = e0
| op(e0,e3) = e1
| op(e0,e3) = e2
| op(e0,e3) = e3 )
& ( op(e1,e0) = e0
| op(e1,e0) = e1
| op(e1,e0) = e2
| op(e1,e0) = e3 )
& ( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 )
& ( op(e1,e2) = e0
| op(e1,e2) = e1
| op(e1,e2) = e2
| op(e1,e2) = e3 )
& ( op(e1,e3) = e0
| op(e1,e3) = e1
| op(e1,e3) = e2
| op(e1,e3) = e3 )
& ( op(e2,e0) = e0
| op(e2,e0) = e1
| op(e2,e0) = e2
| op(e2,e0) = e3 )
& ( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 )
& ( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 )
& ( op(e2,e3) = e0
| op(e2,e3) = e1
| op(e2,e3) = e2
| op(e2,e3) = e3 )
& ( op(e3,e0) = e0
| op(e3,e0) = e1
| op(e3,e0) = e2
| op(e3,e0) = e3 )
& ( op(e3,e1) = e0
| op(e3,e1) = e1
| op(e3,e1) = e2
| op(e3,e1) = e3 )
& ( op(e3,e2) = e0
| op(e3,e2) = e1
| op(e3,e2) = e2
| op(e3,e2) = e3 )
& ( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ) ),
inference(canonicalize,[],[ax1]) ).
fof(normalize_0_48,plain,
( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 ),
inference(conjunct,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
op(e1,e1) != op(e1,e2),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_50,plain,
( ~ definitionFOFtoCNF_2
| op(e1,e1) = e2 ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_51,plain,
op(e0,e0) != op(e2,e0),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_52,plain,
( ~ definitionFOFtoCNF_2
| op(e0,e0) = e2 ),
inference(conjunct,[],[normalize_0_30]) ).
fof(normalize_0_53,plain,
( e0 != op(e3,e1)
| e2 != op(e1,e1) ),
inference(canonicalize,[],[ax21]) ).
fof(normalize_0_54,plain,
( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_55,plain,
( e1 != op(e0,e0)
| e3 != op(e2,e0) ),
inference(canonicalize,[],[ax14]) ).
fof(normalize_0_56,plain,
( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e2,e2) = e1 ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_57,plain,
( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e3,e3) = e1 ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_58,plain,
op(e3,e0) != op(e3,e1),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_59,plain,
op(e3,unit) = e3,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e0,e0) = e1 ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
op(unit,e3) = e3,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( op(e3,e3) = e0
| definitionFOFtoCNF_1 ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
op(e0,e0) != op(e1,e0),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_5,plain,
( op(e0,e0) = e0
| definitionFOFtoCNF_1 ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_6,plain,
( e0 != op(e1,e0)
| op(e0,e0) != e0
| op(e0,e0) = op(e1,e0) ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e0),e0) ),[1],$fot(op(e1,e0))]]) ).
cnf(refute_0_7,plain,
( e0 != op(e1,e0)
| op(e0,e0) = op(e1,e0)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( e0 != op(e1,e0)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e0,e0),op(e1,e0)) )],[refute_0_7,refute_0_4]) ).
cnf(refute_0_9,plain,
op(unit,e0) = e0,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_10,plain,
( op(e2,e2) = e0
| definitionFOFtoCNF_1 ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
op(unit,e2) = e2,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_12,plain,
( unit = e0
| unit = e1
| unit = e2
| unit = e3 ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_13,plain,
( op(unit,e2) != e2
| unit != e2
| op(e2,e2) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e2),e2) ),[0,0],$fot(e2)]]) ).
cnf(refute_0_14,plain,
( op(unit,e2) != e2
| op(e2,e2) = e2
| unit = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(unit,e2) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( op(e2,e2) = e2
| unit = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(unit,e2),e2) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( op(e2,e2) != e0
| op(e2,e2) != e2
| e2 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,e2),e0) ),[0],$fot(e2)]]) ).
cnf(refute_0_17,plain,
( op(e2,e2) != e0
| e2 = e0
| unit = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e2,e2),e2) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( e2 = e0
| unit = e0
| unit = e1
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e2,e2),e0) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
e0 != e2,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_20,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( e2 != e0
| e0 = e2 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(e2)),bind(Y,$fot(e0))]]) ).
cnf(refute_0_24,plain,
e2 != e0,
inference(resolve,[$cnf( $equal(e0,e2) )],[refute_0_23,refute_0_19]) ).
cnf(refute_0_25,plain,
( unit = e0
| unit = e1
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e2,e0) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
( op(unit,e0) != e0
| unit != e1
| op(e1,e0) = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e0),e0) ),[0,0],$fot(e1)]]) ).
cnf(refute_0_27,plain,
( op(unit,e0) != e0
| op(e1,e0) = e0
| unit = e0
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( op(e1,e0) = e0
| unit = e0
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(unit,e0),e0) )],[refute_0_9,refute_0_27]) ).
cnf(refute_0_29,plain,
( e0 != e0
| op(e1,e0) != e0
| e0 = op(e1,e0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e0,op(e1,e0)) ),[1],$fot(e0)]]) ).
cnf(refute_0_30,plain,
( e0 != e0
| e0 = op(e1,e0)
| unit = e0
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e1,e0),e0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( e0 != e0
| unit = e0
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e0,op(e1,e0)) )],[refute_0_30,refute_0_8]) ).
cnf(refute_0_32,plain,
e0 = e0,
introduced(tautology,[refl,[$fot(e0)]]) ).
cnf(refute_0_33,plain,
( unit = e0
| unit = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e0,e0) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
( op(unit,e3) != e3
| unit != e3
| op(e3,e3) = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e3),e3) ),[0,0],$fot(e3)]]) ).
cnf(refute_0_35,plain,
( op(unit,e3) != e3
| op(e3,e3) = e3
| unit = e0
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(unit,e3) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( op(e3,e3) = e3
| unit = e0
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(unit,e3),e3) )],[refute_0_2,refute_0_35]) ).
cnf(refute_0_37,plain,
( op(e3,e3) != e0
| op(e3,e3) != e3
| e3 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e3,e3),e0) ),[0],$fot(e3)]]) ).
cnf(refute_0_38,plain,
( op(e3,e3) != e0
| e3 = e0
| unit = e0
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e3) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( e3 = e0
| unit = e0
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e0) )],[refute_0_3,refute_0_38]) ).
cnf(refute_0_40,plain,
e0 != e3,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_41,plain,
( e3 != e0
| e0 = e3 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(e3)),bind(Y,$fot(e0))]]) ).
cnf(refute_0_42,plain,
e3 != e0,
inference(resolve,[$cnf( $equal(e0,e3) )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
( unit = e0
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e3,e0) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( op(unit,e3) != e3
| unit != e0
| op(e0,e3) = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e3),e3) ),[0,0],$fot(e0)]]) ).
cnf(refute_0_45,plain,
( op(unit,e3) != e3
| op(e0,e3) = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( op(e0,e3) = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(unit,e3),e3) )],[refute_0_2,refute_0_45]) ).
cnf(refute_0_47,plain,
op(e1,e0) != op(e1,e3),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_48,plain,
( e0 != op(e3,e3)
| e1 != op(e2,e3) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_49,plain,
( e0 != e0
| op(e3,e3) != e0
| e0 = op(e3,e3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e0,op(e3,e3)) ),[1],$fot(e0)]]) ).
cnf(refute_0_50,plain,
( e0 != e0
| e0 = op(e3,e3)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e0) )],[refute_0_3,refute_0_49]) ).
cnf(refute_0_51,plain,
( e0 != e0
| e1 != op(e2,e3)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e0,op(e3,e3)) )],[refute_0_50,refute_0_48]) ).
cnf(refute_0_52,plain,
( e1 != op(e2,e3)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e0,e0) )],[refute_0_32,refute_0_51]) ).
cnf(refute_0_53,plain,
( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_54,plain,
( op(e3,e3) != e0
| op(e3,e3) != e1
| e1 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e3,e3),e0) ),[0],$fot(e1)]]) ).
cnf(refute_0_55,plain,
( op(e3,e3) != e0
| e1 = e0
| op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e1) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( e1 = e0
| op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e0) )],[refute_0_3,refute_0_55]) ).
cnf(refute_0_57,plain,
e0 != e1,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_58,plain,
( e1 != e0
| e0 = e1 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(e1)),bind(Y,$fot(e0))]]) ).
cnf(refute_0_59,plain,
e1 != e0,
inference(resolve,[$cnf( $equal(e0,e1) )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e1,e0) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( e1 != e1
| op(e2,e3) != e1
| e1 = op(e2,e3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e1,op(e2,e3)) ),[1],$fot(e1)]]) ).
cnf(refute_0_62,plain,
( e1 != e1
| e1 = op(e2,e3)
| op(e0,e3) = e1
| op(e1,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e2,e3),e1) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( e1 != e1
| op(e0,e3) = e1
| op(e1,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e1,op(e2,e3)) )],[refute_0_62,refute_0_52]) ).
cnf(refute_0_64,plain,
e1 = e1,
introduced(tautology,[refl,[$fot(e1)]]) ).
cnf(refute_0_65,plain,
( op(e0,e3) = e1
| op(e1,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e1,e1) )],[refute_0_64,refute_0_63]) ).
cnf(refute_0_66,plain,
( op(e1,e0) != e1
| op(e1,e3) != e1
| op(e1,e0) = op(e1,e3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e1,e0),op(e1,e3)) ),[1],$fot(e1)]]) ).
cnf(refute_0_67,plain,
( op(e1,e0) != e1
| op(e0,e3) = e1
| op(e1,e0) = op(e1,e3)
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e1,e3),e1) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( op(e1,e0) != e1
| op(e0,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e1,e0),op(e1,e3)) )],[refute_0_67,refute_0_47]) ).
cnf(refute_0_69,plain,
op(e1,unit) = e1,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_70,plain,
( op(e1,unit) != e1
| unit != e0
| op(e1,e0) = e1 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,unit),e1) ),[0,1],$fot(e0)]]) ).
cnf(refute_0_71,plain,
( op(e1,unit) != e1
| op(e1,e0) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_43,refute_0_70]) ).
cnf(refute_0_72,plain,
( op(e1,e0) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e1,unit),e1) )],[refute_0_69,refute_0_71]) ).
cnf(refute_0_73,plain,
( e1 != e1
| op(e1,e0) != e1
| op(e1,e0) = e1 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,e0),e1) ),[0,0],$fot(e1)]]) ).
cnf(refute_0_74,plain,
( e1 != e1
| op(e1,e0) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e1,e0),e1) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( e1 != e1
| op(e0,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e1,e0),e1) )],[refute_0_74,refute_0_68]) ).
cnf(refute_0_76,plain,
( op(e0,e3) = e1
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(e1,e1) )],[refute_0_64,refute_0_75]) ).
cnf(refute_0_77,plain,
( op(e0,e3) != e1
| op(e0,e3) != e3
| e1 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e3),e3) ),[0],$fot(e1)]]) ).
cnf(refute_0_78,plain,
( op(e0,e3) != e3
| e1 = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e0,e3),e1) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( e1 = e3
| definitionFOFtoCNF_1 ),
inference(resolve,[$cnf( $equal(op(e0,e3),e3) )],[refute_0_46,refute_0_78]) ).
cnf(refute_0_80,plain,
e1 != e3,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_81,plain,
definitionFOFtoCNF_1,
inference(resolve,[$cnf( $equal(e1,e3) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ definitionFOFtoCNF_0
| op(e0,e0) = e1 ),
inference(resolve,[$cnf( definitionFOFtoCNF_1 )],[refute_0_81,refute_0_1]) ).
cnf(refute_0_83,plain,
op(e0,e1) != op(e0,e2),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_84,plain,
op(e0,unit) = e0,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_85,plain,
( ~ definitionFOFtoCNF_2
| op(e3,e3) = e2 ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_86,plain,
( e0 != op(e2,e1)
| e3 != op(e1,e1) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_87,plain,
op(e2,e1) != op(e2,e3),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_88,plain,
op(e2,unit) = e2,
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_89,plain,
( op(e0,e0) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_90,plain,
( op(unit,e0) != e0
| unit != e0
| op(e0,e0) = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e0),e0) ),[0,0],$fot(e0)]]) ).
cnf(refute_0_91,plain,
( op(unit,e0) != e0
| op(e0,e0) = e0
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_12,refute_0_90]) ).
cnf(refute_0_92,plain,
( op(e0,e0) = e0
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(unit,e0),e0) )],[refute_0_9,refute_0_91]) ).
cnf(refute_0_93,plain,
( op(e0,e0) != e0
| op(e0,e0) != e3
| e0 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e0),e3) ),[0],$fot(e0)]]) ).
cnf(refute_0_94,plain,
( op(e0,e0) != e3
| e0 = e3
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e0) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( e0 = e3
| unit = e1
| unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e3) )],[refute_0_89,refute_0_94]) ).
cnf(refute_0_96,plain,
( unit = e1
| unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e0,e3) )],[refute_0_95,refute_0_40]) ).
cnf(refute_0_97,plain,
( op(e2,e2) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_98,plain,
( op(e2,e2) != e2
| op(e2,e2) != e3
| e2 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,e2),e3) ),[0],$fot(e2)]]) ).
cnf(refute_0_99,plain,
( op(e2,e2) != e3
| e2 = e3
| unit = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e2,e2),e2) )],[refute_0_15,refute_0_98]) ).
cnf(refute_0_100,plain,
( e2 = e3
| unit = e0
| unit = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e2),e3) )],[refute_0_97,refute_0_99]) ).
cnf(refute_0_101,plain,
e2 != e3,
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_102,plain,
( unit = e0
| unit = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e2,e3) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( unit != e0
| unit != e2
| e0 = e2 ),
introduced(tautology,[equality,[$cnf( $equal(unit,e2) ),[0],$fot(e0)]]) ).
cnf(refute_0_104,plain,
( unit != e2
| e0 = e2
| unit = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( e0 = e2
| unit = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e2) )],[refute_0_96,refute_0_104]) ).
cnf(refute_0_106,plain,
( unit = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e0,e2) )],[refute_0_105,refute_0_19]) ).
cnf(refute_0_107,plain,
( op(e1,e1) = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_108,plain,
( op(e1,unit) != e1
| unit != e1
| op(e1,e1) = e1 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,unit),e1) ),[0,1],$fot(e1)]]) ).
cnf(refute_0_109,plain,
( op(e1,unit) != e1
| op(e1,e1) = e1
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_12,refute_0_108]) ).
cnf(refute_0_110,plain,
( op(e1,e1) = e1
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e1,unit),e1) )],[refute_0_69,refute_0_109]) ).
cnf(refute_0_111,plain,
( op(e1,e1) != e1
| op(e1,e1) != e3
| e1 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,e1),e3) ),[0],$fot(e1)]]) ).
cnf(refute_0_112,plain,
( op(e1,e1) != e3
| e1 = e3
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e1) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( e1 = e3
| unit = e0
| unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e3) )],[refute_0_107,refute_0_112]) ).
cnf(refute_0_114,plain,
( unit = e0
| unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e1,e3) )],[refute_0_113,refute_0_80]) ).
cnf(refute_0_115,plain,
( unit != e0
| unit != e1
| e0 = e1 ),
introduced(tautology,[equality,[$cnf( $equal(unit,e1) ),[0],$fot(e0)]]) ).
cnf(refute_0_116,plain,
( unit != e1
| e0 = e1
| unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( e0 = e1
| unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_106,refute_0_116]) ).
cnf(refute_0_118,plain,
( unit = e2
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e0,e1) )],[refute_0_117,refute_0_57]) ).
cnf(refute_0_119,plain,
( unit != e1
| unit != e2
| e2 = e1 ),
introduced(tautology,[equality,[$cnf( $equal(unit,e1) ),[0],$fot(e2)]]) ).
cnf(refute_0_120,plain,
( unit != e1
| e2 = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e2) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( e2 = e1
| unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_106,refute_0_120]) ).
cnf(refute_0_122,plain,
e1 != e2,
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_123,plain,
( e2 != e1
| e1 = e2 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(e2)),bind(Y,$fot(e1))]]) ).
cnf(refute_0_124,plain,
e2 != e1,
inference(resolve,[$cnf( $equal(e1,e2) )],[refute_0_123,refute_0_122]) ).
cnf(refute_0_125,plain,
( unit = e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e2,e1) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( op(e2,unit) != e2
| unit != e3
| op(e2,e3) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,unit),e2) ),[0,1],$fot(e3)]]) ).
cnf(refute_0_127,plain,
( op(e2,unit) != e2
| op(e2,e3) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e3) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( op(e2,e3) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,unit),e2) )],[refute_0_88,refute_0_127]) ).
cnf(refute_0_129,plain,
( op(e2,e1) != e2
| op(e2,e3) != e2
| op(e2,e1) = op(e2,e3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e2,e1),op(e2,e3)) ),[1],$fot(e2)]]) ).
cnf(refute_0_130,plain,
( op(e2,e1) != e2
| op(e2,e1) = op(e2,e3)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e3),e2) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( op(e2,e1) != e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),op(e2,e3)) )],[refute_0_130,refute_0_87]) ).
cnf(refute_0_132,plain,
op(e2,e1) != op(e3,e1),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_133,plain,
op(unit,e1) = e1,
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_134,plain,
( op(unit,e1) != e1
| unit != e3
| op(e3,e1) = e1 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e1),e1) ),[0,0],$fot(e3)]]) ).
cnf(refute_0_135,plain,
( op(unit,e1) != e1
| op(e3,e1) = e1
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(unit,e3) )],[refute_0_125,refute_0_134]) ).
cnf(refute_0_136,plain,
( op(e3,e1) = e1
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(unit,e1),e1) )],[refute_0_133,refute_0_135]) ).
cnf(refute_0_137,plain,
( op(e2,e1) != e1
| op(e3,e1) != e1
| op(e2,e1) = op(e3,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e2,e1),op(e3,e1)) ),[1],$fot(e1)]]) ).
cnf(refute_0_138,plain,
( op(e2,e1) != e1
| op(e2,e1) = op(e3,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e3,e1),e1) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( op(e2,e1) != e1
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),op(e3,e1)) )],[refute_0_138,refute_0_132]) ).
cnf(refute_0_140,plain,
op(e1,e1) != op(e2,e1),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_141,plain,
( e3 != op(e2,e1)
| op(e1,e1) != e3
| op(e1,e1) = op(e2,e1) ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,e1),e3) ),[1],$fot(op(e2,e1))]]) ).
cnf(refute_0_142,plain,
( e3 != op(e2,e1)
| op(e1,e1) = op(e2,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e3) )],[refute_0_107,refute_0_141]) ).
cnf(refute_0_143,plain,
( e3 != op(e2,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e1,e1),op(e2,e1)) )],[refute_0_142,refute_0_140]) ).
cnf(refute_0_144,plain,
( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_145,plain,
( e3 != e3
| op(e2,e1) != e3
| e3 = op(e2,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e3,op(e2,e1)) ),[1],$fot(e3)]]) ).
cnf(refute_0_146,plain,
( e3 != e3
| e3 = op(e2,e1)
| op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e3) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( e3 != e3
| op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e3,op(e2,e1)) )],[refute_0_146,refute_0_143]) ).
cnf(refute_0_148,plain,
e3 = e3,
introduced(tautology,[refl,[$fot(e3)]]) ).
cnf(refute_0_149,plain,
( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e3,e3) )],[refute_0_148,refute_0_147]) ).
cnf(refute_0_150,plain,
( e1 != e1
| op(e2,e1) != e1
| op(e2,e1) = e1 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,e1),e1) ),[0,1],$fot(e1)]]) ).
cnf(refute_0_151,plain,
( e1 != e1
| op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e1) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( e1 != e1
| op(e2,e1) = e0
| op(e2,e1) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e1) )],[refute_0_151,refute_0_139]) ).
cnf(refute_0_153,plain,
( op(e2,e1) = e0
| op(e2,e1) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e1,e1) )],[refute_0_64,refute_0_152]) ).
cnf(refute_0_154,plain,
( e2 != e2
| op(e2,e1) != e2
| op(e2,e1) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,e1),e2) ),[0,0],$fot(e2)]]) ).
cnf(refute_0_155,plain,
( e2 != e2
| op(e2,e1) = e0
| op(e2,e1) = e2
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e2) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( e2 != e2
| op(e2,e1) = e0
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e2) )],[refute_0_155,refute_0_131]) ).
cnf(refute_0_157,plain,
e2 = e2,
introduced(tautology,[refl,[$fot(e2)]]) ).
cnf(refute_0_158,plain,
( op(e2,e1) = e0
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e2,e2) )],[refute_0_157,refute_0_156]) ).
cnf(refute_0_159,plain,
( e0 != e0
| op(e2,e1) != e0
| e0 = op(e2,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e0,op(e2,e1)) ),[1],$fot(e0)]]) ).
cnf(refute_0_160,plain,
( e0 != e0
| e0 = op(e2,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e0) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( e0 != e0
| e3 != op(e1,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e0,op(e2,e1)) )],[refute_0_160,refute_0_86]) ).
cnf(refute_0_162,plain,
( e3 != op(e1,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e0,e0) )],[refute_0_32,refute_0_161]) ).
cnf(refute_0_163,plain,
( e3 != e3
| op(e1,e1) != e3
| e3 = op(e1,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e3,op(e1,e1)) ),[1],$fot(e3)]]) ).
cnf(refute_0_164,plain,
( e3 != e3
| e3 = op(e1,e1)
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e3) )],[refute_0_107,refute_0_163]) ).
cnf(refute_0_165,plain,
( e3 != e3
| definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e3,op(e1,e1)) )],[refute_0_164,refute_0_162]) ).
cnf(refute_0_166,plain,
( definitionFOFtoCNF_0
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( $equal(e3,e3) )],[refute_0_148,refute_0_165]) ).
cnf(refute_0_167,plain,
( op(e3,e3) = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( definitionFOFtoCNF_2 )],[refute_0_166,refute_0_85]) ).
cnf(refute_0_168,plain,
op(e1,e1) != op(e1,e2),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_169,plain,
( op(unit,e2) != e2
| unit != e1
| op(e1,e2) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e2),e2) ),[0,0],$fot(e1)]]) ).
cnf(refute_0_170,plain,
( op(unit,e2) != e2
| op(e1,e2) = e2
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_12,refute_0_169]) ).
cnf(refute_0_171,plain,
( op(e1,e2) = e2
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(unit,e2),e2) )],[refute_0_11,refute_0_170]) ).
cnf(refute_0_172,plain,
( op(e1,e1) != e2
| op(e1,e2) != e2
| op(e1,e1) = op(e1,e2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e1,e1),op(e1,e2)) ),[1],$fot(e2)]]) ).
cnf(refute_0_173,plain,
( op(e1,e1) != e2
| op(e1,e1) = op(e1,e2)
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e1,e2),e2) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
( op(e1,e1) != e2
| unit = e0
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e1,e1),op(e1,e2)) )],[refute_0_173,refute_0_168]) ).
cnf(refute_0_175,plain,
( ~ definitionFOFtoCNF_2
| op(e1,e1) = e2 ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_176,plain,
( op(e1,e1) = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( definitionFOFtoCNF_2 )],[refute_0_166,refute_0_175]) ).
cnf(refute_0_177,plain,
( e2 != e2
| op(e1,e1) != e2
| op(e1,e1) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,e1),e2) ),[1],$fot(e2)]]) ).
cnf(refute_0_178,plain,
( e2 != e2
| op(e1,e1) = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e2) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( e2 != e2
| unit = e0
| unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e2) )],[refute_0_178,refute_0_174]) ).
cnf(refute_0_180,plain,
( unit = e0
| unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e2,e2) )],[refute_0_157,refute_0_179]) ).
cnf(refute_0_181,plain,
op(e0,e0) != op(e2,e0),
inference(canonicalize,[],[normalize_0_51]) ).
cnf(refute_0_182,plain,
( op(e2,unit) != e2
| unit != e0
| op(e2,e0) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,unit),e2) ),[0,1],$fot(e0)]]) ).
cnf(refute_0_183,plain,
( op(e2,unit) != e2
| op(e2,e0) = e2
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_12,refute_0_182]) ).
cnf(refute_0_184,plain,
( op(e2,e0) = e2
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e2,unit),e2) )],[refute_0_88,refute_0_183]) ).
cnf(refute_0_185,plain,
( op(e0,e0) != e2
| op(e2,e0) != e2
| op(e0,e0) = op(e2,e0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e0,e0),op(e2,e0)) ),[1],$fot(e2)]]) ).
cnf(refute_0_186,plain,
( op(e0,e0) != e2
| op(e0,e0) = op(e2,e0)
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e2,e0),e2) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
( op(e0,e0) != e2
| unit = e1
| unit = e2
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e0,e0),op(e2,e0)) )],[refute_0_186,refute_0_181]) ).
cnf(refute_0_188,plain,
( ~ definitionFOFtoCNF_2
| op(e0,e0) = e2 ),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_189,plain,
( op(e0,e0) = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( definitionFOFtoCNF_2 )],[refute_0_166,refute_0_188]) ).
cnf(refute_0_190,plain,
( e2 != e2
| op(e0,e0) != e2
| op(e0,e0) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e0),e2) ),[1],$fot(e2)]]) ).
cnf(refute_0_191,plain,
( e2 != e2
| op(e0,e0) = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e2) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
( e2 != e2
| unit = e1
| unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e2) )],[refute_0_191,refute_0_187]) ).
cnf(refute_0_193,plain,
( unit = e1
| unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e2,e2) )],[refute_0_157,refute_0_192]) ).
cnf(refute_0_194,plain,
( unit != e0
| unit != e1
| e1 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(unit,e0) ),[0],$fot(e1)]]) ).
cnf(refute_0_195,plain,
( unit != e0
| e1 = e0
| unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
( e1 = e0
| unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_180,refute_0_195]) ).
cnf(refute_0_197,plain,
( unit = e2
| unit = e3
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e1,e0) )],[refute_0_196,refute_0_59]) ).
cnf(refute_0_198,plain,
( op(unit,e3) != e3
| op(e3,e3) = e3
| unit = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(unit,e3) )],[refute_0_197,refute_0_34]) ).
cnf(refute_0_199,plain,
( op(e3,e3) = e3
| unit = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(unit,e3),e3) )],[refute_0_2,refute_0_198]) ).
cnf(refute_0_200,plain,
( op(e3,e3) != e2
| op(e3,e3) != e3
| e3 = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e3,e3),e2) ),[0],$fot(e3)]]) ).
cnf(refute_0_201,plain,
( op(e3,e3) != e2
| e3 = e2
| unit = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e3) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
( e3 = e2
| unit = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e2) )],[refute_0_167,refute_0_201]) ).
cnf(refute_0_203,plain,
( e3 != e2
| e2 = e3 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(e3)),bind(Y,$fot(e2))]]) ).
cnf(refute_0_204,plain,
e3 != e2,
inference(resolve,[$cnf( $equal(e2,e3) )],[refute_0_203,refute_0_101]) ).
cnf(refute_0_205,plain,
( unit = e2
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e3,e2) )],[refute_0_202,refute_0_204]) ).
cnf(refute_0_206,plain,
( op(e0,unit) != e0
| unit != e2
| op(e0,e2) = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,unit),e0) ),[0,1],$fot(e2)]]) ).
cnf(refute_0_207,plain,
( op(e0,unit) != e0
| op(e0,e2) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(unit,e2) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
( op(e0,e2) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,unit),e0) )],[refute_0_84,refute_0_207]) ).
cnf(refute_0_209,plain,
( op(e0,e1) != e0
| op(e0,e2) != e0
| op(e0,e1) = op(e0,e2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e0,e1),op(e0,e2)) ),[1],$fot(e0)]]) ).
cnf(refute_0_210,plain,
( op(e0,e1) != e0
| op(e0,e1) = op(e0,e2)
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,e2),e0) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( op(e0,e1) != e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,e1),op(e0,e2)) )],[refute_0_210,refute_0_83]) ).
cnf(refute_0_212,plain,
( e0 != op(e3,e1)
| e2 != op(e1,e1) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_213,plain,
( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_214,plain,
( e0 != e0
| op(e3,e1) != e0
| e0 = op(e3,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e0,op(e3,e1)) ),[1],$fot(e0)]]) ).
cnf(refute_0_215,plain,
( e0 != e0
| e0 = op(e3,e1)
| op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0 ),
inference(resolve,[$cnf( $equal(op(e3,e1),e0) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( e0 != e0
| e2 != op(e1,e1)
| op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0 ),
inference(resolve,[$cnf( $equal(e0,op(e3,e1)) )],[refute_0_215,refute_0_212]) ).
cnf(refute_0_217,plain,
( e2 != op(e1,e1)
| op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0 ),
inference(resolve,[$cnf( $equal(e0,e0) )],[refute_0_32,refute_0_216]) ).
cnf(refute_0_218,plain,
( e2 != e2
| e2 != op(e1,e1)
| op(e1,e1) = e2 ),
introduced(tautology,[equality,[$cnf( $equal(e2,e2) ),[0],$fot(op(e1,e1))]]) ).
cnf(refute_0_219,plain,
( e2 != op(e1,e1)
| op(e1,e1) = e2 ),
inference(resolve,[$cnf( $equal(e2,e2) )],[refute_0_157,refute_0_218]) ).
cnf(refute_0_220,plain,
( op(e1,e1) != e0
| op(e1,e1) != e2
| e2 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,e1),e0) ),[0],$fot(e2)]]) ).
cnf(refute_0_221,plain,
( e2 != op(e1,e1)
| op(e1,e1) != e0
| e2 = e0 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e2) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
( e2 != op(e1,e1)
| e2 = e0
| op(e0,e1) = e0
| op(e2,e1) = e0 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e0) )],[refute_0_217,refute_0_221]) ).
cnf(refute_0_223,plain,
( e2 != op(e1,e1)
| op(e0,e1) = e0
| op(e2,e1) = e0 ),
inference(resolve,[$cnf( $equal(e2,e0) )],[refute_0_222,refute_0_24]) ).
cnf(refute_0_224,plain,
( e2 != e2
| op(e1,e1) != e2
| e2 = op(e1,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e2,op(e1,e1)) ),[1],$fot(e2)]]) ).
cnf(refute_0_225,plain,
( e2 != e2
| e2 = op(e1,e1)
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e1,e1),e2) )],[refute_0_176,refute_0_224]) ).
cnf(refute_0_226,plain,
( e2 != e2
| op(e0,e1) = e0
| op(e2,e1) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e2,op(e1,e1)) )],[refute_0_225,refute_0_223]) ).
cnf(refute_0_227,plain,
( op(e0,e1) = e0
| op(e2,e1) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e2,e2) )],[refute_0_157,refute_0_226]) ).
cnf(refute_0_228,plain,
( op(unit,e1) != e1
| unit != e2
| op(e2,e1) = e1 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e1),e1) ),[0,0],$fot(e2)]]) ).
cnf(refute_0_229,plain,
( op(unit,e1) != e1
| op(e2,e1) = e1
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(unit,e2) )],[refute_0_205,refute_0_228]) ).
cnf(refute_0_230,plain,
( op(e2,e1) = e1
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(unit,e1),e1) )],[refute_0_133,refute_0_229]) ).
cnf(refute_0_231,plain,
( op(e2,e1) != e0
| op(e2,e1) != e1
| e1 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,e1),e0) ),[0],$fot(e1)]]) ).
cnf(refute_0_232,plain,
( op(e2,e1) != e0
| e1 = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e1) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( e1 = e0
| op(e0,e1) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e2,e1),e0) )],[refute_0_227,refute_0_232]) ).
cnf(refute_0_234,plain,
( op(e0,e1) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(e1,e0) )],[refute_0_233,refute_0_59]) ).
cnf(refute_0_235,plain,
( e0 != e0
| op(e0,e1) != e0
| op(e0,e1) = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e1),e0) ),[0,0],$fot(e0)]]) ).
cnf(refute_0_236,plain,
( e0 != e0
| op(e0,e1) = e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,e1),e0) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
( e0 != e0
| definitionFOFtoCNF_0 ),
inference(resolve,[$cnf( $equal(op(e0,e1),e0) )],[refute_0_236,refute_0_211]) ).
cnf(refute_0_238,plain,
definitionFOFtoCNF_0,
inference(resolve,[$cnf( $equal(e0,e0) )],[refute_0_32,refute_0_237]) ).
cnf(refute_0_239,plain,
op(e0,e0) = e1,
inference(resolve,[$cnf( definitionFOFtoCNF_0 )],[refute_0_238,refute_0_82]) ).
cnf(refute_0_240,plain,
( op(e0,e0) != e1
| op(e0,e0) != e3
| e1 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e0),e3) ),[0],$fot(e1)]]) ).
cnf(refute_0_241,plain,
( op(e0,e0) != e3
| e1 = e3 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e1) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( e1 = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e3) )],[refute_0_0,refute_0_241]) ).
cnf(refute_0_243,plain,
( op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 ),
inference(resolve,[$cnf( $equal(e1,e3) )],[refute_0_242,refute_0_80]) ).
cnf(refute_0_244,plain,
( e1 != op(e0,e0)
| e3 != op(e2,e0) ),
inference(canonicalize,[],[normalize_0_55]) ).
cnf(refute_0_245,plain,
( e1 != e1
| op(e0,e0) != e1
| e1 = op(e0,e0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(e1,op(e0,e0)) ),[1],$fot(e1)]]) ).
cnf(refute_0_246,plain,
( e1 != e1
| e1 = op(e0,e0) ),
inference(resolve,[$cnf( $equal(op(e0,e0),e1) )],[refute_0_239,refute_0_245]) ).
cnf(refute_0_247,plain,
( e1 != e1
| e3 != op(e2,e0) ),
inference(resolve,[$cnf( $equal(e1,op(e0,e0)) )],[refute_0_246,refute_0_244]) ).
cnf(refute_0_248,plain,
e3 != op(e2,e0),
inference(resolve,[$cnf( $equal(e1,e1) )],[refute_0_64,refute_0_247]) ).
cnf(refute_0_249,plain,
( op(e2,e0) != e3
| e3 = op(e2,e0) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(op(e2,e0))),bind(Y,$fot(e3))]]) ).
cnf(refute_0_250,plain,
op(e2,e0) != e3,
inference(resolve,[$cnf( $equal(e3,op(e2,e0)) )],[refute_0_249,refute_0_248]) ).
cnf(refute_0_251,plain,
( op(e1,e0) = e3
| op(e3,e0) = e3 ),
inference(resolve,[$cnf( $equal(op(e2,e0),e3) )],[refute_0_243,refute_0_250]) ).
cnf(refute_0_252,plain,
( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e2,e2) = e1 ),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_253,plain,
( ~ definitionFOFtoCNF_0
| op(e2,e2) = e1 ),
inference(resolve,[$cnf( definitionFOFtoCNF_1 )],[refute_0_81,refute_0_252]) ).
cnf(refute_0_254,plain,
op(e2,e2) = e1,
inference(resolve,[$cnf( definitionFOFtoCNF_0 )],[refute_0_238,refute_0_253]) ).
cnf(refute_0_255,plain,
( op(e2,e2) != e1
| op(e2,e2) != e2
| e1 = e2 ),
introduced(tautology,[equality,[$cnf( $equal(op(e2,e2),e2) ),[0],$fot(e1)]]) ).
cnf(refute_0_256,plain,
( op(e2,e2) != e2
| e1 = e2 ),
inference(resolve,[$cnf( $equal(op(e2,e2),e1) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( e1 = e2
| unit = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e2,e2),e2) )],[refute_0_15,refute_0_256]) ).
cnf(refute_0_258,plain,
( unit = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(e1,e2) )],[refute_0_257,refute_0_122]) ).
cnf(refute_0_259,plain,
( op(unit,e0) != e0
| op(e0,e0) = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(unit,e0) )],[refute_0_258,refute_0_90]) ).
cnf(refute_0_260,plain,
( op(e0,e0) = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(unit,e0),e0) )],[refute_0_9,refute_0_259]) ).
cnf(refute_0_261,plain,
( op(e0,e0) != e0
| op(e0,e0) != e1
| e1 = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(e0,e0),e0) ),[0],$fot(e1)]]) ).
cnf(refute_0_262,plain,
( op(e0,e0) != e0
| e1 = e0 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e1) )],[refute_0_239,refute_0_261]) ).
cnf(refute_0_263,plain,
( e1 = e0
| unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(op(e0,e0),e0) )],[refute_0_260,refute_0_262]) ).
cnf(refute_0_264,plain,
( unit = e1
| unit = e3 ),
inference(resolve,[$cnf( $equal(e1,e0) )],[refute_0_263,refute_0_59]) ).
cnf(refute_0_265,plain,
( op(unit,e3) != e3
| op(e3,e3) = e3
| unit = e1 ),
inference(resolve,[$cnf( $equal(unit,e3) )],[refute_0_264,refute_0_34]) ).
cnf(refute_0_266,plain,
( op(e3,e3) = e3
| unit = e1 ),
inference(resolve,[$cnf( $equal(op(unit,e3),e3) )],[refute_0_2,refute_0_265]) ).
cnf(refute_0_267,plain,
( ~ definitionFOFtoCNF_0
| ~ definitionFOFtoCNF_1
| op(e3,e3) = e1 ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_268,plain,
( ~ definitionFOFtoCNF_0
| op(e3,e3) = e1 ),
inference(resolve,[$cnf( definitionFOFtoCNF_1 )],[refute_0_81,refute_0_267]) ).
cnf(refute_0_269,plain,
op(e3,e3) = e1,
inference(resolve,[$cnf( definitionFOFtoCNF_0 )],[refute_0_238,refute_0_268]) ).
cnf(refute_0_270,plain,
( op(e3,e3) != e1
| op(e3,e3) != e3
| e1 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e3,e3),e3) ),[0],$fot(e1)]]) ).
cnf(refute_0_271,plain,
( op(e3,e3) != e3
| e1 = e3 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e1) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( e1 = e3
| unit = e1 ),
inference(resolve,[$cnf( $equal(op(e3,e3),e3) )],[refute_0_266,refute_0_271]) ).
cnf(refute_0_273,plain,
unit = e1,
inference(resolve,[$cnf( $equal(e1,e3) )],[refute_0_272,refute_0_80]) ).
cnf(refute_0_274,plain,
op(unit,e0) = op(unit,e0),
introduced(tautology,[refl,[$fot(op(unit,e0))]]) ).
cnf(refute_0_275,plain,
( op(unit,e0) != op(unit,e0)
| unit != e1
| op(unit,e0) = op(e1,e0) ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e0),op(unit,e0)) ),[1,0],$fot(e1)]]) ).
cnf(refute_0_276,plain,
( unit != e1
| op(unit,e0) = op(e1,e0) ),
inference(resolve,[$cnf( $equal(op(unit,e0),op(unit,e0)) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
op(unit,e0) = op(e1,e0),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( op(unit,e0) != e0
| op(unit,e0) != op(e1,e0)
| op(e1,e0) = e0 ),
introduced(tautology,[equality,[$cnf( $equal(op(unit,e0),e0) ),[0],$fot(op(e1,e0))]]) ).
cnf(refute_0_279,plain,
( op(unit,e0) != e0
| op(e1,e0) = e0 ),
inference(resolve,[$cnf( $equal(op(unit,e0),op(e1,e0)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
op(e1,e0) = e0,
inference(resolve,[$cnf( $equal(op(unit,e0),e0) )],[refute_0_9,refute_0_279]) ).
cnf(refute_0_281,plain,
( op(e1,e0) != e0
| op(e1,e0) != e3
| e0 = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e1,e0),e3) ),[0],$fot(e0)]]) ).
cnf(refute_0_282,plain,
( op(e1,e0) != e3
| e0 = e3 ),
inference(resolve,[$cnf( $equal(op(e1,e0),e0) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
( e0 = e3
| op(e3,e0) = e3 ),
inference(resolve,[$cnf( $equal(op(e1,e0),e3) )],[refute_0_251,refute_0_282]) ).
cnf(refute_0_284,plain,
op(e3,e0) = e3,
inference(resolve,[$cnf( $equal(e0,e3) )],[refute_0_283,refute_0_40]) ).
cnf(refute_0_285,plain,
op(e3,e0) != op(e3,e1),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_286,plain,
op(e3,unit) = e3,
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_287,plain,
op(e3,unit) = op(e3,unit),
introduced(tautology,[refl,[$fot(op(e3,unit))]]) ).
cnf(refute_0_288,plain,
( op(e3,unit) != op(e3,unit)
| unit != e1
| op(e3,unit) = op(e3,e1) ),
introduced(tautology,[equality,[$cnf( $equal(op(e3,unit),op(e3,unit)) ),[1,1],$fot(e1)]]) ).
cnf(refute_0_289,plain,
( unit != e1
| op(e3,unit) = op(e3,e1) ),
inference(resolve,[$cnf( $equal(op(e3,unit),op(e3,unit)) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
op(e3,unit) = op(e3,e1),
inference(resolve,[$cnf( $equal(unit,e1) )],[refute_0_273,refute_0_289]) ).
cnf(refute_0_291,plain,
( op(e3,unit) != e3
| op(e3,unit) != op(e3,e1)
| op(e3,e1) = e3 ),
introduced(tautology,[equality,[$cnf( $equal(op(e3,unit),e3) ),[0],$fot(op(e3,e1))]]) ).
cnf(refute_0_292,plain,
( op(e3,unit) != e3
| op(e3,e1) = e3 ),
inference(resolve,[$cnf( $equal(op(e3,unit),op(e3,e1)) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
op(e3,e1) = e3,
inference(resolve,[$cnf( $equal(op(e3,unit),e3) )],[refute_0_286,refute_0_292]) ).
cnf(refute_0_294,plain,
( op(e3,e0) != e3
| op(e3,e1) != e3
| op(e3,e0) = op(e3,e1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(op(e3,e0),op(e3,e1)) ),[1],$fot(e3)]]) ).
cnf(refute_0_295,plain,
( op(e3,e0) != e3
| op(e3,e0) = op(e3,e1) ),
inference(resolve,[$cnf( $equal(op(e3,e1),e3) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
op(e3,e0) != e3,
inference(resolve,[$cnf( $equal(op(e3,e0),op(e3,e1)) )],[refute_0_295,refute_0_285]) ).
cnf(refute_0_297,plain,
$false,
inference(resolve,[$cnf( $equal(op(e3,e0),e3) )],[refute_0_284,refute_0_296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Wed Jun 8 13:07:36 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.87/3.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.87/3.08
% 2.87/3.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.87/3.10
%------------------------------------------------------------------------------