TSTP Solution File: ALG006-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:30:33 EDT 2022
% Result : Unsatisfiable 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 49
% Syntax : Number of clauses : 208 ( 109 unt; 0 nHn; 103 RR)
% Number of literals : 353 ( 352 equ; 147 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 445 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
difference(X,difference(Y,X)) = X ).
cnf(set_difference_2,axiom,
difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ).
cnf(set_difference_3,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)) ).
cnf(prove_set_difference_3_simplified,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c) ).
cnf(refute_0_0,plain,
difference(difference(Y,X_5),difference(Y,difference(Y,X_5))) = difference(Y,X_5),
inference(subst,[],[set_difference_1:[bind(X,$fot(difference(Y,X_5)))]]) ).
cnf(refute_0_1,plain,
difference(Y,difference(Y,X_5)) = difference(X_5,difference(X_5,Y)),
inference(subst,[],[set_difference_2:[bind(X,$fot(Y)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_2,plain,
( difference(Y,difference(Y,X_5)) != difference(X_5,difference(X_5,Y))
| difference(difference(Y,X_5),difference(Y,difference(Y,X_5))) != difference(Y,X_5)
| difference(difference(Y,X_5),difference(X_5,difference(X_5,Y))) = difference(Y,X_5) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,X_5),difference(Y,difference(Y,X_5))),difference(Y,X_5)) ),[0,1],$fot(difference(X_5,difference(X_5,Y)))]]) ).
cnf(refute_0_3,plain,
( difference(difference(Y,X_5),difference(Y,difference(Y,X_5))) != difference(Y,X_5)
| difference(difference(Y,X_5),difference(X_5,difference(X_5,Y))) = difference(Y,X_5) ),
inference(resolve,[$cnf( $equal(difference(Y,difference(Y,X_5)),difference(X_5,difference(X_5,Y))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
difference(difference(Y,X_5),difference(X_5,difference(X_5,Y))) = difference(Y,X_5),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_5),difference(Y,difference(Y,X_5))),difference(Y,X_5)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,difference(X_16,difference(X_16,Y))),
inference(subst,[],[refute_0_4:[bind(X_5,$fot(difference(X_16,difference(X_16,Y))))]]) ).
cnf(refute_0_6,plain,
difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) = difference(Y,difference(Y,difference(Y,X_5))),
inference(subst,[],[set_difference_2:[bind(X,$fot(difference(Y,X_5)))]]) ).
cnf(refute_0_7,plain,
( difference(Y,difference(Y,X_5)) != difference(X_5,difference(X_5,Y))
| difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) != difference(Y,difference(Y,difference(Y,X_5)))
| difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) = difference(Y,difference(X_5,difference(X_5,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,X_5),difference(difference(Y,X_5),Y)),difference(Y,difference(Y,difference(Y,X_5)))) ),[1,1],$fot(difference(X_5,difference(X_5,Y)))]]) ).
cnf(refute_0_8,plain,
( difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) != difference(Y,difference(Y,difference(Y,X_5)))
| difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) = difference(Y,difference(X_5,difference(X_5,Y))) ),
inference(resolve,[$cnf( $equal(difference(Y,difference(Y,X_5)),difference(X_5,difference(X_5,Y))) )],[refute_0_1,refute_0_7]) ).
cnf(refute_0_9,plain,
difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) = difference(Y,difference(X_5,difference(X_5,Y))),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_5),difference(difference(Y,X_5),Y)),difference(Y,difference(Y,difference(Y,X_5)))) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) != difference(Y,difference(Y,difference(Y,X_5)))
| difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) != difference(Y,difference(X_5,difference(X_5,Y)))
| difference(Y,difference(Y,difference(Y,X_5))) = difference(Y,difference(X_5,difference(X_5,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,X_5),difference(difference(Y,X_5),Y)),difference(Y,difference(X_5,difference(X_5,Y)))) ),[0],$fot(difference(Y,difference(Y,difference(Y,X_5))))]]) ).
cnf(refute_0_11,plain,
( difference(difference(Y,X_5),difference(difference(Y,X_5),Y)) != difference(Y,difference(X_5,difference(X_5,Y)))
| difference(Y,difference(Y,difference(Y,X_5))) = difference(Y,difference(X_5,difference(X_5,Y))) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_5),difference(difference(Y,X_5),Y)),difference(Y,difference(Y,difference(Y,X_5)))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
difference(Y,difference(Y,difference(Y,X_5))) = difference(Y,difference(X_5,difference(X_5,Y))),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_5),difference(difference(Y,X_5),Y)),difference(Y,difference(X_5,difference(X_5,Y)))) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
difference(Y,difference(Y,difference(Y,X_16))) = difference(Y,difference(X_16,difference(X_16,Y))),
inference(subst,[],[refute_0_12:[bind(X_5,$fot(X_16))]]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( difference(Y,difference(Y,difference(Y,X_16))) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(Y,difference(X_16,difference(X_16,Y))) = difference(Y,difference(Y,difference(Y,X_16))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(difference(Y,difference(Y,difference(Y,X_16))))),bind(Y0,$fot(difference(Y,difference(X_16,difference(X_16,Y)))))]]) ).
cnf(refute_0_18,plain,
difference(Y,difference(X_16,difference(X_16,Y))) = difference(Y,difference(Y,difference(Y,X_16))),
inference(resolve,[$cnf( $equal(difference(Y,difference(Y,difference(Y,X_16))),difference(Y,difference(X_16,difference(X_16,Y)))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( difference(Y,difference(X_16,difference(X_16,Y))) != difference(Y,difference(Y,difference(Y,X_16)))
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,difference(Y,difference(Y,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))),difference(Y,difference(X_16,difference(X_16,Y)))) ),[1],$fot(difference(Y,difference(Y,difference(Y,X_16))))]]) ).
cnf(refute_0_20,plain,
( difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,difference(Y,difference(Y,X_16))) ),
inference(resolve,[$cnf( $equal(difference(Y,difference(X_16,difference(X_16,Y))),difference(Y,difference(Y,difference(Y,X_16)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,difference(Y,difference(Y,X_16))),
inference(resolve,[$cnf( $equal(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))),difference(Y,difference(X_16,difference(X_16,Y)))) )],[refute_0_5,refute_0_20]) ).
cnf(refute_0_22,plain,
difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,difference(Y,difference(Y,X_16))),
inference(subst,[],[set_difference_2:[bind(X,$fot(difference(Y,X_16)))]]) ).
cnf(refute_0_23,plain,
( difference(Y,difference(Y,difference(Y,X_16))) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) != difference(Y,difference(Y,difference(Y,X_16)))
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,difference(X_16,difference(X_16,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)),difference(Y,difference(Y,difference(Y,X_16)))) ),[1],$fot(difference(Y,difference(X_16,difference(X_16,Y))))]]) ).
cnf(refute_0_24,plain,
( difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) != difference(Y,difference(Y,difference(Y,X_16)))
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,difference(X_16,difference(X_16,Y))) ),
inference(resolve,[$cnf( $equal(difference(Y,difference(Y,difference(Y,X_16))),difference(Y,difference(X_16,difference(X_16,Y)))) )],[refute_0_13,refute_0_23]) ).
cnf(refute_0_25,plain,
difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,difference(X_16,difference(X_16,Y))),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)),difference(Y,difference(Y,difference(Y,X_16)))) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
difference(X,difference(X,X)) = difference(X,difference(X,X)),
inference(subst,[],[set_difference_2:[bind(Y,$fot(X))]]) ).
cnf(refute_0_27,plain,
difference(difference(X_1,X_5),difference(difference(X_1,X_5),X_5)) = difference(X_5,difference(X_5,difference(X_1,X_5))),
inference(subst,[],[set_difference_2:[bind(X,$fot(difference(X_1,X_5))),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_28,plain,
difference(difference(X_1,Y),difference(Y,difference(X_1,Y))) = difference(X_1,Y),
inference(subst,[],[set_difference_1:[bind(X,$fot(difference(X_1,Y)))]]) ).
cnf(refute_0_29,plain,
difference(Y,difference(X_1,Y)) = Y,
inference(subst,[],[set_difference_1:[bind(X,$fot(Y)),bind(Y,$fot(X_1))]]) ).
cnf(refute_0_30,plain,
( difference(Y,difference(X_1,Y)) != Y
| difference(difference(X_1,Y),difference(Y,difference(X_1,Y))) != difference(X_1,Y)
| difference(difference(X_1,Y),Y) = difference(X_1,Y) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_1,Y),difference(Y,difference(X_1,Y))),difference(X_1,Y)) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_31,plain,
( difference(difference(X_1,Y),difference(Y,difference(X_1,Y))) != difference(X_1,Y)
| difference(difference(X_1,Y),Y) = difference(X_1,Y) ),
inference(resolve,[$cnf( $equal(difference(Y,difference(X_1,Y)),Y) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
difference(difference(X_1,Y),Y) = difference(X_1,Y),
inference(resolve,[$cnf( $equal(difference(difference(X_1,Y),difference(Y,difference(X_1,Y))),difference(X_1,Y)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
difference(difference(X_1,X_5),X_5) = difference(X_1,X_5),
inference(subst,[],[refute_0_32:[bind(Y,$fot(X_5))]]) ).
cnf(refute_0_34,plain,
( difference(difference(X_1,X_5),X_5) != difference(X_1,X_5)
| difference(difference(X_1,X_5),difference(difference(X_1,X_5),X_5)) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_5),difference(X_1,X_5)) = difference(X_5,difference(X_5,difference(X_1,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_1,X_5),difference(difference(X_1,X_5),X_5)),difference(X_5,difference(X_5,difference(X_1,X_5)))) ),[0,1],$fot(difference(X_1,X_5))]]) ).
cnf(refute_0_35,plain,
( difference(difference(X_1,X_5),difference(difference(X_1,X_5),X_5)) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_5),difference(X_1,X_5)) = difference(X_5,difference(X_5,difference(X_1,X_5))) ),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_5),X_5),difference(X_1,X_5)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
difference(difference(X_1,X_5),difference(X_1,X_5)) = difference(X_5,difference(X_5,difference(X_1,X_5))),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_5),difference(difference(X_1,X_5),X_5)),difference(X_5,difference(X_5,difference(X_1,X_5)))) )],[refute_0_27,refute_0_35]) ).
cnf(refute_0_37,plain,
( difference(difference(X,Y),Z) != difference(difference(X,Z),difference(Y,Z))
| difference(difference(X,Z),difference(Y,Z)) = difference(difference(X,Y),Z) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(difference(difference(X,Y),Z))),bind(Y0,$fot(difference(difference(X,Z),difference(Y,Z))))]]) ).
cnf(refute_0_38,plain,
difference(difference(X,Z),difference(Y,Z)) = difference(difference(X,Y),Z),
inference(resolve,[$cnf( $equal(difference(difference(X,Y),Z),difference(difference(X,Z),difference(Y,Z))) )],[set_difference_3,refute_0_37]) ).
cnf(refute_0_39,plain,
difference(difference(X_1,X_5),difference(X_1,X_5)) = difference(difference(X_1,X_1),X_5),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_1)),bind(Y,$fot(X_1)),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_40,plain,
( difference(difference(X_1,X_5),difference(X_1,X_5)) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_5),difference(X_1,X_5)) != difference(difference(X_1,X_1),X_5)
| difference(difference(X_1,X_1),X_5) = difference(X_5,difference(X_5,difference(X_1,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_1,X_5),difference(X_1,X_5)),difference(X_5,difference(X_5,difference(X_1,X_5)))) ),[0],$fot(difference(difference(X_1,X_1),X_5))]]) ).
cnf(refute_0_41,plain,
( difference(difference(X_1,X_5),difference(X_1,X_5)) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_1),X_5) = difference(X_5,difference(X_5,difference(X_1,X_5))) ),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_5),difference(X_1,X_5)),difference(difference(X_1,X_1),X_5)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
difference(X_5,difference(X_1,X_5)) = X_5,
inference(subst,[],[set_difference_1:[bind(X,$fot(X_5)),bind(Y,$fot(X_1))]]) ).
cnf(refute_0_43,plain,
difference(X_5,difference(X_5,difference(X_1,X_5))) = difference(X_5,difference(X_5,difference(X_1,X_5))),
introduced(tautology,[refl,[$fot(difference(X_5,difference(X_5,difference(X_1,X_5))))]]) ).
cnf(refute_0_44,plain,
( difference(X_5,difference(X_1,X_5)) != X_5
| difference(X_5,difference(X_5,difference(X_1,X_5))) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(X_5,difference(X_5,difference(X_1,X_5))) = difference(X_5,X_5) ),
introduced(tautology,[equality,[$cnf( $equal(difference(X_5,difference(X_5,difference(X_1,X_5))),difference(X_5,difference(X_5,difference(X_1,X_5)))) ),[1,1],$fot(X_5)]]) ).
cnf(refute_0_45,plain,
( difference(X_5,difference(X_1,X_5)) != X_5
| difference(X_5,difference(X_5,difference(X_1,X_5))) = difference(X_5,X_5) ),
inference(resolve,[$cnf( $equal(difference(X_5,difference(X_5,difference(X_1,X_5))),difference(X_5,difference(X_5,difference(X_1,X_5)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
difference(X_5,difference(X_5,difference(X_1,X_5))) = difference(X_5,X_5),
inference(resolve,[$cnf( $equal(difference(X_5,difference(X_1,X_5)),X_5) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( difference(X_5,difference(X_5,difference(X_1,X_5))) != difference(X_5,X_5)
| difference(difference(X_1,X_1),X_5) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_1),X_5) = difference(X_5,X_5) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_1,X_1),X_5),difference(X_5,difference(X_5,difference(X_1,X_5)))) ),[1],$fot(difference(X_5,X_5))]]) ).
cnf(refute_0_48,plain,
( difference(difference(X_1,X_1),X_5) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_1),X_5) = difference(X_5,X_5) ),
inference(resolve,[$cnf( $equal(difference(X_5,difference(X_5,difference(X_1,X_5))),difference(X_5,X_5)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( difference(difference(X_1,X_5),difference(X_1,X_5)) != difference(X_5,difference(X_5,difference(X_1,X_5)))
| difference(difference(X_1,X_1),X_5) = difference(X_5,X_5) ),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_1),X_5),difference(X_5,difference(X_5,difference(X_1,X_5)))) )],[refute_0_41,refute_0_48]) ).
cnf(refute_0_50,plain,
difference(difference(X_1,X_1),X_5) = difference(X_5,X_5),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_5),difference(X_1,X_5)),difference(X_5,difference(X_5,difference(X_1,X_5)))) )],[refute_0_36,refute_0_49]) ).
cnf(refute_0_51,plain,
difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))) = difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))),
inference(subst,[],[refute_0_50:[bind(X_1,$fot(X_9)),bind(X_5,$fot(difference(Y,difference(X_9,X_9))))]]) ).
cnf(refute_0_52,plain,
difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))) = difference(X_9,X_9),
inference(subst,[],[set_difference_1:[bind(X,$fot(difference(X_9,X_9)))]]) ).
cnf(refute_0_53,plain,
( difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))) != difference(X_9,X_9)
| difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))) != difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))
| difference(X_9,X_9) = difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))),difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))) ),[0],$fot(difference(X_9,X_9))]]) ).
cnf(refute_0_54,plain,
( difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))) != difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))
| difference(X_9,X_9) = difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))),difference(X_9,X_9)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
difference(X_9,X_9) = difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(Y,difference(X_9,X_9))),difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
difference(X,difference(X,difference(X_9,X_9))) = difference(difference(X_9,X_9),difference(difference(X_9,X_9),X)),
inference(subst,[],[set_difference_2:[bind(Y,$fot(difference(X_9,X_9)))]]) ).
cnf(refute_0_57,plain,
difference(difference(X_9,X_9),X) = difference(X,X),
inference(subst,[],[refute_0_50:[bind(X_1,$fot(X_9)),bind(X_5,$fot(X))]]) ).
cnf(refute_0_58,plain,
( difference(X,difference(X,difference(X_9,X_9))) != difference(difference(X_9,X_9),difference(difference(X_9,X_9),X))
| difference(difference(X_9,X_9),X) != difference(X,X)
| difference(X,difference(X,difference(X_9,X_9))) = difference(difference(X_9,X_9),difference(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(X,difference(X,difference(X_9,X_9))),difference(difference(X_9,X_9),difference(difference(X_9,X_9),X))) ),[1,1],$fot(difference(X,X))]]) ).
cnf(refute_0_59,plain,
( difference(X,difference(X,difference(X_9,X_9))) != difference(difference(X_9,X_9),difference(difference(X_9,X_9),X))
| difference(X,difference(X,difference(X_9,X_9))) = difference(difference(X_9,X_9),difference(X,X)) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),X),difference(X,X)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
difference(X,difference(X,difference(X_9,X_9))) = difference(difference(X_9,X_9),difference(X,X)),
inference(resolve,[$cnf( $equal(difference(X,difference(X,difference(X_9,X_9))),difference(difference(X_9,X_9),difference(difference(X_9,X_9),X))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
difference(difference(X_1,X_1),difference(X_9,X_9)) = difference(difference(X_9,X_9),difference(X_9,X_9)),
inference(subst,[],[refute_0_50:[bind(X_5,$fot(difference(X_9,X_9)))]]) ).
cnf(refute_0_62,plain,
difference(X_9,difference(X_9,X_9)) = X_9,
inference(subst,[],[set_difference_1:[bind(X,$fot(X_9)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_63,plain,
difference(X_9,difference(X_9,difference(X_9,X_9))) = difference(X_9,difference(X_9,difference(X_9,X_9))),
introduced(tautology,[refl,[$fot(difference(X_9,difference(X_9,difference(X_9,X_9))))]]) ).
cnf(refute_0_64,plain,
( difference(X_9,difference(X_9,X_9)) != X_9
| difference(X_9,difference(X_9,difference(X_9,X_9))) != difference(X_9,difference(X_9,difference(X_9,X_9)))
| difference(X_9,difference(X_9,difference(X_9,X_9))) = difference(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(difference(X_9,difference(X_9,difference(X_9,X_9))),difference(X_9,difference(X_9,difference(X_9,X_9)))) ),[1,1],$fot(X_9)]]) ).
cnf(refute_0_65,plain,
( difference(X_9,difference(X_9,X_9)) != X_9
| difference(X_9,difference(X_9,difference(X_9,X_9))) = difference(X_9,X_9) ),
inference(resolve,[$cnf( $equal(difference(X_9,difference(X_9,difference(X_9,X_9))),difference(X_9,difference(X_9,difference(X_9,X_9)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
difference(X_9,difference(X_9,difference(X_9,X_9))) = difference(X_9,X_9),
inference(resolve,[$cnf( $equal(difference(X_9,difference(X_9,X_9)),X_9) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
difference(difference(X_6,X_7),difference(Y,X_6)) = difference(difference(X_6,difference(Y,X_6)),difference(X_7,difference(Y,X_6))),
inference(subst,[],[set_difference_3:[bind(X,$fot(X_6)),bind(Y,$fot(X_7)),bind(Z,$fot(difference(Y,X_6)))]]) ).
cnf(refute_0_68,plain,
difference(X_6,difference(Y,X_6)) = X_6,
inference(subst,[],[set_difference_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_69,plain,
( difference(X_6,difference(Y,X_6)) != X_6
| difference(difference(X_6,X_7),difference(Y,X_6)) != difference(difference(X_6,difference(Y,X_6)),difference(X_7,difference(Y,X_6)))
| difference(difference(X_6,X_7),difference(Y,X_6)) = difference(X_6,difference(X_7,difference(Y,X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_6,X_7),difference(Y,X_6)),difference(difference(X_6,difference(Y,X_6)),difference(X_7,difference(Y,X_6)))) ),[1,0],$fot(X_6)]]) ).
cnf(refute_0_70,plain,
( difference(difference(X_6,X_7),difference(Y,X_6)) != difference(difference(X_6,difference(Y,X_6)),difference(X_7,difference(Y,X_6)))
| difference(difference(X_6,X_7),difference(Y,X_6)) = difference(X_6,difference(X_7,difference(Y,X_6))) ),
inference(resolve,[$cnf( $equal(difference(X_6,difference(Y,X_6)),X_6) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
difference(difference(X_6,X_7),difference(Y,X_6)) = difference(X_6,difference(X_7,difference(Y,X_6))),
inference(resolve,[$cnf( $equal(difference(difference(X_6,X_7),difference(Y,X_6)),difference(difference(X_6,difference(Y,X_6)),difference(X_7,difference(Y,X_6)))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
difference(difference(X_9,X_9),difference(X_9,X_9)) = difference(X_9,difference(X_9,difference(X_9,X_9))),
inference(subst,[],[refute_0_71:[bind(Y,$fot(X_9)),bind(X_6,$fot(X_9)),bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_73,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_74,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_16,refute_0_73]) ).
cnf(refute_0_75,plain,
( difference(X_9,difference(X_9,difference(X_9,X_9))) != difference(X_9,X_9)
| difference(difference(X_9,X_9),difference(X_9,X_9)) != difference(X_9,difference(X_9,difference(X_9,X_9)))
| difference(difference(X_9,X_9),difference(X_9,X_9)) = difference(X_9,X_9) ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(difference(X_9,X_9),difference(X_9,X_9)))),bind(Y0,$fot(difference(X_9,difference(X_9,difference(X_9,X_9))))),bind(Z0,$fot(difference(X_9,X_9)))]]) ).
cnf(refute_0_76,plain,
( difference(X_9,difference(X_9,difference(X_9,X_9))) != difference(X_9,X_9)
| difference(difference(X_9,X_9),difference(X_9,X_9)) = difference(X_9,X_9) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(X_9,X_9)),difference(X_9,difference(X_9,difference(X_9,X_9)))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
difference(difference(X_9,X_9),difference(X_9,X_9)) = difference(X_9,X_9),
inference(resolve,[$cnf( $equal(difference(X_9,difference(X_9,difference(X_9,X_9))),difference(X_9,X_9)) )],[refute_0_66,refute_0_76]) ).
cnf(refute_0_78,plain,
( difference(difference(X_1,X_1),difference(X_9,X_9)) != difference(difference(X_9,X_9),difference(X_9,X_9))
| difference(difference(X_9,X_9),difference(X_9,X_9)) != difference(X_9,X_9)
| difference(difference(X_1,X_1),difference(X_9,X_9)) = difference(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(difference(X_1,X_1),difference(X_9,X_9)),difference(X_9,X_9)) ),[0],$fot(difference(difference(X_9,X_9),difference(X_9,X_9)))]]) ).
cnf(refute_0_79,plain,
( difference(difference(X_1,X_1),difference(X_9,X_9)) != difference(difference(X_9,X_9),difference(X_9,X_9))
| difference(difference(X_1,X_1),difference(X_9,X_9)) = difference(X_9,X_9) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(X_9,X_9)),difference(X_9,X_9)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
difference(difference(X_1,X_1),difference(X_9,X_9)) = difference(X_9,X_9),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_1),difference(X_9,X_9)),difference(difference(X_9,X_9),difference(X_9,X_9))) )],[refute_0_61,refute_0_79]) ).
cnf(refute_0_81,plain,
difference(difference(X_9,X_9),difference(X,X)) = difference(X,X),
inference(subst,[],[refute_0_80:[bind(X_1,$fot(X_9)),bind(X_9,$fot(X))]]) ).
cnf(refute_0_82,plain,
( difference(X,difference(X,difference(X_9,X_9))) != difference(difference(X_9,X_9),difference(X,X))
| difference(difference(X_9,X_9),difference(X,X)) != difference(X,X)
| difference(X,difference(X,difference(X_9,X_9))) = difference(X,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(X,difference(X,difference(X_9,X_9))),difference(X,X)) ),[0],$fot(difference(difference(X_9,X_9),difference(X,X)))]]) ).
cnf(refute_0_83,plain,
( difference(X,difference(X,difference(X_9,X_9))) != difference(difference(X_9,X_9),difference(X,X))
| difference(X,difference(X,difference(X_9,X_9))) = difference(X,X) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(X,X)),difference(X,X)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
difference(X,difference(X,difference(X_9,X_9))) = difference(X,X),
inference(resolve,[$cnf( $equal(difference(X,difference(X,difference(X_9,X_9))),difference(difference(X_9,X_9),difference(X,X))) )],[refute_0_60,refute_0_83]) ).
cnf(refute_0_85,plain,
difference(Y,difference(Y,difference(X_9,X_9))) = difference(Y,Y),
inference(subst,[],[refute_0_84:[bind(X,$fot(Y))]]) ).
cnf(refute_0_86,plain,
difference(difference(X,difference(X_9,X_9)),Z) = difference(difference(X,Z),difference(difference(X_9,X_9),Z)),
inference(subst,[],[set_difference_3:[bind(Y,$fot(difference(X_9,X_9)))]]) ).
cnf(refute_0_87,plain,
difference(difference(X_9,X_9),Z) = difference(Z,Z),
inference(subst,[],[refute_0_50:[bind(X_1,$fot(X_9)),bind(X_5,$fot(Z))]]) ).
cnf(refute_0_88,plain,
( difference(difference(X,difference(X_9,X_9)),Z) != difference(difference(X,Z),difference(difference(X_9,X_9),Z))
| difference(difference(X_9,X_9),Z) != difference(Z,Z)
| difference(difference(X,difference(X_9,X_9)),Z) = difference(difference(X,Z),difference(Z,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X,difference(X_9,X_9)),Z),difference(difference(X,Z),difference(difference(X_9,X_9),Z))) ),[1,1],$fot(difference(Z,Z))]]) ).
cnf(refute_0_89,plain,
( difference(difference(X,difference(X_9,X_9)),Z) != difference(difference(X,Z),difference(difference(X_9,X_9),Z))
| difference(difference(X,difference(X_9,X_9)),Z) = difference(difference(X,Z),difference(Z,Z)) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),Z),difference(Z,Z)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
difference(difference(X,difference(X_9,X_9)),Z) = difference(difference(X,Z),difference(Z,Z)),
inference(resolve,[$cnf( $equal(difference(difference(X,difference(X_9,X_9)),Z),difference(difference(X,Z),difference(difference(X_9,X_9),Z))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
difference(difference(X,Z),Z) = difference(X,Z),
inference(subst,[],[refute_0_32:[bind(Y,$fot(Z)),bind(X_1,$fot(X))]]) ).
cnf(refute_0_92,plain,
difference(difference(X,Z),difference(Z,Z)) = difference(difference(X,Z),Z),
inference(subst,[],[refute_0_38:[bind(Y,$fot(Z))]]) ).
cnf(refute_0_93,plain,
( difference(difference(X,Z),Z) != difference(X,Z)
| difference(difference(X,Z),difference(Z,Z)) != difference(difference(X,Z),Z)
| difference(difference(X,Z),difference(Z,Z)) = difference(X,Z) ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(difference(X,Z),difference(Z,Z)))),bind(Y0,$fot(difference(difference(X,Z),Z))),bind(Z0,$fot(difference(X,Z)))]]) ).
cnf(refute_0_94,plain,
( difference(difference(X,Z),Z) != difference(X,Z)
| difference(difference(X,Z),difference(Z,Z)) = difference(X,Z) ),
inference(resolve,[$cnf( $equal(difference(difference(X,Z),difference(Z,Z)),difference(difference(X,Z),Z)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
difference(difference(X,Z),difference(Z,Z)) = difference(X,Z),
inference(resolve,[$cnf( $equal(difference(difference(X,Z),Z),difference(X,Z)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( difference(difference(X,Z),difference(Z,Z)) != difference(X,Z)
| difference(difference(X,difference(X_9,X_9)),Z) != difference(difference(X,Z),difference(Z,Z))
| difference(difference(X,difference(X_9,X_9)),Z) = difference(X,Z) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X,difference(X_9,X_9)),Z),difference(difference(X,Z),difference(Z,Z))) ),[1],$fot(difference(X,Z))]]) ).
cnf(refute_0_97,plain,
( difference(difference(X,difference(X_9,X_9)),Z) != difference(difference(X,Z),difference(Z,Z))
| difference(difference(X,difference(X_9,X_9)),Z) = difference(X,Z) ),
inference(resolve,[$cnf( $equal(difference(difference(X,Z),difference(Z,Z)),difference(X,Z)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
difference(difference(X,difference(X_9,X_9)),Z) = difference(X,Z),
inference(resolve,[$cnf( $equal(difference(difference(X,difference(X_9,X_9)),Z),difference(difference(X,Z),difference(Z,Z))) )],[refute_0_90,refute_0_97]) ).
cnf(refute_0_99,plain,
difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) = difference(Y,difference(Y,difference(X_9,X_9))),
inference(subst,[],[refute_0_98:[bind(X,$fot(Y)),bind(Z,$fot(difference(Y,difference(X_9,X_9))))]]) ).
cnf(refute_0_100,plain,
( difference(Y,difference(Y,difference(X_9,X_9))) != difference(Y,Y)
| difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) != difference(Y,difference(Y,difference(X_9,X_9)))
| difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) = difference(Y,Y) ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))))),bind(Y0,$fot(difference(Y,difference(Y,difference(X_9,X_9))))),bind(Z0,$fot(difference(Y,Y)))]]) ).
cnf(refute_0_101,plain,
( difference(Y,difference(Y,difference(X_9,X_9))) != difference(Y,Y)
| difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) = difference(Y,Y) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))),difference(Y,difference(Y,difference(X_9,X_9)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) = difference(Y,Y),
inference(resolve,[$cnf( $equal(difference(Y,difference(Y,difference(X_9,X_9))),difference(Y,Y)) )],[refute_0_85,refute_0_101]) ).
cnf(refute_0_103,plain,
( difference(X_9,X_9) != difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))
| difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))) != difference(Y,Y)
| difference(X_9,X_9) = difference(Y,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(X_9,X_9),difference(Y,Y)) ),[0],$fot(difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))))]]) ).
cnf(refute_0_104,plain,
( difference(X_9,X_9) != difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))
| difference(X_9,X_9) = difference(Y,Y) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9))),difference(Y,Y)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
difference(X_9,X_9) = difference(Y,Y),
inference(resolve,[$cnf( $equal(difference(X_9,X_9),difference(difference(Y,difference(X_9,X_9)),difference(Y,difference(X_9,X_9)))) )],[refute_0_55,refute_0_104]) ).
cnf(refute_0_106,plain,
difference(X,X) = difference(X_11,X_11),
inference(subst,[],[refute_0_105:[bind(Y,$fot(X_11)),bind(X_9,$fot(X))]]) ).
cnf(refute_0_107,plain,
( difference(X,X) != difference(X_11,X_11)
| difference(X,difference(X,X)) != difference(X,difference(X,X))
| difference(X,difference(X,X)) = difference(X,difference(X_11,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(X,difference(X,X)),difference(X,difference(X,X))) ),[1,1],$fot(difference(X_11,X_11))]]) ).
cnf(refute_0_108,plain,
( difference(X,difference(X,X)) != difference(X,difference(X,X))
| difference(X,difference(X,X)) = difference(X,difference(X_11,X_11)) ),
inference(resolve,[$cnf( $equal(difference(X,X),difference(X_11,X_11)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
difference(X,difference(X,X)) = difference(X,difference(X_11,X_11)),
inference(resolve,[$cnf( $equal(difference(X,difference(X,X)),difference(X,difference(X,X))) )],[refute_0_26,refute_0_108]) ).
cnf(refute_0_110,plain,
difference(X,difference(X,X)) = X,
inference(subst,[],[set_difference_1:[bind(Y,$fot(X))]]) ).
cnf(refute_0_111,plain,
( difference(X,difference(X,X)) != X
| difference(X,difference(X,X)) != difference(X,difference(X_11,X_11))
| X = difference(X,difference(X_11,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(X,difference(X,X)),difference(X,difference(X_11,X_11))) ),[0],$fot(X)]]) ).
cnf(refute_0_112,plain,
( difference(X,difference(X,X)) != difference(X,difference(X_11,X_11))
| X = difference(X,difference(X_11,X_11)) ),
inference(resolve,[$cnf( $equal(difference(X,difference(X,X)),X) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
X = difference(X,difference(X_11,X_11)),
inference(resolve,[$cnf( $equal(difference(X,difference(X,X)),difference(X,difference(X_11,X_11))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( X != difference(X,difference(X_11,X_11))
| difference(X,difference(X_11,X_11)) = X ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(X)),bind(Y0,$fot(difference(X,difference(X_11,X_11))))]]) ).
cnf(refute_0_115,plain,
difference(X,difference(X_11,X_11)) = X,
inference(resolve,[$cnf( $equal(X,difference(X,difference(X_11,X_11))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
difference(X_16,difference(Y,Y)) = X_16,
inference(subst,[],[refute_0_115:[bind(X,$fot(X_16)),bind(X_11,$fot(Y))]]) ).
cnf(refute_0_117,plain,
difference(difference(X_9,X_9),difference(Y,X_9)) = difference(difference(Y,X_9),difference(Y,X_9)),
inference(subst,[],[refute_0_50:[bind(X_1,$fot(X_9)),bind(X_5,$fot(difference(Y,X_9)))]]) ).
cnf(refute_0_118,plain,
difference(difference(X_9,Y),X_9) = difference(difference(X_9,X_9),difference(Y,X_9)),
inference(subst,[],[set_difference_3:[bind(X,$fot(X_9)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_119,plain,
( difference(difference(X_9,Y),X_9) != difference(difference(X_9,X_9),difference(Y,X_9))
| difference(difference(X_9,X_9),difference(Y,X_9)) = difference(difference(X_9,Y),X_9) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(difference(difference(X_9,Y),X_9))),bind(Y0,$fot(difference(difference(X_9,X_9),difference(Y,X_9))))]]) ).
cnf(refute_0_120,plain,
difference(difference(X_9,X_9),difference(Y,X_9)) = difference(difference(X_9,Y),X_9),
inference(resolve,[$cnf( $equal(difference(difference(X_9,Y),X_9),difference(difference(X_9,X_9),difference(Y,X_9))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( difference(difference(X_9,X_9),difference(Y,X_9)) != difference(difference(Y,X_9),difference(Y,X_9))
| difference(difference(X_9,X_9),difference(Y,X_9)) != difference(difference(X_9,Y),X_9)
| difference(difference(X_9,Y),X_9) = difference(difference(Y,X_9),difference(Y,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_9,X_9),difference(Y,X_9)),difference(difference(Y,X_9),difference(Y,X_9))) ),[0],$fot(difference(difference(X_9,Y),X_9))]]) ).
cnf(refute_0_122,plain,
( difference(difference(X_9,X_9),difference(Y,X_9)) != difference(difference(Y,X_9),difference(Y,X_9))
| difference(difference(X_9,Y),X_9) = difference(difference(Y,X_9),difference(Y,X_9)) ),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(Y,X_9)),difference(difference(X_9,Y),X_9)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
difference(difference(X_9,Y),X_9) = difference(difference(Y,X_9),difference(Y,X_9)),
inference(resolve,[$cnf( $equal(difference(difference(X_9,X_9),difference(Y,X_9)),difference(difference(Y,X_9),difference(Y,X_9))) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
( difference(X_9,X_9) != difference(Y,Y)
| difference(Y,Y) = difference(X_9,X_9) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(difference(X_9,X_9))),bind(Y0,$fot(difference(Y,Y)))]]) ).
cnf(refute_0_125,plain,
difference(Y,Y) = difference(X_9,X_9),
inference(resolve,[$cnf( $equal(difference(X_9,X_9),difference(Y,Y)) )],[refute_0_105,refute_0_124]) ).
cnf(refute_0_126,plain,
difference(difference(Y,X_9),difference(Y,X_9)) = difference(X_9,X_9),
inference(subst,[],[refute_0_125:[bind(Y,$fot(difference(Y,X_9)))]]) ).
cnf(refute_0_127,plain,
( difference(difference(Y,X_9),difference(Y,X_9)) != difference(X_9,X_9)
| difference(difference(X_9,Y),X_9) != difference(difference(Y,X_9),difference(Y,X_9))
| difference(difference(X_9,Y),X_9) = difference(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(X_9,Y),X_9),difference(difference(Y,X_9),difference(Y,X_9))) ),[1],$fot(difference(X_9,X_9))]]) ).
cnf(refute_0_128,plain,
( difference(difference(X_9,Y),X_9) != difference(difference(Y,X_9),difference(Y,X_9))
| difference(difference(X_9,Y),X_9) = difference(X_9,X_9) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_9),difference(Y,X_9)),difference(X_9,X_9)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
difference(difference(X_9,Y),X_9) = difference(X_9,X_9),
inference(resolve,[$cnf( $equal(difference(difference(X_9,Y),X_9),difference(difference(Y,X_9),difference(Y,X_9))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
difference(difference(Y,X_16),Y) = difference(Y,Y),
inference(subst,[],[refute_0_129:[bind(Y,$fot(X_16)),bind(X_9,$fot(Y))]]) ).
cnf(refute_0_131,plain,
difference(X_16,difference(difference(Y,X_16),Y)) = difference(X_16,difference(difference(Y,X_16),Y)),
introduced(tautology,[refl,[$fot(difference(X_16,difference(difference(Y,X_16),Y)))]]) ).
cnf(refute_0_132,plain,
( difference(X_16,difference(difference(Y,X_16),Y)) != difference(X_16,difference(difference(Y,X_16),Y))
| difference(difference(Y,X_16),Y) != difference(Y,Y)
| difference(X_16,difference(difference(Y,X_16),Y)) = difference(X_16,difference(Y,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(X_16,difference(difference(Y,X_16),Y)),difference(X_16,difference(difference(Y,X_16),Y))) ),[1,1],$fot(difference(Y,Y))]]) ).
cnf(refute_0_133,plain,
( difference(difference(Y,X_16),Y) != difference(Y,Y)
| difference(X_16,difference(difference(Y,X_16),Y)) = difference(X_16,difference(Y,Y)) ),
inference(resolve,[$cnf( $equal(difference(X_16,difference(difference(Y,X_16),Y)),difference(X_16,difference(difference(Y,X_16),Y))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
difference(X_16,difference(difference(Y,X_16),Y)) = difference(X_16,difference(Y,Y)),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_16),Y),difference(Y,Y)) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( difference(X_16,difference(Y,Y)) != X_16
| difference(X_16,difference(difference(Y,X_16),Y)) != difference(X_16,difference(Y,Y))
| difference(X_16,difference(difference(Y,X_16),Y)) = X_16 ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(X_16,difference(difference(Y,X_16),Y)))),bind(Y0,$fot(difference(X_16,difference(Y,Y)))),bind(Z0,$fot(X_16))]]) ).
cnf(refute_0_136,plain,
( difference(X_16,difference(Y,Y)) != X_16
| difference(X_16,difference(difference(Y,X_16),Y)) = X_16 ),
inference(resolve,[$cnf( $equal(difference(X_16,difference(difference(Y,X_16),Y)),difference(X_16,difference(Y,Y))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
difference(X_16,difference(difference(Y,X_16),Y)) = X_16,
inference(resolve,[$cnf( $equal(difference(X_16,difference(Y,Y)),X_16) )],[refute_0_116,refute_0_136]) ).
cnf(refute_0_138,plain,
difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) = difference(Y,difference(X_16,difference(difference(Y,X_16),Y))),
introduced(tautology,[refl,[$fot(difference(Y,difference(X_16,difference(difference(Y,X_16),Y))))]]) ).
cnf(refute_0_139,plain,
( difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) != difference(Y,difference(X_16,difference(difference(Y,X_16),Y)))
| difference(X_16,difference(difference(Y,X_16),Y)) != X_16
| difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) = difference(Y,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(difference(Y,difference(X_16,difference(difference(Y,X_16),Y))),difference(Y,difference(X_16,difference(difference(Y,X_16),Y)))) ),[1,1],$fot(X_16)]]) ).
cnf(refute_0_140,plain,
( difference(X_16,difference(difference(Y,X_16),Y)) != X_16
| difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) = difference(Y,X_16) ),
inference(resolve,[$cnf( $equal(difference(Y,difference(X_16,difference(difference(Y,X_16),Y))),difference(Y,difference(X_16,difference(difference(Y,X_16),Y)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) = difference(Y,X_16),
inference(resolve,[$cnf( $equal(difference(X_16,difference(difference(Y,X_16),Y)),X_16) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,difference(X_16,difference(difference(Y,X_16),Y))),
inference(subst,[],[refute_0_71:[bind(Y,$fot(difference(Y,X_16))),bind(X_6,$fot(Y)),bind(X_7,$fot(X_16))]]) ).
cnf(refute_0_143,plain,
( difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) != difference(Y,X_16)
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) != difference(Y,difference(X_16,difference(difference(Y,X_16),Y)))
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,X_16) ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)))),bind(Y0,$fot(difference(Y,difference(X_16,difference(difference(Y,X_16),Y))))),bind(Z0,$fot(difference(Y,X_16)))]]) ).
cnf(refute_0_144,plain,
( difference(Y,difference(X_16,difference(difference(Y,X_16),Y))) != difference(Y,X_16)
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,X_16) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)),difference(Y,difference(X_16,difference(difference(Y,X_16),Y)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) = difference(Y,X_16),
inference(resolve,[$cnf( $equal(difference(Y,difference(X_16,difference(difference(Y,X_16),Y))),difference(Y,X_16)) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) != difference(Y,X_16)
| difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(Y,X_16) = difference(Y,difference(X_16,difference(X_16,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)),difference(Y,difference(X_16,difference(X_16,Y)))) ),[0],$fot(difference(Y,X_16))]]) ).
cnf(refute_0_147,plain,
( difference(difference(Y,X_16),difference(difference(Y,X_16),Y)) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(Y,X_16) = difference(Y,difference(X_16,difference(X_16,Y))) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)),difference(Y,X_16)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
difference(Y,X_16) = difference(Y,difference(X_16,difference(X_16,Y))),
inference(resolve,[$cnf( $equal(difference(difference(Y,X_16),difference(difference(Y,X_16),Y)),difference(Y,difference(X_16,difference(X_16,Y)))) )],[refute_0_25,refute_0_147]) ).
cnf(refute_0_149,plain,
( difference(Y,X_16) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(Y,difference(X_16,difference(X_16,Y))) = difference(Y,X_16) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(difference(Y,X_16))),bind(Y0,$fot(difference(Y,difference(X_16,difference(X_16,Y)))))]]) ).
cnf(refute_0_150,plain,
difference(Y,difference(X_16,difference(X_16,Y))) = difference(Y,X_16),
inference(resolve,[$cnf( $equal(difference(Y,X_16),difference(Y,difference(X_16,difference(X_16,Y)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( difference(Y,difference(X_16,difference(X_16,Y))) != difference(Y,X_16)
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) != difference(Y,difference(X_16,difference(X_16,Y)))
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,X_16) ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))))),bind(Y0,$fot(difference(Y,difference(X_16,difference(X_16,Y))))),bind(Z0,$fot(difference(Y,X_16)))]]) ).
cnf(refute_0_152,plain,
( difference(Y,difference(X_16,difference(X_16,Y))) != difference(Y,X_16)
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,X_16) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))),difference(Y,difference(X_16,difference(X_16,Y)))) )],[refute_0_5,refute_0_151]) ).
cnf(refute_0_153,plain,
difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) = difference(Y,X_16),
inference(resolve,[$cnf( $equal(difference(Y,difference(X_16,difference(X_16,Y))),difference(Y,X_16)) )],[refute_0_150,refute_0_152]) ).
cnf(refute_0_154,plain,
( difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) != difference(Y,X_16)
| difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) != difference(Y,difference(Y,difference(Y,X_16)))
| difference(Y,X_16) = difference(Y,difference(Y,difference(Y,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))),difference(Y,difference(Y,difference(Y,X_16)))) ),[0],$fot(difference(Y,X_16))]]) ).
cnf(refute_0_155,plain,
( difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))) != difference(Y,difference(Y,difference(Y,X_16)))
| difference(Y,X_16) = difference(Y,difference(Y,difference(Y,X_16))) ),
inference(resolve,[$cnf( $equal(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))),difference(Y,X_16)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
difference(Y,X_16) = difference(Y,difference(Y,difference(Y,X_16))),
inference(resolve,[$cnf( $equal(difference(difference(Y,difference(X_16,difference(X_16,Y))),difference(difference(X_16,difference(X_16,Y)),difference(difference(X_16,difference(X_16,Y)),Y))),difference(Y,difference(Y,difference(Y,X_16)))) )],[refute_0_21,refute_0_155]) ).
cnf(refute_0_157,plain,
difference(difference(difference(X_1,X_32),X_7),X_32) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),X_32))),
inference(subst,[],[refute_0_156:[bind(Y,$fot(difference(difference(X_1,X_32),X_7))),bind(X_16,$fot(X_32))]]) ).
cnf(refute_0_158,plain,
difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(difference(X_1,X_8),X_8),difference(X_7,X_8)),
inference(subst,[],[set_difference_3:[bind(X,$fot(difference(X_1,X_8))),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_159,plain,
difference(difference(X_1,X_8),X_8) = difference(X_1,X_8),
inference(subst,[],[refute_0_32:[bind(Y,$fot(X_8))]]) ).
cnf(refute_0_160,plain,
( difference(difference(X_1,X_8),X_8) != difference(X_1,X_8)
| difference(difference(difference(X_1,X_8),X_7),X_8) != difference(difference(difference(X_1,X_8),X_8),difference(X_7,X_8))
| difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(X_1,X_8),difference(X_7,X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(X_1,X_8),X_7),X_8),difference(difference(difference(X_1,X_8),X_8),difference(X_7,X_8))) ),[1,0],$fot(difference(X_1,X_8))]]) ).
cnf(refute_0_161,plain,
( difference(difference(difference(X_1,X_8),X_7),X_8) != difference(difference(difference(X_1,X_8),X_8),difference(X_7,X_8))
| difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(X_1,X_8),difference(X_7,X_8)) ),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_8),X_8),difference(X_1,X_8)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(X_1,X_8),difference(X_7,X_8)),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_8),X_7),X_8),difference(difference(difference(X_1,X_8),X_8),difference(X_7,X_8))) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
difference(difference(X_1,X_8),difference(X_7,X_8)) = difference(difference(X_1,X_7),X_8),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_1)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_164,plain,
( difference(difference(X_1,X_8),difference(X_7,X_8)) != difference(difference(X_1,X_7),X_8)
| difference(difference(difference(X_1,X_8),X_7),X_8) != difference(difference(X_1,X_8),difference(X_7,X_8))
| difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(X_1,X_7),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(X_1,X_8),X_7),X_8),difference(difference(X_1,X_8),difference(X_7,X_8))) ),[1],$fot(difference(difference(X_1,X_7),X_8))]]) ).
cnf(refute_0_165,plain,
( difference(difference(difference(X_1,X_8),X_7),X_8) != difference(difference(X_1,X_8),difference(X_7,X_8))
| difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(X_1,X_7),X_8) ),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_8),difference(X_7,X_8)),difference(difference(X_1,X_7),X_8)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
difference(difference(difference(X_1,X_8),X_7),X_8) = difference(difference(X_1,X_7),X_8),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_8),X_7),X_8),difference(difference(X_1,X_8),difference(X_7,X_8))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
difference(difference(difference(X_1,X_32),X_7),X_32) = difference(difference(X_1,X_7),X_32),
inference(subst,[],[refute_0_166:[bind(X_8,$fot(X_32))]]) ).
cnf(refute_0_168,plain,
( difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(X_1,X_7),X_32)
| difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),X_32)))
| difference(difference(difference(X_1,X_32),X_7),X_32) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),X_32),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),X_32)))) ),[1,1,1],$fot(difference(difference(X_1,X_7),X_32))]]) ).
cnf(refute_0_169,plain,
( difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),X_32)))
| difference(difference(difference(X_1,X_32),X_7),X_32) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),X_32),difference(difference(X_1,X_7),X_32)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
difference(difference(difference(X_1,X_32),X_7),X_32) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),X_32),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),X_32)))) )],[refute_0_157,refute_0_169]) ).
cnf(refute_0_171,plain,
( difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(X_1,X_7),X_32)
| difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))
| difference(difference(X_1,X_7),X_32) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),X_32),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))) ),[0],$fot(difference(difference(X_1,X_7),X_32))]]) ).
cnf(refute_0_172,plain,
( difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))
| difference(difference(X_1,X_7),X_32) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),X_32),difference(difference(X_1,X_7),X_32)) )],[refute_0_167,refute_0_171]) ).
cnf(refute_0_173,plain,
difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)) = difference(difference(X_1,X_32),X_7),
inference(subst,[],[refute_0_115:[bind(X,$fot(difference(difference(X_1,X_32),X_7))),bind(X_11,$fot(X_7))]]) ).
cnf(refute_0_174,plain,
difference(difference(difference(difference(X_26,Y),X_27),Y),difference(difference(X_26,Y),X_27)) = difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)),
inference(subst,[],[refute_0_129:[bind(X_9,$fot(difference(difference(X_26,Y),X_27)))]]) ).
cnf(refute_0_175,plain,
difference(difference(difference(X_26,Y),X_27),Y) = difference(difference(X_26,X_27),Y),
inference(subst,[],[refute_0_166:[bind(X_1,$fot(X_26)),bind(X_7,$fot(X_27)),bind(X_8,$fot(Y))]]) ).
cnf(refute_0_176,plain,
( difference(difference(difference(X_26,Y),X_27),Y) != difference(difference(X_26,X_27),Y)
| difference(difference(difference(difference(X_26,Y),X_27),Y),difference(difference(X_26,Y),X_27)) != difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))
| difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) = difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(difference(X_26,Y),X_27),Y),difference(difference(X_26,Y),X_27)),difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))) ),[0,0],$fot(difference(difference(X_26,X_27),Y))]]) ).
cnf(refute_0_177,plain,
( difference(difference(difference(difference(X_26,Y),X_27),Y),difference(difference(X_26,Y),X_27)) != difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))
| difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) = difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_26,Y),X_27),Y),difference(difference(X_26,X_27),Y)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) = difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)),
inference(resolve,[$cnf( $equal(difference(difference(difference(difference(X_26,Y),X_27),Y),difference(difference(X_26,Y),X_27)),difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
difference(X_12,X_12) = difference(Y,Y),
inference(subst,[],[refute_0_105:[bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_180,plain,
difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)) = difference(Y,Y),
inference(subst,[],[refute_0_179:[bind(X_12,$fot(difference(difference(X_26,Y),X_27)))]]) ).
cnf(refute_0_181,plain,
( difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)) != difference(Y,Y)
| difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) != difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))
| difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) = difference(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)),difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))) ),[1],$fot(difference(Y,Y))]]) ).
cnf(refute_0_182,plain,
( difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) != difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))
| difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) = difference(Y,Y) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27)),difference(Y,Y)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)) = difference(Y,Y),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_26,X_27),Y),difference(difference(X_26,Y),X_27)),difference(difference(difference(X_26,Y),X_27),difference(difference(X_26,Y),X_27))) )],[refute_0_178,refute_0_182]) ).
cnf(refute_0_184,plain,
difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)) = difference(X_7,X_7),
inference(subst,[],[refute_0_183:[bind(Y,$fot(X_7)),bind(X_26,$fot(X_1)),bind(X_27,$fot(X_32))]]) ).
cnf(refute_0_185,plain,
difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))),
introduced(tautology,[refl,[$fot(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))))]]) ).
cnf(refute_0_186,plain,
( difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)) != difference(X_7,X_7)
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))) ),[1,1],$fot(difference(X_7,X_7))]]) ).
cnf(refute_0_187,plain,
( difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)) != difference(X_7,X_7)
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)),difference(X_7,X_7)) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
( difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)) != difference(difference(X_1,X_32),X_7)
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) != difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7))
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(X_1,X_32),X_7) ),
inference(subst,[],[refute_0_74:[bind(X0,$fot(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))))),bind(Y0,$fot(difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)))),bind(Z0,$fot(difference(difference(X_1,X_32),X_7)))]]) ).
cnf(refute_0_190,plain,
( difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)) != difference(difference(X_1,X_32),X_7)
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(X_1,X_32),X_7) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))),difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) = difference(difference(X_1,X_32),X_7),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),difference(X_7,X_7)),difference(difference(X_1,X_32),X_7)) )],[refute_0_173,refute_0_190]) ).
cnf(refute_0_192,plain,
( difference(difference(X_1,X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))
| difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))) != difference(difference(X_1,X_32),X_7)
| difference(difference(X_1,X_7),X_32) = difference(difference(X_1,X_32),X_7) ),
introduced(tautology,[equality,[$cnf( ~ $equal(difference(difference(X_1,X_7),X_32),difference(difference(X_1,X_32),X_7)) ),[0],$fot(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))))]]) ).
cnf(refute_0_193,plain,
( difference(difference(X_1,X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))
| difference(difference(X_1,X_7),X_32) = difference(difference(X_1,X_32),X_7) ),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32))),difference(difference(X_1,X_32),X_7)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
( difference(difference(difference(X_1,X_32),X_7),X_32) != difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))
| difference(difference(X_1,X_7),X_32) = difference(difference(X_1,X_32),X_7) ),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_7),X_32),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))) )],[refute_0_172,refute_0_193]) ).
cnf(refute_0_195,plain,
difference(difference(X_1,X_7),X_32) = difference(difference(X_1,X_32),X_7),
inference(resolve,[$cnf( $equal(difference(difference(difference(X_1,X_32),X_7),X_32),difference(difference(difference(X_1,X_32),X_7),difference(difference(difference(X_1,X_32),X_7),difference(difference(X_1,X_7),X_32)))) )],[refute_0_170,refute_0_194]) ).
cnf(refute_0_196,plain,
( difference(difference(X_1,X_7),X_32) != difference(difference(X_1,X_32),X_7)
| difference(difference(X_1,X_32),X_7) = difference(difference(X_1,X_7),X_32) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(difference(difference(X_1,X_7),X_32))),bind(Y0,$fot(difference(difference(X_1,X_32),X_7)))]]) ).
cnf(refute_0_197,plain,
difference(difference(X_1,X_32),X_7) = difference(difference(X_1,X_7),X_32),
inference(resolve,[$cnf( $equal(difference(difference(X_1,X_7),X_32),difference(difference(X_1,X_32),X_7)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
difference(difference(a,c),b) = difference(difference(a,b),c),
inference(subst,[],[refute_0_197:[bind(X_1,$fot(a)),bind(X_32,$fot(c)),bind(X_7,$fot(b))]]) ).
cnf(refute_0_199,plain,
( difference(difference(a,b),c) != difference(difference(a,b),c)
| difference(difference(a,c),b) != difference(difference(a,b),c)
| difference(difference(a,c),b) = difference(difference(a,b),c) ),
introduced(tautology,[equality,[$cnf( $equal(difference(difference(a,c),b),difference(difference(a,b),c)) ),[1],$fot(difference(difference(a,b),c))]]) ).
cnf(refute_0_200,plain,
( difference(difference(a,b),c) != difference(difference(a,b),c)
| difference(difference(a,c),b) = difference(difference(a,b),c) ),
inference(resolve,[$cnf( $equal(difference(difference(a,c),b),difference(difference(a,b),c)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
difference(difference(a,b),c) != difference(difference(a,b),c),
inference(resolve,[$cnf( $equal(difference(difference(a,c),b),difference(difference(a,b),c)) )],[refute_0_200,prove_set_difference_3_simplified]) ).
cnf(refute_0_202,plain,
difference(difference(a,b),c) = difference(difference(a,b),c),
introduced(tautology,[refl,[$fot(difference(difference(a,b),c))]]) ).
cnf(refute_0_203,plain,
$false,
inference(resolve,[$cnf( $equal(difference(difference(a,b),c),difference(difference(a,b),c)) )],[refute_0_202,refute_0_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 06:21:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.53
% 0.18/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.56
%------------------------------------------------------------------------------