TSTP Solution File: ALG012-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 17:30:35 EDT 2022
% Result : Unsatisfiable 57.59s 57.79s
% Output : CNFRefutation 57.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 39
% Syntax : Number of clauses : 193 ( 57 unt; 42 nHn; 186 RR)
% Number of literals : 386 ( 158 equ; 157 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f_is_associative,axiom,
f(X,f(Y,Z)) = f(f(X,Y),Z) ).
cnf(partitions_union,axiom,
( c(X)
| d1(X)
| d2(X) ) ).
cnf(partitions_exclusive_c_d1,hypothesis,
( ~ c(X)
| ~ d1(X) ) ).
cnf(partitions_exclusive_c_d2,hypothesis,
( ~ c(X)
| ~ d2(X) ) ).
cnf(partition_d2_not_empty,hypothesis,
d2(a3) ).
cnf(conjecture_1,negated_conjecture,
( d2(f(X,Y))
| d1(f(X,Y))
| ~ c(X)
| ~ c(Y) ) ).
cnf(conjecture_2,negated_conjecture,
( c(f(X,Y))
| ~ d1(X)
| ~ d1(Y) ) ).
cnf(conjecture_3,negated_conjecture,
( c(f(X,Y))
| ~ d2(X)
| ~ d2(Y) ) ).
cnf(refute_0_0,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))
| ~ d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
inference(subst,[],[partitions_exclusive_c_d1:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))))]]) ).
cnf(refute_0_1,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))
| ~ d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
inference(subst,[],[partitions_exclusive_c_d2:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))))]]) ).
cnf(refute_0_2,plain,
( ~ d2(a3)
| c(f(a3,a3)) ),
inference(subst,[],[conjecture_3:[bind(X,$fot(a3)),bind(Y,$fot(a3))]]) ).
cnf(refute_0_3,plain,
c(f(a3,a3)),
inference(resolve,[$cnf( d2(a3) )],[partition_d2_not_empty,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ c(X_24)
| ~ c(f(a3,a3))
| d1(f(f(a3,a3),X_24))
| d2(f(f(a3,a3),X_24)) ),
inference(subst,[],[conjecture_1:[bind(X,$fot(f(a3,a3))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_5,plain,
( ~ c(X_24)
| d1(f(f(a3,a3),X_24))
| d2(f(f(a3,a3),X_24)) ),
inference(resolve,[$cnf( c(f(a3,a3)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( f(X,f(Y,Z)) != f(f(X,Y),Z)
| f(f(X,Y),Z) = f(X,f(Y,Z)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(f(X,f(Y,Z)))),bind(Y0,$fot(f(f(X,Y),Z)))]]) ).
cnf(refute_0_10,plain,
f(f(X,Y),Z) = f(X,f(Y,Z)),
inference(resolve,[$cnf( $equal(f(X,f(Y,Z)),f(f(X,Y),Z)) )],[f_is_associative,refute_0_9]) ).
cnf(refute_0_11,plain,
f(f(a3,a3),X_24) = f(a3,f(a3,X_24)),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(a3)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_12,plain,
( f(f(a3,a3),X_24) != f(a3,f(a3,X_24))
| ~ d1(f(f(a3,a3),X_24))
| d1(f(a3,f(a3,X_24))) ),
introduced(tautology,[equality,[$cnf( d1(f(f(a3,a3),X_24)) ),[0],$fot(f(a3,f(a3,X_24)))]]) ).
cnf(refute_0_13,plain,
( ~ d1(f(f(a3,a3),X_24))
| d1(f(a3,f(a3,X_24))) ),
inference(resolve,[$cnf( $equal(f(f(a3,a3),X_24),f(a3,f(a3,X_24))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ c(X_24)
| d1(f(a3,f(a3,X_24)))
| d2(f(f(a3,a3),X_24)) ),
inference(resolve,[$cnf( d1(f(f(a3,a3),X_24)) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
( f(f(a3,a3),X_24) != f(a3,f(a3,X_24))
| ~ d2(f(f(a3,a3),X_24))
| d2(f(a3,f(a3,X_24))) ),
introduced(tautology,[equality,[$cnf( d2(f(f(a3,a3),X_24)) ),[0],$fot(f(a3,f(a3,X_24)))]]) ).
cnf(refute_0_16,plain,
( ~ d2(f(f(a3,a3),X_24))
| d2(f(a3,f(a3,X_24))) ),
inference(resolve,[$cnf( $equal(f(f(a3,a3),X_24),f(a3,f(a3,X_24))) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c(X_24)
| d1(f(a3,f(a3,X_24)))
| d2(f(a3,f(a3,X_24))) ),
inference(resolve,[$cnf( d2(f(f(a3,a3),X_24)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
inference(subst,[],[refute_0_17:[bind(X_24,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))]]) ).
cnf(refute_0_19,plain,
( ~ d1(f(a3,f(a3,f(a3,a3))))
| c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[conjecture_2:[bind(X,$fot(f(a3,f(a3,f(a3,a3))))),bind(Y,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_20,plain,
( ~ c(f(a3,a3))
| d1(f(f(a3,a3),f(a3,a3)))
| d2(f(f(a3,a3),f(a3,a3))) ),
inference(subst,[],[conjecture_1:[bind(X,$fot(f(a3,a3))),bind(Y,$fot(f(a3,a3)))]]) ).
cnf(refute_0_21,plain,
( d1(f(f(a3,a3),f(a3,a3)))
| d2(f(f(a3,a3),f(a3,a3))) ),
inference(resolve,[$cnf( c(f(a3,a3)) )],[refute_0_3,refute_0_20]) ).
cnf(refute_0_22,plain,
f(f(a3,a3),f(a3,a3)) = f(a3,f(a3,f(a3,a3))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(a3)),bind(Z,$fot(f(a3,a3)))]]) ).
cnf(refute_0_23,plain,
( f(f(a3,a3),f(a3,a3)) != f(a3,f(a3,f(a3,a3)))
| ~ d1(f(f(a3,a3),f(a3,a3)))
| d1(f(a3,f(a3,f(a3,a3)))) ),
introduced(tautology,[equality,[$cnf( d1(f(f(a3,a3),f(a3,a3))) ),[0],$fot(f(a3,f(a3,f(a3,a3))))]]) ).
cnf(refute_0_24,plain,
( ~ d1(f(f(a3,a3),f(a3,a3)))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( $equal(f(f(a3,a3),f(a3,a3)),f(a3,f(a3,f(a3,a3)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( d1(f(a3,f(a3,f(a3,a3))))
| d2(f(f(a3,a3),f(a3,a3))) ),
inference(resolve,[$cnf( d1(f(f(a3,a3),f(a3,a3))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( f(f(a3,a3),f(a3,a3)) != f(a3,f(a3,f(a3,a3)))
| ~ d2(f(f(a3,a3),f(a3,a3)))
| d2(f(a3,f(a3,f(a3,a3)))) ),
introduced(tautology,[equality,[$cnf( d2(f(f(a3,a3),f(a3,a3))) ),[0],$fot(f(a3,f(a3,f(a3,a3))))]]) ).
cnf(refute_0_27,plain,
( ~ d2(f(f(a3,a3),f(a3,a3)))
| d2(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( $equal(f(f(a3,a3),f(a3,a3)),f(a3,f(a3,f(a3,a3)))) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( d1(f(a3,f(a3,f(a3,a3))))
| d2(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d2(f(f(a3,a3),f(a3,a3))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ d2(X_16)
| ~ d2(a3)
| c(f(a3,X_16)) ),
inference(subst,[],[conjecture_3:[bind(X,$fot(a3)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_30,plain,
( ~ d2(X_16)
| c(f(a3,X_16)) ),
inference(resolve,[$cnf( d2(a3) )],[partition_d2_not_empty,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ d2(f(a3,f(a3,f(a3,a3))))
| c(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[refute_0_30:[bind(X_16,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_32,plain,
( c(f(a3,f(a3,f(a3,f(a3,a3)))))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,a3)))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,a3)))))
| ~ d1(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[partitions_exclusive_c_d1:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_34,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,a3)))))
| ~ d2(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[partitions_exclusive_c_d2:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_35,plain,
( ~ c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,f(a3,a3)))))
| d2(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[refute_0_17:[bind(X_24,$fot(f(a3,f(a3,a3))))]]) ).
cnf(refute_0_36,plain,
( ~ d2(f(a3,f(a3,f(a3,a3))))
| c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[conjecture_3:[bind(X,$fot(f(a3,f(a3,f(a3,a3))))),bind(Y,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_37,plain,
( c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,a3)))) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
f(f(a3,a3),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(a3)),bind(Z,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_39,plain,
f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) = f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_40,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) != f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3)))))
| f(f(a3,a3),f(a3,f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3)))))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_41,plain,
( f(f(a3,a3),f(a3,f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3)))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(resolve,[$cnf( $equal(f(f(a3,a3),f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) = f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,a3))),bind(Z,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_44,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_45,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_8,refute_0_44]) ).
cnf(refute_0_46,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) != f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))))),bind(Y0,$fot(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))]]) ).
cnf(refute_0_47,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))),f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3)))))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,a3))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) = f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_50,plain,
( f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) != f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_51,plain,
( f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))) = f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,f(a3,a3)))),bind(Z,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_54,plain,
( f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))) != f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))))),bind(Y0,$fot(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))]]) ).
cnf(refute_0_55,plain,
( f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))),f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3)))))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,a3))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
( f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| ~ c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
introduced(tautology,[equality,[$cnf( c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) ),[0],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))]]) ).
cnf(refute_0_58,plain,
( ~ c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) )],[refute_0_37,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| ~ d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(subst,[],[partitions_exclusive_c_d1:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))]]) ).
cnf(refute_0_61,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| ~ d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(subst,[],[partitions_exclusive_c_d2:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))]]) ).
cnf(refute_0_62,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(subst,[],[refute_0_17:[bind(X_24,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_63,plain,
( ~ d1(f(a3,f(a3,a3)))
| c(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),
inference(subst,[],[conjecture_2:[bind(X,$fot(f(a3,f(a3,a3)))),bind(Y,$fot(f(a3,f(a3,a3))))]]) ).
cnf(refute_0_64,plain,
( c(X_17)
| d1(X_17)
| d2(X_17) ),
inference(subst,[],[partitions_union:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_65,plain,
( ~ d2(X_17)
| c(f(a3,X_17)) ),
inference(subst,[],[refute_0_30:[bind(X_16,$fot(X_17))]]) ).
cnf(refute_0_66,plain,
( c(X_17)
| c(f(a3,X_17))
| d1(X_17) ),
inference(resolve,[$cnf( d2(X_17) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( c(f(a3,f(a3,a3)))
| c(f(a3,f(a3,f(a3,a3))))
| d1(f(a3,f(a3,a3))) ),
inference(subst,[],[refute_0_66:[bind(X_17,$fot(f(a3,f(a3,a3))))]]) ).
cnf(refute_0_68,plain,
( ~ c(f(a3,f(a3,f(a3,a3))))
| ~ d1(f(a3,f(a3,f(a3,a3)))) ),
inference(subst,[],[partitions_exclusive_c_d1:[bind(X,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_69,plain,
( ~ c(f(a3,f(a3,f(a3,a3))))
| ~ d2(f(a3,f(a3,f(a3,a3)))) ),
inference(subst,[],[partitions_exclusive_c_d2:[bind(X,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_70,plain,
( ~ c(f(a3,f(a3,f(a3,a3))))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,a3)))) )],[refute_0_28,refute_0_69]) ).
cnf(refute_0_71,plain,
( c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,a3)))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ c(f(a3,f(a3,f(a3,a3))))
| c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,a3))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,a3)))) )],[refute_0_71,refute_0_68]) ).
cnf(refute_0_73,plain,
( c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,a3))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,a3)))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
( c(f(a3,f(a3,a3)))
| c(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,a3))) )],[refute_0_73,refute_0_63]) ).
cnf(refute_0_75,plain,
f(f(a3,a3),f(a3,f(a3,a3))) = f(a3,f(a3,f(a3,f(a3,a3)))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(a3)),bind(Z,$fot(f(a3,f(a3,a3))))]]) ).
cnf(refute_0_76,plain,
f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) = f(a3,f(f(a3,a3),f(a3,f(a3,a3)))),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,a3),f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_77,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) != f(a3,f(f(a3,a3),f(a3,f(a3,a3))))
| f(f(a3,a3),f(a3,f(a3,a3))) != f(a3,f(a3,f(a3,f(a3,a3))))
| f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,a3)))),f(a3,f(f(a3,a3),f(a3,f(a3,a3))))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_78,plain,
( f(f(a3,a3),f(a3,f(a3,a3))) != f(a3,f(a3,f(a3,f(a3,a3))))
| f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,a3)))),f(a3,f(f(a3,a3),f(a3,f(a3,a3))))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))),
inference(resolve,[$cnf( $equal(f(f(a3,a3),f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) = f(a3,f(f(a3,a3),f(a3,f(a3,a3)))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,a3))),bind(Z,$fot(f(a3,f(a3,a3))))]]) ).
cnf(refute_0_81,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) != f(a3,f(f(a3,a3),f(a3,f(a3,a3))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))),bind(Y0,$fot(f(a3,f(f(a3,a3),f(a3,f(a3,a3)))))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_82,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,a3)))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))),f(a3,f(f(a3,a3),f(a3,f(a3,a3))))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| ~ c(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
introduced(tautology,[equality,[$cnf( c(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),[0],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_85,plain,
( ~ c(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( c(f(a3,f(a3,a3)))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( c(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) )],[refute_0_74,refute_0_85]) ).
cnf(refute_0_87,plain,
( c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_86,refute_0_62]) ).
cnf(refute_0_88,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_87,refute_0_61]) ).
cnf(refute_0_89,plain,
( c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,a3))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_59,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_89,refute_0_60]) ).
cnf(refute_0_91,plain,
( c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_59,refute_0_90]) ).
cnf(refute_0_92,plain,
( c(f(a3,f(a3,a3)))
| c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,a3)))) )],[refute_0_91,refute_0_19]) ).
cnf(refute_0_93,plain,
( c(f(a3,f(a3,a3)))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) )],[refute_0_92,refute_0_58]) ).
cnf(refute_0_94,plain,
( c(f(a3,f(a3,a3)))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_93,refute_0_88]) ).
cnf(refute_0_95,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| c(f(a3,f(a3,a3))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_94,refute_0_60]) ).
cnf(refute_0_96,plain,
c(f(a3,f(a3,a3))),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_93,refute_0_95]) ).
cnf(refute_0_97,plain,
( d1(f(a3,f(a3,f(a3,f(a3,a3)))))
| d2(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,a3))) )],[refute_0_96,refute_0_35]) ).
cnf(refute_0_98,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,a3)))))
| d1(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_97,refute_0_34]) ).
cnf(refute_0_99,plain,
( d1(f(a3,f(a3,f(a3,a3))))
| d1(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_32,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,a3)))))
| d1(f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_99,refute_0_33]) ).
cnf(refute_0_101,plain,
d1(f(a3,f(a3,f(a3,a3)))),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_32,refute_0_100]) ).
cnf(refute_0_102,plain,
c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,a3)))) )],[refute_0_101,refute_0_19]) ).
cnf(refute_0_103,plain,
c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))),
inference(resolve,[$cnf( c(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,a3))))) )],[refute_0_102,refute_0_58]) ).
cnf(refute_0_104,plain,
( d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_103,refute_0_18]) ).
cnf(refute_0_105,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) )],[refute_0_104,refute_0_1]) ).
cnf(refute_0_106,plain,
( ~ d1(f(a3,f(a3,f(a3,f(a3,a3)))))
| c(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(subst,[],[conjecture_2:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,a3)))))),bind(Y,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_107,plain,
( ~ d2(X_15)
| ~ d2(a3)
| c(f(X_15,a3)) ),
inference(subst,[],[conjecture_3:[bind(X,$fot(X_15)),bind(Y,$fot(a3))]]) ).
cnf(refute_0_108,plain,
( ~ d2(X_15)
| c(f(X_15,a3)) ),
inference(resolve,[$cnf( d2(a3) )],[partition_d2_not_empty,refute_0_107]) ).
cnf(refute_0_109,plain,
( ~ d2(f(a3,f(a3,f(a3,f(a3,a3)))))
| c(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3)) ),
inference(subst,[],[refute_0_108:[bind(X_15,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_110,plain,
( c(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3))
| d1(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_97,refute_0_109]) ).
cnf(refute_0_111,plain,
f(f(a3,a3),a3) = f(a3,f(a3,a3)),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(a3)),bind(Z,$fot(a3))]]) ).
cnf(refute_0_112,plain,
f(a3,f(f(a3,a3),a3)) = f(a3,f(f(a3,a3),a3)),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,a3),a3)))]]) ).
cnf(refute_0_113,plain,
( f(a3,f(f(a3,a3),a3)) != f(a3,f(f(a3,a3),a3))
| f(f(a3,a3),a3) != f(a3,f(a3,a3))
| f(a3,f(f(a3,a3),a3)) = f(a3,f(a3,f(a3,a3))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,a3),a3)),f(a3,f(f(a3,a3),a3))) ),[1,1],$fot(f(a3,f(a3,a3)))]]) ).
cnf(refute_0_114,plain,
( f(f(a3,a3),a3) != f(a3,f(a3,a3))
| f(a3,f(f(a3,a3),a3)) = f(a3,f(a3,f(a3,a3))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),a3)),f(a3,f(f(a3,a3),a3))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
f(a3,f(f(a3,a3),a3)) = f(a3,f(a3,f(a3,a3))),
inference(resolve,[$cnf( $equal(f(f(a3,a3),a3),f(a3,f(a3,a3))) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
f(f(a3,f(a3,a3)),a3) = f(a3,f(f(a3,a3),a3)),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,a3))),bind(Z,$fot(a3))]]) ).
cnf(refute_0_117,plain,
( f(a3,f(f(a3,a3),a3)) != f(a3,f(a3,f(a3,a3)))
| f(f(a3,f(a3,a3)),a3) != f(a3,f(f(a3,a3),a3))
| f(f(a3,f(a3,a3)),a3) = f(a3,f(a3,f(a3,a3))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,a3)),a3))),bind(Y0,$fot(f(a3,f(f(a3,a3),a3)))),bind(Z0,$fot(f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_118,plain,
( f(a3,f(f(a3,a3),a3)) != f(a3,f(a3,f(a3,a3)))
| f(f(a3,f(a3,a3)),a3) = f(a3,f(a3,f(a3,a3))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),a3),f(a3,f(f(a3,a3),a3))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
f(f(a3,f(a3,a3)),a3) = f(a3,f(a3,f(a3,a3))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),a3)),f(a3,f(a3,f(a3,a3)))) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
f(a3,f(f(a3,f(a3,a3)),a3)) = f(a3,f(f(a3,f(a3,a3)),a3)),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,f(a3,a3)),a3)))]]) ).
cnf(refute_0_121,plain,
( f(a3,f(f(a3,f(a3,a3)),a3)) != f(a3,f(f(a3,f(a3,a3)),a3))
| f(f(a3,f(a3,a3)),a3) != f(a3,f(a3,f(a3,a3)))
| f(a3,f(f(a3,f(a3,a3)),a3)) = f(a3,f(a3,f(a3,f(a3,a3)))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),a3)),f(a3,f(f(a3,f(a3,a3)),a3))) ),[1,1],$fot(f(a3,f(a3,f(a3,a3))))]]) ).
cnf(refute_0_122,plain,
( f(f(a3,f(a3,a3)),a3) != f(a3,f(a3,f(a3,a3)))
| f(a3,f(f(a3,f(a3,a3)),a3)) = f(a3,f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),a3)),f(a3,f(f(a3,f(a3,a3)),a3))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
f(a3,f(f(a3,f(a3,a3)),a3)) = f(a3,f(a3,f(a3,f(a3,a3)))),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),a3),f(a3,f(a3,f(a3,a3)))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
f(f(a3,f(a3,f(a3,a3))),a3) = f(a3,f(f(a3,f(a3,a3)),a3)),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,f(a3,a3)))),bind(Z,$fot(a3))]]) ).
cnf(refute_0_125,plain,
( f(a3,f(f(a3,f(a3,a3)),a3)) != f(a3,f(a3,f(a3,f(a3,a3))))
| f(f(a3,f(a3,f(a3,a3))),a3) != f(a3,f(f(a3,f(a3,a3)),a3))
| f(f(a3,f(a3,f(a3,a3))),a3) = f(a3,f(a3,f(a3,f(a3,a3)))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,f(a3,a3))),a3))),bind(Y0,$fot(f(a3,f(f(a3,f(a3,a3)),a3)))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_126,plain,
( f(a3,f(f(a3,f(a3,a3)),a3)) != f(a3,f(a3,f(a3,f(a3,a3))))
| f(f(a3,f(a3,f(a3,a3))),a3) = f(a3,f(a3,f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,a3))),a3),f(a3,f(f(a3,f(a3,a3)),a3))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
f(f(a3,f(a3,f(a3,a3))),a3) = f(a3,f(a3,f(a3,f(a3,a3)))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),a3)),f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) = f(a3,f(f(a3,f(a3,f(a3,a3))),a3)),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,f(a3,f(a3,a3))),a3)))]]) ).
cnf(refute_0_129,plain,
( f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) != f(a3,f(f(a3,f(a3,f(a3,a3))),a3))
| f(f(a3,f(a3,f(a3,a3))),a3) != f(a3,f(a3,f(a3,f(a3,a3))))
| f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,f(a3,f(a3,a3))),a3)),f(a3,f(f(a3,f(a3,f(a3,a3))),a3))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,a3)))))]]) ).
cnf(refute_0_130,plain,
( f(f(a3,f(a3,f(a3,a3))),a3) != f(a3,f(a3,f(a3,f(a3,a3))))
| f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,f(a3,a3))),a3)),f(a3,f(f(a3,f(a3,f(a3,a3))),a3))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,a3))),a3),f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
f(f(a3,f(a3,f(a3,f(a3,a3)))),a3) = f(a3,f(f(a3,f(a3,f(a3,a3))),a3)),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,f(a3,f(a3,a3))))),bind(Z,$fot(a3))]]) ).
cnf(refute_0_133,plain,
( f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,f(a3,f(a3,a3)))),a3) != f(a3,f(f(a3,f(a3,f(a3,a3))),a3))
| f(f(a3,f(a3,f(a3,f(a3,a3)))),a3) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3))),bind(Y0,$fot(f(a3,f(f(a3,f(a3,f(a3,a3))),a3)))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_134,plain,
( f(a3,f(f(a3,f(a3,f(a3,a3))),a3)) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| f(f(a3,f(a3,f(a3,f(a3,a3)))),a3) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3),f(a3,f(f(a3,f(a3,f(a3,a3))),a3))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
f(f(a3,f(a3,f(a3,f(a3,a3)))),a3) = f(a3,f(a3,f(a3,f(a3,f(a3,a3))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,f(a3,a3))),a3)),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( f(f(a3,f(a3,f(a3,f(a3,a3)))),a3) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| ~ c(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
introduced(tautology,[equality,[$cnf( c(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3)) ),[0],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_137,plain,
( ~ c(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( c(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| d1(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( c(f(f(a3,f(a3,f(a3,f(a3,a3)))),a3)) )],[refute_0_110,refute_0_137]) ).
cnf(refute_0_139,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| ~ d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(subst,[],[partitions_exclusive_c_d1:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_140,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| ~ d2(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(subst,[],[partitions_exclusive_c_d2:[bind(X,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_141,plain,
( ~ c(f(a3,f(a3,a3)))
| d1(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),
inference(subst,[],[conjecture_1:[bind(X,$fot(f(a3,f(a3,a3)))),bind(Y,$fot(f(a3,f(a3,a3))))]]) ).
cnf(refute_0_142,plain,
( d1(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,a3))) )],[refute_0_96,refute_0_141]) ).
cnf(refute_0_143,plain,
( f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| ~ d1(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
introduced(tautology,[equality,[$cnf( d1(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),[0],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_144,plain,
( ~ d1(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_83,refute_0_143]) ).
cnf(refute_0_145,plain,
( d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),
inference(resolve,[$cnf( d1(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) )],[refute_0_142,refute_0_144]) ).
cnf(refute_0_146,plain,
( f(f(a3,f(a3,a3)),f(a3,f(a3,a3))) != f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))
| ~ d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
introduced(tautology,[equality,[$cnf( d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) ),[0],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_147,plain,
( ~ d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_83,refute_0_146]) ).
cnf(refute_0_148,plain,
( d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| d2(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( d2(f(f(a3,f(a3,a3)),f(a3,f(a3,a3)))) )],[refute_0_145,refute_0_147]) ).
cnf(refute_0_149,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( d2(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_148,refute_0_140]) ).
cnf(refute_0_150,plain,
( d1(f(a3,f(a3,f(a3,f(a3,a3)))))
| d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) ),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_138,refute_0_149]) ).
cnf(refute_0_151,plain,
( ~ c(f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| d1(f(a3,f(a3,f(a3,f(a3,a3))))) ),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_150,refute_0_139]) ).
cnf(refute_0_152,plain,
d1(f(a3,f(a3,f(a3,f(a3,a3))))),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_138,refute_0_151]) ).
cnf(refute_0_153,plain,
c(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,f(a3,a3))))) )],[refute_0_152,refute_0_106]) ).
cnf(refute_0_154,plain,
f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(a3)),bind(Z,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_155,plain,
f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_156,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_157,plain,
( f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))
| f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))),
inference(resolve,[$cnf( $equal(f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,a3))),bind(Z,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_160,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))))),bind(Y0,$fot(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))]]) ).
cnf(refute_0_161,plain,
( f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,a3),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_164,plain,
( f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))]]) ).
cnf(refute_0_165,plain,
( f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))
| f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,f(a3,a3)))),bind(Z,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_168,plain,
( f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))))),bind(Y0,$fot(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))]]) ).
cnf(refute_0_169,plain,
( f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,a3)),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))),
introduced(tautology,[refl,[$fot(f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))))]]) ).
cnf(refute_0_172,plain,
( f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))) ),
introduced(tautology,[equality,[$cnf( $equal(f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))))) ),[1,1],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))]]) ).
cnf(refute_0_173,plain,
( f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))
| f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))) ),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(a3)),bind(Y,$fot(f(a3,f(a3,f(a3,a3))))),bind(Z,$fot(f(a3,f(a3,f(a3,f(a3,a3))))))]]) ).
cnf(refute_0_176,plain,
( f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))
| f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))))
| f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))))),bind(Y0,$fot(f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))))),bind(Z0,$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))))]]) ).
cnf(refute_0_177,plain,
( f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))
| f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3))))))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))) = f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))),
inference(resolve,[$cnf( $equal(f(a3,f(f(a3,f(a3,f(a3,a3))),f(a3,f(a3,f(a3,f(a3,a3)))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
( f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))) != f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))
| ~ c(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
introduced(tautology,[equality,[$cnf( c(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3)))))) ),[0],$fot(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3))))))))))]]) ).
cnf(refute_0_180,plain,
( ~ c(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))))
| c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) ),
inference(resolve,[$cnf( $equal(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3))))),f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))),
inference(resolve,[$cnf( c(f(f(a3,f(a3,f(a3,f(a3,a3)))),f(a3,f(a3,f(a3,f(a3,a3)))))) )],[refute_0_153,refute_0_180]) ).
cnf(refute_0_182,plain,
d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))),
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) )],[refute_0_181,refute_0_105]) ).
cnf(refute_0_183,plain,
~ c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))),
inference(resolve,[$cnf( d1(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) )],[refute_0_182,refute_0_0]) ).
cnf(refute_0_184,plain,
$false,
inference(resolve,[$cnf( c(f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,f(a3,a3)))))))))) )],[refute_0_181,refute_0_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 22:56:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 57.59/57.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.59/57.79
% 57.59/57.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.67/57.82
%------------------------------------------------------------------------------