TSTP Solution File: COL065-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL065-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 : Fri Jul 15 00:36:25 EDT 2022
% Result : Unsatisfiable 38.51s 38.67s
% Output : CNFRefutation 38.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of clauses : 55 ( 35 unt; 0 nHn; 44 RR)
% Number of literals : 85 ( 84 equ; 51 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(t_definition,axiom,
apply(apply(t,X),Y) = apply(Y,X) ).
cnf(prove_g_combinator,negated_conjecture,
apply(apply(apply(apply(X,f(X)),g(X)),h(X)),i(X)) != apply(apply(f(X),i(X)),apply(g(X),h(X))) ).
cnf(refute_0_0,plain,
apply(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))) != apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4)))),
inference(subst,[],[prove_g_combinator:[bind(X,$fot(apply(apply(b,X_3),X_4)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))) = apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),
inference(subst,[],[b_definition:[bind(X,$fot(X_3)),bind(Y,$fot(X_4)),bind(Z,$fot(f(apply(apply(b,X_3),X_4))))]]) ).
cnf(refute_0_2,plain,
( apply(apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))) != apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))))
| apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))) != apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4))))
| apply(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))) = apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))),apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))))) ),[0,0,0,0],$fot(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))) != apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))))
| apply(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))) = apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))) != apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),i(apply(apply(b,X_3),X_4))),apply(apply(f(apply(apply(b,X_3),X_4)),i(apply(apply(b,X_3),X_4))),apply(g(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
apply(apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))),i(apply(apply(b,b),X_9))) != apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))),
inference(subst,[],[refute_0_4:[bind(X_3,$fot(b)),bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))) = apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_9,f(apply(apply(b,b),X_9))))),bind(Y,$fot(g(apply(apply(b,b),X_9)))),bind(Z,$fot(h(apply(apply(b,b),X_9))))]]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))),i(apply(apply(b,b),X_9))) != apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9))))
| apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))) != apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9))))
| apply(apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))),i(apply(apply(b,b),X_9))) = apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))),i(apply(apply(b,b),X_9))),apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9))))) ),[0,0],$fot(apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))),i(apply(apply(b,b),X_9))) != apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9))))
| apply(apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))),i(apply(apply(b,b),X_9))) = apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))),apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(X_9,f(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))),i(apply(apply(b,b),X_9))) != apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(X_9,f(apply(apply(b,b),X_9)))),g(apply(apply(b,b),X_9))),h(apply(apply(b,b),X_9))),i(apply(apply(b,b),X_9))),apply(apply(f(apply(apply(b,b),X_9)),i(apply(apply(b,b),X_9))),apply(g(apply(apply(b,b),X_9)),h(apply(apply(b,b),X_9))))) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),
inference(subst,[],[refute_0_9:[bind(X_9,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_11,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))) = apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,b),apply(apply(b,X),Y)))))]]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y)))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))) != apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y)))))
| apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))) = apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y)))))) ),[0,0,0],$fot(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y)))))
| apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))) = apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))),apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y)))))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y))))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(apply(f(apply(apply(b,b),apply(apply(b,X),Y))),i(apply(apply(b,b),apply(apply(b,X),Y)))),apply(g(apply(apply(b,b),apply(apply(b,X),Y))),h(apply(apply(b,b),apply(apply(b,X),Y)))))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
apply(apply(apply(X_86,apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_86)),bind(Y,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_16,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) = apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(X_86,apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) != apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))
| apply(apply(apply(X_86,apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(X_86,apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))) ),[0,0,0,1],$fot(apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(X_86,apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))
| apply(apply(apply(X_86,apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(X_86,apply(X,apply(Y,f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(X_86,apply(apply(apply(b,X),Y),f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(apply(f(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),i(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))),apply(g(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y)))),h(apply(apply(b,b),apply(apply(b,X_86),apply(apply(b,X),Y))))))) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
apply(apply(apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_1292)),bind(Y,$fot(X_1293)),bind(X_86,$fot(apply(t,X)))]]) ).
cnf(refute_0_21,plain,
apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))) = apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X),
inference(subst,[],[t_definition:[bind(Y,$fot(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))
| apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))) != apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X)
| apply(apply(apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))) ),[0,0,0],$fot(apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X))]]) ).
cnf(refute_0_23,plain,
( apply(apply(apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))
| apply(apply(apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))),apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),X),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(t,X),apply(X_1292,apply(X_1293,f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),i(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293)))),h(apply(apply(b,b),apply(apply(b,apply(t,X)),apply(apply(b,X_1292),X_1293))))))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
apply(apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_3301)),bind(X_1292,$fot(b)),bind(X_1293,$fot(X_3303))]]) ).
cnf(refute_0_26,plain,
apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))) = apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))),bind(Y,$fot(X_3301)),bind(Z,$fot(apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))))]]) ).
cnf(refute_0_27,plain,
( apply(apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))
| apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))) != apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))))
| apply(apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))) ),[0,0],$fot(apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))))]]) ).
cnf(refute_0_28,plain,
( apply(apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))
| apply(apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(apply(apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(X_3301,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(X_3303,f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),X_3301),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3301)),apply(apply(b,b),X_3303))))))) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
apply(apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),
inference(subst,[],[refute_0_29:[bind(X_3301,$fot(X_3304)),bind(X_3303,$fot(t))]]) ).
cnf(refute_0_31,plain,
apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))) = apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),
inference(subst,[],[t_definition:[bind(X,$fot(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),bind(Y,$fot(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))
| apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))) != apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))
| apply(apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))) ),[0,0],$fot(apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))
| apply(apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))),apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(t,f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(X_3304,apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,X_3304)),apply(apply(b,b),t))))))) )],[refute_0_33,refute_0_30]) ).
cnf(refute_0_35,plain,
apply(apply(apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),
inference(subst,[],[refute_0_34:[bind(X_3304,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_36,plain,
apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))) = apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))),
inference(subst,[],[b_definition:[bind(Z,$fot(apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))))]]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))
| apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))) != apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))))
| apply(apply(apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))) ),[0,0,0],$fot(apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))))]]) ).
cnf(refute_0_38,plain,
( apply(apply(apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))
| apply(apply(apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(apply(X,apply(Y,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X),Y),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),
inference(subst,[],[refute_0_39:[bind(X,$fot(b)),bind(Y,$fot(X_17747))]]) ).
cnf(refute_0_41,plain,
apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))) = apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))))),bind(Y,$fot(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),bind(Z,$fot(i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_42,plain,
( apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))
| apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))) != apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))
| apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))) ),[1],$fot(apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))))]]) ).
cnf(refute_0_43,plain,
( apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))
| apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
apply(apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_17747,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))),f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),X_17747))),apply(apply(b,b),t))))))) )],[refute_0_43,refute_0_40]) ).
cnf(refute_0_45,plain,
apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),
inference(subst,[],[refute_0_44:[bind(X_17747,$fot(t))]]) ).
cnf(refute_0_46,plain,
apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),
inference(subst,[],[t_definition:[bind(X,$fot(apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))),bind(Y,$fot(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))))]]) ).
cnf(refute_0_47,plain,
( apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))
| apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))
| apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))) ),[1],$fot(apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))))]]) ).
cnf(refute_0_48,plain,
( apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))
| apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) != apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),
inference(resolve,[$cnf( $equal(apply(apply(t,apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))) )],[refute_0_48,refute_0_45]) ).
cnf(refute_0_50,plain,
apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))) = apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),
introduced(tautology,[refl,[$fot(apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))))]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))),apply(apply(f(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),i(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(g(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,b),apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))) )],[refute_0_50,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL065-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 04:14:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 38.51/38.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.51/38.67
% 38.51/38.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.57/38.72
%------------------------------------------------------------------------------