%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL064-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 00:36:23 EDT 2022
% Result : Unsatisfiable 20.42s 20.59s
% Output : CNFRefutation 20.45s
% 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 111 ( 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_v_combinator,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(h(X),f(X)),g(X)) ).
cnf(refute_0_0,plain,
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))) != apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),
inference(subst,[],[prove_v_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(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))) != apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(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(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))) = apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4)))) ),[0,0,0],$fot(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(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))) != apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4)))
| 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))) = apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))) != apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(apply(h(apply(apply(b,X_3),X_4)),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4)))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
apply(apply(apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))) != apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),
inference(subst,[],[refute_0_4:[bind(X_3,$fot(apply(apply(b,X),Y))),bind(X_4,$fot(X_10))]]) ).
cnf(refute_0_6,plain,
apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))) = apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10))))),
inference(subst,[],[b_definition:[bind(Z,$fot(apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))))]]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10))))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))) != apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10)))
| apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))) != apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))))
| apply(apply(apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))) = apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))),apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10)))) ),[0,0,0],$fot(apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10))))))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10))))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))) != apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10)))
| apply(apply(apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))) = apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))),apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(X,apply(Y,apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10))))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))) != apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X),Y),apply(X_10,f(apply(apply(b,apply(apply(b,X),Y)),X_10)))),g(apply(apply(b,apply(apply(b,X),Y)),X_10))),h(apply(apply(b,apply(apply(b,X),Y)),X_10))),apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),X_10)),f(apply(apply(b,apply(apply(b,X),Y)),X_10))),g(apply(apply(b,apply(apply(b,X),Y)),X_10)))) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
apply(apply(apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),
inference(subst,[],[refute_0_9:[bind(X,$fot(apply(t,X))),bind(Y,$fot(X_73)),bind(X_10,$fot(X_74))]]) ).
cnf(refute_0_11,plain,
apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))) = apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X),
inference(subst,[],[t_definition:[bind(Y,$fot(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))))]]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))
| apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))) != apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X)
| apply(apply(apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))) ),[0,0,0],$fot(apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))
| apply(apply(apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))),apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))),X),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(t,X),apply(X_73,apply(X_74,f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)),f(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74))),g(apply(apply(b,apply(apply(b,apply(t,X)),X_73)),X_74)))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
apply(apply(apply(apply(X_310,apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_309)),bind(X_73,$fot(X_310)),bind(X_74,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_16,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) = apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(apply(X_310,apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) != apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))))
| apply(apply(apply(apply(X_310,apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(X_310,apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))) ),[0,0,0,0,1],$fot(apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(apply(X_310,apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))
| apply(apply(apply(apply(X_310,apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(apply(X_310,apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(X_310,apply(apply(apply(b,X),Y),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))),X_309),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))),f(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y)))),g(apply(apply(b,apply(apply(b,apply(t,X_309)),X_310)),apply(apply(b,X),Y))))) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
apply(apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_2213)),bind(Y,$fot(X_2214)),bind(X_309,$fot(X_2215)),bind(X_310,$fot(b))]]) ).
cnf(refute_0_21,plain,
apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) = apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))))),bind(Y,$fot(X_2215)),bind(Z,$fot(g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))
| apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) != apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))
| apply(apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))) ),[0,0],$fot(apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))))]]) ).
cnf(refute_0_23,plain,
( apply(apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))
| apply(apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),apply(X_2215,g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(X_2213,apply(X_2214,f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))))),X_2215),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))),f(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214)))),g(apply(apply(b,apply(apply(b,apply(t,X_2215)),b)),apply(apply(b,X_2213),X_2214))))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),
inference(subst,[],[refute_0_24:[bind(X_2213,$fot(b)),bind(X_2214,$fot(X_3386)),bind(X_2215,$fot(X_3387))]]) ).
cnf(refute_0_26,plain,
apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) = apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))),bind(Y,$fot(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))),bind(Z,$fot(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))]]) ).
cnf(refute_0_27,plain,
( apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))
| apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) != apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))
| apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))) ),[1],$fot(apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))]]) ).
cnf(refute_0_28,plain,
( apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))
| apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_3386,f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),apply(X_3387,g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))),h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))),f(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386)))),g(apply(apply(b,apply(apply(b,apply(t,X_3387)),b)),apply(apply(b,b),X_3386))))) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_29:[bind(X_3386,$fot(t)),bind(X_3387,$fot(X_3398))]]) ).
cnf(refute_0_31,plain,
apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) = apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),
inference(subst,[],[t_definition:[bind(X,$fot(f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))),bind(Y,$fot(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))
| apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) != apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))
| apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))),apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) ),[1],$fot(apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))
| apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))),apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),apply(apply(X_3398,g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,X_3398)),b)),apply(apply(b,b),t))))) )],[refute_0_33,refute_0_30]) ).
cnf(refute_0_35,plain,
apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_34:[bind(X_3398,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_36,plain,
apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) = apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))),
inference(subst,[],[b_definition:[bind(Z,$fot(g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))
| apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) != apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))))
| apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))) ),[0,0,0],$fot(apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_38,plain,
( apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))
| apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),apply(apply(b,b),t))))) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_39:[bind(X,$fot(b)),bind(Y,$fot(X_13824))]]) ).
cnf(refute_0_41,plain,
apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) = apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))))),bind(Y,$fot(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),bind(Z,$fot(f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_42,plain,
( apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))
| apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) != apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))))
| apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))))) ),[1],$fot(apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_43,plain,
( apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))
| apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
apply(apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_13824,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X_13824))),b)),apply(apply(b,b),t))))) )],[refute_0_43,refute_0_40]) ).
cnf(refute_0_45,plain,
apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_44:[bind(X_13824,$fot(t))]]) ).
cnf(refute_0_46,plain,
apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),
inference(subst,[],[t_definition:[bind(X,$fot(g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))),bind(Y,$fot(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_47,plain,
( apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))
| apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))
| apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) ),[1],$fot(apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_48,plain,
( apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))
| apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) )],[refute_0_48,refute_0_45]) ).
cnf(refute_0_50,plain,
apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))) = apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),
introduced(tautology,[refl,[$fot(apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t)))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),apply(apply(b,b),t))))) )],[refute_0_50,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COL064-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 16:25:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 20.42/20.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.42/20.59
% 20.42/20.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.45/20.64
%------------------------------------------------------------------------------