TSTP Solution File: COL063-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL063-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 00:36:21 EDT 2022
% Result : Unsatisfiable 3.29s 3.45s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 45 ( 29 unt; 0 nHn; 36 RR)
% Number of literals : 69 ( 68 equ; 41 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 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 : 86 ( 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_f_combinator,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(h(X),g(X)),f(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)),g(apply(apply(b,X_3),X_4))),f(apply(apply(b,X_3),X_4))),
inference(subst,[],[prove_f_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)),g(apply(apply(b,X_3),X_4))),f(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)),g(apply(apply(b,X_3),X_4))),f(apply(apply(b,X_3),X_4))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4))),f(apply(apply(b,X_3),X_4)))) ),[0,0,0],$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)),g(apply(apply(b,X_3),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)),g(apply(apply(b,X_3),X_4))),f(apply(apply(b,X_3),X_4))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))) != apply(apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4))),f(apply(apply(b,X_3),X_4))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4))),f(apply(apply(b,X_3),X_4)))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
apply(apply(apply(X_9,apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y)))),
inference(subst,[],[refute_0_4:[bind(X_3,$fot(X_9)),bind(X_4,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_6,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y)))) = apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,X_9),apply(apply(b,X),Y)))))]]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(X_9,apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y)))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y)))) != apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y)))))
| apply(apply(apply(X_9,apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))) = apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(X_9,apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))),apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y))))) ),[0,0,0,1],$fot(apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(X_9,apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y)))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y))))
| apply(apply(apply(X_9,apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))) = apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y)))),apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y)))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(X_9,apply(X,apply(Y,f(apply(apply(b,X_9),apply(apply(b,X),Y)))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))) != apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(X_9,apply(apply(apply(b,X),Y),f(apply(apply(b,X_9),apply(apply(b,X),Y))))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),h(apply(apply(b,X_9),apply(apply(b,X),Y)))),apply(apply(h(apply(apply(b,X_9),apply(apply(b,X),Y))),g(apply(apply(b,X_9),apply(apply(b,X),Y)))),f(apply(apply(b,X_9),apply(apply(b,X),Y))))) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
apply(apply(apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) != apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(X_9,$fot(apply(t,X)))]]) ).
cnf(refute_0_11,plain,
apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))) = apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X),
inference(subst,[],[t_definition:[bind(Y,$fot(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))))]]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) != apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))
| apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))) != apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X)
| apply(apply(apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) = apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))) ),[0,0,0],$fot(apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) != apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))
| apply(apply(apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) = apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))),apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))),X),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))) != apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(t,X),apply(X_68,apply(X_69,f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69)))),f(apply(apply(b,apply(t,X)),apply(apply(b,X_68),X_69))))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
apply(apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) != apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_83)),bind(X_68,$fot(b)),bind(X_69,$fot(X_85))]]) ).
cnf(refute_0_16,plain,
apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) = apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))))),bind(Y,$fot(X_83)),bind(Z,$fot(g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) != apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))
| apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) != apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))))
| apply(apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) = apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))) ),[0,0],$fot(apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) != apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))
| apply(apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) = apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(X_83,g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))) != apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(X_85,f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))),X_83),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),apply(apply(h(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))),g(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85)))),f(apply(apply(b,apply(t,X_83)),apply(apply(b,b),X_85))))) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) != apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),
inference(subst,[],[refute_0_19:[bind(X_83,$fot(X_181)),bind(X_85,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_21,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) = apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) != apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) != apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))))
| apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) = apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))) ),[0,0,0],$fot(apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))))]]) ).
cnf(refute_0_23,plain,
( apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) != apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))
| apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) = apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))) != apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(X_181,g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(apply(h(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,X_181)),apply(apply(b,b),apply(apply(b,X),Y)))))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) != apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),
inference(subst,[],[refute_0_24:[bind(X,$fot(b)),bind(Y,$fot(X_1555)),bind(X_181,$fot(X_1556))]]) ).
cnf(refute_0_26,plain,
apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) = apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))),bind(Y,$fot(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))),bind(Z,$fot(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))]]) ).
cnf(refute_0_27,plain,
( apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))) != apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))
| apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) != apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))
| apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) = apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))) ),[1],$fot(apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))]]) ).
cnf(refute_0_28,plain,
( apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))) != apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))
| apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) = apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))) != apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_1555,f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),apply(X_1556,g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))),h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),apply(apply(h(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))),g(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555))))),f(apply(apply(b,apply(t,X_1556)),apply(apply(b,b),apply(apply(b,b),X_1555)))))) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) != apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(subst,[],[refute_0_29:[bind(X_1555,$fot(t)),bind(X_1556,$fot(X_2546))]]) ).
cnf(refute_0_31,plain,
apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) = apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(subst,[],[t_definition:[bind(X,$fot(f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))),bind(Y,$fot(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))
| apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) != apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))
| apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) = apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))),apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) ),[1],$fot(apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))
| apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) = apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))),apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(resolve,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(X_2546,g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))),apply(apply(h(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X_2546)),apply(apply(b,b),apply(apply(b,b),t)))))) )],[refute_0_33,refute_0_30]) ).
cnf(refute_0_35,plain,
apply(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(subst,[],[refute_0_34:[bind(X_2546,$fot(t))]]) ).
cnf(refute_0_36,plain,
apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) = apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(subst,[],[t_definition:[bind(X,$fot(g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))),bind(Y,$fot(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_37,plain,
( apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))
| apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))
| apply(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))) ),[0,0],$fot(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_38,plain,
( apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))
| apply(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) != apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))) = apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),
introduced(tautology,[refl,[$fot(apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,t)),apply(apply(b,b),apply(apply(b,b),t)))))) )],[refute_0_40,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL063-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 06:13:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.29/3.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/3.45
% 3.29/3.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.29/3.48
%------------------------------------------------------------------------------