%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL062-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 1.90s 2.06s
% Output : CNFRefutation 1.92s
% 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 : 11 ( 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 : 76 ( 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_c_combinator,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(f(X),h(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(f(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),
inference(subst,[],[prove_c_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(f(apply(apply(b,X_3),X_4)),h(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(f(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(apply(f(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4)))) ),[0,0,0],$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(f(apply(apply(b,X_3),X_4)),h(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(f(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))) != apply(apply(f(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(apply(f(apply(apply(b,X_3),X_4)),h(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4)))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
apply(apply(apply(X_10,apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),
inference(subst,[],[refute_0_4:[bind(X_3,$fot(X_10)),bind(X_4,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_6,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y)))) = apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,X_10),apply(apply(b,X),Y)))))]]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(X_10,apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y)))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y)))) != apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y)))))
| apply(apply(apply(X_10,apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))) = apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(X_10,apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y))))) ),[0,0,0,1],$fot(apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(X_10,apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y)))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y))))
| apply(apply(apply(X_10,apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))) = apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y)))),apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y)))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(X_10,apply(X,apply(Y,f(apply(apply(b,X_10),apply(apply(b,X),Y)))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))) != apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(X_10,apply(apply(apply(b,X),Y),f(apply(apply(b,X_10),apply(apply(b,X),Y))))),g(apply(apply(b,X_10),apply(apply(b,X),Y)))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),apply(apply(f(apply(apply(b,X_10),apply(apply(b,X),Y))),h(apply(apply(b,X_10),apply(apply(b,X),Y)))),g(apply(apply(b,X_10),apply(apply(b,X),Y))))) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
apply(apply(apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) != apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(X_10,$fot(apply(t,X)))]]) ).
cnf(refute_0_11,plain,
apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))) = apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X),
inference(subst,[],[t_definition:[bind(Y,$fot(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))))]]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) != apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))
| apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))) != apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X)
| apply(apply(apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) = apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))) ),[0,0,0],$fot(apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) != apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))
| apply(apply(apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) = apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))),apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))),X),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))) != apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(t,X),apply(X_71,apply(X_72,f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),apply(apply(f(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))),h(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72)))),g(apply(apply(b,apply(t,X)),apply(apply(b,X_71),X_72))))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
apply(apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) != apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_84)),bind(X_71,$fot(b)),bind(X_72,$fot(X_86))]]) ).
cnf(refute_0_16,plain,
apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) = apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))))),bind(Y,$fot(X_84)),bind(Z,$fot(g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) != apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))
| apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) != apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))))
| apply(apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) = apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))) ),[0,0],$fot(apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) != apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))
| apply(apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) = apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(X_84,g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))) != apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(X_86,f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))),X_84),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),apply(apply(f(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))),h(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86)))),g(apply(apply(b,apply(t,X_84)),apply(apply(b,b),X_86))))) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
apply(apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_19:[bind(X_84,$fot(X_186)),bind(X_86,$fot(t))]]) ).
cnf(refute_0_21,plain,
apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))) = apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),
inference(subst,[],[t_definition:[bind(X,$fot(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),bind(Y,$fot(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))
| apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))) != apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))
| apply(apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))) ),[0,0],$fot(apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_23,plain,
( apply(apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))
| apply(apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(t,f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(X_186,g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))),h(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X_186)),apply(apply(b,b),t))))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_24:[bind(X_186,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_26,plain,
apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) = apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),
inference(subst,[],[b_definition:[bind(Z,$fot(g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_27,plain,
( apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))
| apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) != apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))
| apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) ),[0,0,0],$fot(apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_28,plain,
( apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))
| apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X),Y),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,X),Y))),apply(apply(b,b),t))))) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_29:[bind(X,$fot(b)),bind(Y,$fot(X_1250))]]) ).
cnf(refute_0_31,plain,
apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) = apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))))),bind(Y,$fot(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),bind(Z,$fot(h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_32,plain,
( apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))
| apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) != apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))))
| apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))))) ),[1],$fot(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_33,plain,
( apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))
| apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_1250,g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),X_1250))),apply(apply(b,b),t))))) )],[refute_0_33,refute_0_30]) ).
cnf(refute_0_35,plain,
apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(subst,[],[refute_0_34:[bind(X_1250,$fot(t))]]) ).
cnf(refute_0_36,plain,
apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(subst,[],[t_definition:[bind(X,$fot(g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),bind(Y,$fot(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))))]]) ).
cnf(refute_0_37,plain,
( apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))
| apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))
| apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) ),[1],$fot(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_38,plain,
( apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))
| apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) != apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(resolve,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
introduced(tautology,[refl,[$fot(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))))]]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) )],[refute_0_40,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL062-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.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 13:23:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.90/2.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.90/2.06
% 1.90/2.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.92/2.09
%------------------------------------------------------------------------------