%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL061-1 : 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 00:36:20 EDT 2022
% Result : Unsatisfiable 0.47s 0.63s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 23 unt; 0 nHn; 28 RR)
% Number of literals : 53 ( 52 equ; 31 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 : 56 ( 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_q1_combinator,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(f(X),apply(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(f(apply(apply(b,X_3),X_4)),apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4)))),
inference(subst,[],[prove_q1_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(f(apply(apply(b,X_3),X_4)),apply(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(f(apply(apply(b,X_3),X_4)),apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(f(apply(apply(b,X_3),X_4)),apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4))))) ),[0,0,0],$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(f(apply(apply(b,X_3),X_4)),apply(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(f(apply(apply(b,X_3),X_4)),apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(X_3,apply(X_4,f(apply(apply(b,X_3),X_4)))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))) != apply(f(apply(apply(b,X_3),X_4)),apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,X_3),X_4),f(apply(apply(b,X_3),X_4))),g(apply(apply(b,X_3),X_4))),h(apply(apply(b,X_3),X_4))),apply(f(apply(apply(b,X_3),X_4)),apply(h(apply(apply(b,X_3),X_4)),g(apply(apply(b,X_3),X_4))))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
apply(apply(apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))) != apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9)))),
inference(subst,[],[refute_0_4:[bind(X_3,$fot(apply(t,X))),bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))) = apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X),
inference(subst,[],[t_definition:[bind(Y,$fot(apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))))]]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))) != apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9))))
| apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))) != apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X)
| apply(apply(apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))) = apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))),apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9))))) ),[0,0,0],$fot(apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))) != apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9))))
| apply(apply(apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))) = apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9)))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))),apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(apply(X_9,f(apply(apply(b,apply(t,X)),X_9))),X),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))) != apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(t,X),apply(X_9,f(apply(apply(b,apply(t,X)),X_9)))),g(apply(apply(b,apply(t,X)),X_9))),h(apply(apply(b,apply(t,X)),X_9))),apply(f(apply(apply(b,apply(t,X)),X_9)),apply(h(apply(apply(b,apply(t,X)),X_9)),g(apply(apply(b,apply(t,X)),X_9))))) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
apply(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) != apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_23)),bind(X_9,$fot(apply(apply(b,X),Y)))]]) ).
cnf(refute_0_11,plain,
apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) = apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))),
inference(subst,[],[b_definition:[bind(Z,$fot(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))]]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) != apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))
| apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) != apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))
| apply(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) = apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))) ),[0,0,0,0],$fot(apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) != apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))
| apply(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) = apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))) != apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(apply(b,X),Y),f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),X_23),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))),apply(f(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),apply(h(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,X_23)),apply(apply(b,X),Y)))))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
apply(apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) != apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),
inference(subst,[],[refute_0_14:[bind(X,$fot(b)),bind(Y,$fot(X_199)),bind(X_23,$fot(X_200))]]) ).
cnf(refute_0_16,plain,
apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) = apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))),bind(Y,$fot(X_200)),bind(Z,$fot(g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) != apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))
| apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) != apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))
| apply(apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) = apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))) ),[0,0],$fot(apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) != apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))
| apply(apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) = apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(X_200,g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))) != apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(X_199,f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))))),X_200),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))),apply(f(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),apply(h(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199))),g(apply(apply(b,apply(t,X_200)),apply(apply(b,b),X_199)))))) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))) != apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),
inference(subst,[],[refute_0_19:[bind(X_199,$fot(b)),bind(X_200,$fot(X_202))]]) ).
cnf(refute_0_21,plain,
apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))) = apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),
inference(subst,[],[b_definition:[bind(X,$fot(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),bind(Y,$fot(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))),bind(Z,$fot(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))) != apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))
| apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))
| apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))) = apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))) ),[0],$fot(apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))))]]) ).
cnf(refute_0_23,plain,
( apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))
| apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))) = apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(X_202,g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))))),h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))),apply(f(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X_202)),apply(apply(b,b),b)))))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),
inference(subst,[],[refute_0_24:[bind(X_202,$fot(t))]]) ).
cnf(refute_0_26,plain,
apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))) = apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),
inference(subst,[],[t_definition:[bind(X,$fot(g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),bind(Y,$fot(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))]]) ).
cnf(refute_0_27,plain,
( apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))) != apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))
| apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))
| apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) = apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))) ),[0,1],$fot(apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))]]) ).
cnf(refute_0_28,plain,
( apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))
| apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) = apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) ),
inference(resolve,[$cnf( $equal(apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),
inference(resolve,[$cnf( $equal(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(apply(t,g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))) )],[refute_0_28,refute_0_25]) ).
cnf(refute_0_30,plain,
apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) = apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),
introduced(tautology,[refl,[$fot(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))))]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( $equal(apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b)))))) )],[refute_0_30,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL061-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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 08:03:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.63
% 0.47/0.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.47/0.66
%------------------------------------------------------------------------------