TSTP Solution File: COL064-11 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL064-11 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:36:23 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of clauses : 66 ( 34 unt; 0 nHn; 63 RR)
% Number of literals : 115 ( 114 equ; 51 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(t_definition,axiom,
apply(apply(t,X),Y) = apply(Y,X) ).
cnf(prove_v_combinator,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) != apply(apply(z,x),y) ).
cnf(refute_0_0,plain,
apply(apply(t,x),z) = apply(z,x),
inference(subst,[],[t_definition:[bind(X,$fot(x)),bind(Y,$fot(z))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(t,x),z),y) = apply(apply(apply(t,x),z),y),
introduced(tautology,[refl,[$fot(apply(apply(apply(t,x),z),y))]]) ).
cnf(refute_0_2,plain,
( apply(apply(apply(t,x),z),y) != apply(apply(apply(t,x),z),y)
| apply(apply(t,x),z) != apply(z,x)
| apply(apply(apply(t,x),z),y) = apply(apply(z,x),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(t,x),z),y),apply(apply(apply(t,x),z),y)) ),[1,0],$fot(apply(z,x))]]) ).
cnf(refute_0_3,plain,
( apply(apply(t,x),z) != apply(z,x)
| apply(apply(apply(t,x),z),y) = apply(apply(z,x),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(t,x),z),y),apply(apply(apply(t,x),z),y)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(t,x),z),y) = apply(apply(z,x),y),
inference(resolve,[$cnf( $equal(apply(apply(t,x),z),apply(z,x)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(apply(t,y),apply(apply(t,x),z)) = apply(apply(apply(t,x),z),y),
inference(subst,[],[t_definition:[bind(X,$fot(y)),bind(Y,$fot(apply(apply(t,x),z)))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( apply(apply(apply(t,x),z),y) != apply(apply(z,x),y)
| apply(apply(t,y),apply(apply(t,x),z)) != apply(apply(apply(t,x),z),y)
| apply(apply(t,y),apply(apply(t,x),z)) = apply(apply(z,x),y) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(t,y),apply(apply(t,x),z)))),bind(Y0,$fot(apply(apply(apply(t,x),z),y))),bind(Z0,$fot(apply(apply(z,x),y)))]]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(t,x),z),y) != apply(apply(z,x),y)
| apply(apply(t,y),apply(apply(t,x),z)) = apply(apply(z,x),y) ),
inference(resolve,[$cnf( $equal(apply(apply(t,y),apply(apply(t,x),z)),apply(apply(apply(t,x),z),y)) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
apply(apply(t,y),apply(apply(t,x),z)) = apply(apply(z,x),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(t,x),z),y),apply(apply(z,x),y)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(b,apply(t,y)),apply(t,x)),z) = apply(apply(t,y),apply(apply(t,x),z)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(t,y))),bind(Y,$fot(apply(t,x))),bind(Z,$fot(z))]]) ).
cnf(refute_0_15,plain,
( apply(apply(apply(b,apply(t,y)),apply(t,x)),z) != apply(apply(t,y),apply(apply(t,x),z))
| apply(apply(t,y),apply(apply(t,x),z)) != apply(apply(z,x),y)
| apply(apply(apply(b,apply(t,y)),apply(t,x)),z) = apply(apply(z,x),y) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(t,y)),apply(t,x)),z))),bind(Y0,$fot(apply(apply(t,y),apply(apply(t,x),z)))),bind(Z0,$fot(apply(apply(z,x),y)))]]) ).
cnf(refute_0_16,plain,
( apply(apply(t,y),apply(apply(t,x),z)) != apply(apply(z,x),y)
| apply(apply(apply(b,apply(t,y)),apply(t,x)),z) = apply(apply(z,x),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,y)),apply(t,x)),z),apply(apply(t,y),apply(apply(t,x),z))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
apply(apply(apply(b,apply(t,y)),apply(t,x)),z) = apply(apply(z,x),y),
inference(resolve,[$cnf( $equal(apply(apply(t,y),apply(apply(t,x),z)),apply(apply(z,x),y)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
apply(apply(apply(b,b),t),y) = apply(b,apply(t,y)),
inference(subst,[],[b_definition:[bind(X,$fot(b)),bind(Y,$fot(t)),bind(Z,$fot(y))]]) ).
cnf(refute_0_19,plain,
apply(apply(apply(apply(b,b),t),y),apply(t,x)) = apply(apply(apply(apply(b,b),t),y),apply(t,x)),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(b,b),t),y),apply(t,x)))]]) ).
cnf(refute_0_20,plain,
( apply(apply(apply(apply(b,b),t),y),apply(t,x)) != apply(apply(apply(apply(b,b),t),y),apply(t,x))
| apply(apply(apply(b,b),t),y) != apply(b,apply(t,y))
| apply(apply(apply(apply(b,b),t),y),apply(t,x)) = apply(apply(b,apply(t,y)),apply(t,x)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(b,b),t),y),apply(t,x)),apply(apply(apply(apply(b,b),t),y),apply(t,x))) ),[1,0],$fot(apply(b,apply(t,y)))]]) ).
cnf(refute_0_21,plain,
( apply(apply(apply(b,b),t),y) != apply(b,apply(t,y))
| apply(apply(apply(apply(b,b),t),y),apply(t,x)) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,b),t),y),apply(t,x)),apply(apply(apply(apply(b,b),t),y),apply(t,x))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
apply(apply(apply(apply(b,b),t),y),apply(t,x)) = apply(apply(b,apply(t,y)),apply(t,x)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,b),t),y),apply(b,apply(t,y))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) = apply(apply(apply(apply(b,b),t),y),apply(t,x)),
inference(subst,[],[t_definition:[bind(X,$fot(apply(t,x))),bind(Y,$fot(apply(apply(apply(b,b),t),y)))]]) ).
cnf(refute_0_24,plain,
( apply(apply(apply(apply(b,b),t),y),apply(t,x)) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) != apply(apply(apply(apply(b,b),t),y),apply(t,x))
| apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)))),bind(Y0,$fot(apply(apply(apply(apply(b,b),t),y),apply(t,x)))),bind(Z0,$fot(apply(apply(b,apply(t,y)),apply(t,x))))]]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(apply(b,b),t),y),apply(t,x)) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(resolve,[$cnf( $equal(apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)),apply(apply(apply(apply(b,b),t),y),apply(t,x))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) = apply(apply(b,apply(t,y)),apply(t,x)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,b),t),y),apply(t,x)),apply(apply(b,apply(t,y)),apply(t,x))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(t,apply(t,x)))),bind(Y,$fot(apply(apply(b,b),t))),bind(Z,$fot(y))]]) ).
cnf(refute_0_28,plain,
( apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) != apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y))
| apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y))),bind(Y0,$fot(apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)))),bind(Z0,$fot(apply(apply(b,apply(t,y)),apply(t,x))))]]) ).
cnf(refute_0_29,plain,
( apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y),apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(b,apply(t,y)),apply(t,x)),
inference(resolve,[$cnf( $equal(apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)),apply(apply(b,apply(t,y)),apply(t,x))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),
inference(subst,[],[t_definition:[bind(X,$fot(apply(apply(b,b),t))),bind(Y,$fot(apply(b,apply(t,apply(t,x)))))]]) ).
cnf(refute_0_32,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) = apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(t,apply(apply(b,b),t)))),bind(Y,$fot(b)),bind(Z,$fot(apply(t,apply(t,x))))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) != apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x))))
| apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))))),bind(Y0,$fot(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))))),bind(Z0,$fot(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))))]]) ).
cnf(refute_0_34,plain,
( apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))),apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),
inference(resolve,[$cnf( $equal(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(t,apply(t,x)))),apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) = apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(apply(b,apply(t,apply(apply(b,b),t))),b))),bind(Y,$fot(t)),bind(Z,$fot(apply(t,x)))]]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) != apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x)))
| apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)))),bind(Y0,$fot(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))))),bind(Z0,$fot(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))))]]) ).
cnf(refute_0_38,plain,
( apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)),apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),b),apply(t,apply(t,x))),apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) = apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t))),bind(Y,$fot(t)),bind(Z,$fot(x))]]) ).
cnf(refute_0_41,plain,
( apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) != apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x))
| apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x))),bind(Y0,$fot(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)))),bind(Z0,$fot(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))))]]) ).
cnf(refute_0_42,plain,
( apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t),apply(t,x)),apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y))]]) ).
cnf(refute_0_45,plain,
( apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) != apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y)
| apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y)) ),[1,0],$fot(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)))]]) ).
cnf(refute_0_46,plain,
( apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x) != apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))
| apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) != apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y)
| apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y))),bind(Y0,$fot(apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y))),bind(Z0,$fot(apply(apply(b,apply(t,y)),apply(t,x))))]]) ).
cnf(refute_0_49,plain,
( apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(b,apply(t,y)),apply(t,x)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) = apply(apply(b,apply(t,y)),apply(t,x)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y),apply(apply(b,apply(t,y)),apply(t,x))) )],[refute_0_30,refute_0_49]) ).
cnf(refute_0_51,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z))]]) ).
cnf(refute_0_52,plain,
( apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) != apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z)
| apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(apply(b,apply(t,y)),apply(t,x)),z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z)) ),[1,0],$fot(apply(apply(b,apply(t,y)),apply(t,x)))]]) ).
cnf(refute_0_53,plain,
( apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y) != apply(apply(b,apply(t,y)),apply(t,x))
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(apply(b,apply(t,y)),apply(t,x)),z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(apply(b,apply(t,y)),apply(t,x)),z),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),apply(apply(b,apply(t,y)),apply(t,x))) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) != apply(apply(apply(b,apply(t,y)),apply(t,x)),z)
| apply(apply(apply(b,apply(t,y)),apply(t,x)),z) != apply(apply(z,x),y)
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(z,x),y) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z))),bind(Y0,$fot(apply(apply(apply(b,apply(t,y)),apply(t,x)),z))),bind(Z0,$fot(apply(apply(z,x),y)))]]) ).
cnf(refute_0_56,plain,
( apply(apply(apply(b,apply(t,y)),apply(t,x)),z) != apply(apply(z,x),y)
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(z,x),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),apply(apply(apply(b,apply(t,y)),apply(t,x)),z)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(z,x),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,y)),apply(t,x)),z),apply(apply(z,x),y)) )],[refute_0_17,refute_0_56]) ).
cnf(refute_0_58,plain,
( apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) != apply(apply(z,x),y)
| apply(apply(z,x),y) != apply(apply(z,x),y)
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(z,x),y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),apply(apply(z,x),y)) ),[0],$fot(apply(apply(z,x),y))]]) ).
cnf(refute_0_59,plain,
( apply(apply(z,x),y) != apply(apply(z,x),y)
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z) = apply(apply(z,x),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),apply(apply(z,x),y)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
apply(apply(z,x),y) != apply(apply(z,x),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),t),x),y),z),apply(apply(z,x),y)) )],[refute_0_59,prove_v_combinator]) ).
cnf(refute_0_61,plain,
apply(apply(z,x),y) = apply(apply(z,x),y),
introduced(tautology,[refl,[$fot(apply(apply(z,x),y))]]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(z,x),y),apply(apply(z,x),y)) )],[refute_0_61,refute_0_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL064-11 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.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 14:22:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38
%------------------------------------------------------------------------------