TSTP Solution File: COL066-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL066-3 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 00:36:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of clauses : 90 ( 48 unt; 0 nHn; 75 RR)
% Number of literals : 153 ( 152 equ; 66 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ).
cnf(w_definition,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y) ).
cnf(prove_p_combinator,negated_conjecture,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)) ).
cnf(refute_0_0,plain,
apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x) = apply(apply(w,apply(q,apply(q,q))),apply(q,x)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(w,apply(q,apply(q,q))))),bind(Y,$fot(q)),bind(Z,$fot(x))]]) ).
cnf(refute_0_1,plain,
apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) = apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),
introduced(tautology,[refl,[$fot(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)))]]) ).
cnf(refute_0_2,plain,
( apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x) != apply(apply(w,apply(q,apply(q,q))),apply(q,x))
| apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) != apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x))
| apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) = apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x))) ),[1,1],$fot(apply(apply(w,apply(q,apply(q,q))),apply(q,x)))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x) != apply(apply(w,apply(q,apply(q,q))),apply(q,x))
| apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) = apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) ),
inference(resolve,[$cnf( $equal(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) = apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),apply(apply(w,apply(q,apply(q,q))),apply(q,x))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) = apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),
introduced(tautology,[refl,[$fot(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y))]]) ).
cnf(refute_0_6,plain,
( apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) != apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y)
| apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) != apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x)))
| apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y)) ),[1,0],$fot(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))))]]) ).
cnf(refute_0_7,plain,
( apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)) != apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x)))
| apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) ),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),
inference(resolve,[$cnf( $equal(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x)))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_11,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( apply(apply(w,X),Y) != apply(apply(X,Y),Y)
| apply(apply(X,Y),Y) = apply(apply(w,X),Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(apply(apply(w,X),Y))),bind(Y0,$fot(apply(apply(X,Y),Y)))]]) ).
cnf(refute_0_13,plain,
apply(apply(X,Y),Y) = apply(apply(w,X),Y),
inference(resolve,[$cnf( $equal(apply(apply(w,X),Y),apply(apply(X,Y),Y)) )],[w_definition,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) = apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),
inference(subst,[],[refute_0_13:[bind(X,$fot(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x))),bind(Y,$fot(y))]]) ).
cnf(refute_0_15,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) != apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y)
| apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) != apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)
| apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y))),bind(Y0,$fot(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y))),bind(Z0,$fot(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)))]]) ).
cnf(refute_0_18,plain,
( apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y) != apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)
| apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)) )],[refute_0_8,refute_0_18]) ).
cnf(refute_0_20,plain,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) = apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z))]]) ).
cnf(refute_0_21,plain,
( apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z)
| apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) != apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)
| apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) = apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z)) ),[1,0],$fot(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y) != apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)
| apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) = apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) = apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z)
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(x,y),apply(apply(x,y),z))) ),[0],$fot(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z))]]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z),apply(apply(x,y),apply(apply(x,y),z))) )],[refute_0_25,prove_p_combinator]) ).
cnf(refute_0_27,plain,
apply(apply(apply(q,X_12),X_12),X_13) = apply(X_12,apply(X_12,X_13)),
inference(subst,[],[q_definition:[bind(X,$fot(X_12)),bind(Y,$fot(X_12)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_28,plain,
apply(apply(w,q),X_12) = apply(apply(q,X_12),X_12),
inference(subst,[],[w_definition:[bind(X,$fot(q)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_29,plain,
( apply(apply(w,q),X_12) != apply(apply(q,X_12),X_12)
| apply(apply(q,X_12),X_12) = apply(apply(w,q),X_12) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(apply(apply(w,q),X_12))),bind(Y0,$fot(apply(apply(q,X_12),X_12)))]]) ).
cnf(refute_0_30,plain,
apply(apply(q,X_12),X_12) = apply(apply(w,q),X_12),
inference(resolve,[$cnf( $equal(apply(apply(w,q),X_12),apply(apply(q,X_12),X_12)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( apply(apply(apply(q,X_12),X_12),X_13) != apply(X_12,apply(X_12,X_13))
| apply(apply(q,X_12),X_12) != apply(apply(w,q),X_12)
| apply(apply(apply(w,q),X_12),X_13) = apply(X_12,apply(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(q,X_12),X_12),X_13),apply(X_12,apply(X_12,X_13))) ),[0,0],$fot(apply(apply(w,q),X_12))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(q,X_12),X_12),X_13) != apply(X_12,apply(X_12,X_13))
| apply(apply(apply(w,q),X_12),X_13) = apply(X_12,apply(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(apply(apply(q,X_12),X_12),apply(apply(w,q),X_12)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
apply(apply(apply(w,q),X_12),X_13) = apply(X_12,apply(X_12,X_13)),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_12),X_12),X_13),apply(X_12,apply(X_12,X_13))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(w,q),apply(x,y)),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(subst,[],[refute_0_33:[bind(X_12,$fot(apply(x,y))),bind(X_13,$fot(z))]]) ).
cnf(refute_0_35,plain,
apply(apply(q,apply(x,y)),apply(x,y)) = apply(apply(w,q),apply(x,y)),
inference(subst,[],[refute_0_13:[bind(X,$fot(q)),bind(Y,$fot(apply(x,y)))]]) ).
cnf(refute_0_36,plain,
apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(q,apply(x,y)),apply(x,y)),
inference(subst,[],[q_definition:[bind(X,$fot(x)),bind(Y,$fot(apply(q,apply(x,y)))),bind(Z,$fot(y))]]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(q,x),apply(q,apply(x,y))),y) != apply(apply(q,apply(x,y)),apply(x,y))
| apply(apply(q,apply(x,y)),apply(x,y)) != apply(apply(w,q),apply(x,y))
| apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(w,q),apply(x,y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(apply(q,x),apply(q,apply(x,y))),y))),bind(Y0,$fot(apply(apply(q,apply(x,y)),apply(x,y)))),bind(Z0,$fot(apply(apply(w,q),apply(x,y))))]]) ).
cnf(refute_0_38,plain,
( apply(apply(q,apply(x,y)),apply(x,y)) != apply(apply(w,q),apply(x,y))
| apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(w,q),apply(x,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,x),apply(q,apply(x,y))),y),apply(apply(q,apply(x,y)),apply(x,y))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(w,q),apply(x,y)),
inference(resolve,[$cnf( $equal(apply(apply(q,apply(x,y)),apply(x,y)),apply(apply(w,q),apply(x,y))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
apply(apply(apply(q,q),apply(q,x)),apply(x,y)) = apply(apply(q,x),apply(q,apply(x,y))),
inference(subst,[],[q_definition:[bind(X,$fot(q)),bind(Y,$fot(apply(q,x))),bind(Z,$fot(apply(x,y)))]]) ).
cnf(refute_0_41,plain,
apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y))]]) ).
cnf(refute_0_42,plain,
( apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) != apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y)
| apply(apply(apply(q,q),apply(q,x)),apply(x,y)) != apply(apply(q,x),apply(q,apply(x,y)))
| apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(apply(q,x),apply(q,apply(x,y))),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y)) ),[1,0],$fot(apply(apply(q,x),apply(q,apply(x,y))))]]) ).
cnf(refute_0_43,plain,
( apply(apply(apply(q,q),apply(q,x)),apply(x,y)) != apply(apply(q,x),apply(q,apply(x,y)))
| apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(apply(q,x),apply(q,apply(x,y))),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(apply(q,x),apply(q,apply(x,y))),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),apply(apply(q,x),apply(q,apply(x,y)))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) != apply(apply(apply(q,x),apply(q,apply(x,y))),y)
| apply(apply(apply(q,x),apply(q,apply(x,y))),y) != apply(apply(w,q),apply(x,y))
| apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(w,q),apply(x,y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y))),bind(Y0,$fot(apply(apply(apply(q,x),apply(q,apply(x,y))),y))),bind(Z0,$fot(apply(apply(w,q),apply(x,y))))]]) ).
cnf(refute_0_46,plain,
( apply(apply(apply(q,x),apply(q,apply(x,y))),y) != apply(apply(w,q),apply(x,y))
| apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(w,q),apply(x,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),apply(apply(apply(q,x),apply(q,apply(x,y))),y)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(w,q),apply(x,y)),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,x),apply(q,apply(x,y))),y),apply(apply(w,q),apply(x,y))) )],[refute_0_39,refute_0_46]) ).
cnf(refute_0_48,plain,
apply(apply(w,apply(apply(q,X_11),X_12)),Y) = apply(apply(apply(apply(q,X_11),X_12),Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(apply(apply(q,X_11),X_12)))]]) ).
cnf(refute_0_49,plain,
apply(apply(apply(q,X_11),X_12),Y) = apply(X_12,apply(X_11,Y)),
inference(subst,[],[q_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_50,plain,
( apply(apply(apply(q,X_11),X_12),Y) != apply(X_12,apply(X_11,Y))
| apply(apply(w,apply(apply(q,X_11),X_12)),Y) != apply(apply(apply(apply(q,X_11),X_12),Y),Y)
| apply(apply(w,apply(apply(q,X_11),X_12)),Y) = apply(apply(X_12,apply(X_11,Y)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(apply(q,X_11),X_12)),Y),apply(apply(apply(apply(q,X_11),X_12),Y),Y)) ),[1,0],$fot(apply(X_12,apply(X_11,Y)))]]) ).
cnf(refute_0_51,plain,
( apply(apply(w,apply(apply(q,X_11),X_12)),Y) != apply(apply(apply(apply(q,X_11),X_12),Y),Y)
| apply(apply(w,apply(apply(q,X_11),X_12)),Y) = apply(apply(X_12,apply(X_11,Y)),Y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_11),X_12),Y),apply(X_12,apply(X_11,Y))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
apply(apply(w,apply(apply(q,X_11),X_12)),Y) = apply(apply(X_12,apply(X_11,Y)),Y),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(q,X_11),X_12)),Y),apply(apply(apply(apply(q,X_11),X_12),Y),Y)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) = apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),
inference(subst,[],[refute_0_52:[bind(Y,$fot(y)),bind(X_11,$fot(x)),bind(X_12,$fot(apply(apply(q,q),apply(q,x))))]]) ).
cnf(refute_0_54,plain,
( apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) != apply(apply(w,q),apply(x,y))
| apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) != apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y)
| apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) = apply(apply(w,q),apply(x,y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y))),bind(Y0,$fot(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y))),bind(Z0,$fot(apply(apply(w,q),apply(x,y))))]]) ).
cnf(refute_0_55,plain,
( apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) != apply(apply(w,q),apply(x,y))
| apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) = apply(apply(w,q),apply(x,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) = apply(apply(w,q),apply(x,y)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),apply(apply(w,q),apply(x,y))) )],[refute_0_47,refute_0_55]) ).
cnf(refute_0_57,plain,
apply(apply(w,apply(q,X_11)),Y) = apply(apply(apply(q,X_11),Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(apply(q,X_11)))]]) ).
cnf(refute_0_58,plain,
apply(apply(apply(q,X_11),Y),Y) = apply(Y,apply(X_11,Y)),
inference(subst,[],[q_definition:[bind(X,$fot(X_11)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_59,plain,
( apply(apply(apply(q,X_11),Y),Y) != apply(Y,apply(X_11,Y))
| apply(apply(w,apply(q,X_11)),Y) != apply(apply(apply(q,X_11),Y),Y)
| apply(apply(w,apply(q,X_11)),Y) = apply(Y,apply(X_11,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(q,X_11)),Y),apply(apply(apply(q,X_11),Y),Y)) ),[1],$fot(apply(Y,apply(X_11,Y)))]]) ).
cnf(refute_0_60,plain,
( apply(apply(w,apply(q,X_11)),Y) != apply(apply(apply(q,X_11),Y),Y)
| apply(apply(w,apply(q,X_11)),Y) = apply(Y,apply(X_11,Y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_11),Y),Y),apply(Y,apply(X_11,Y))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
apply(apply(w,apply(q,X_11)),Y) = apply(Y,apply(X_11,Y)),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(q,X_11)),Y),apply(apply(apply(q,X_11),Y),Y)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
apply(apply(w,apply(q,apply(q,q))),apply(q,x)) = apply(apply(q,x),apply(apply(q,q),apply(q,x))),
inference(subst,[],[refute_0_61:[bind(Y,$fot(apply(q,x))),bind(X_11,$fot(apply(q,q)))]]) ).
cnf(refute_0_63,plain,
apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) = apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),
introduced(tautology,[refl,[$fot(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))))]]) ).
cnf(refute_0_64,plain,
( apply(apply(w,apply(q,apply(q,q))),apply(q,x)) != apply(apply(q,x),apply(apply(q,q),apply(q,x)))
| apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) != apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x)))
| apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) = apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x)))) ),[1,1],$fot(apply(apply(q,x),apply(apply(q,q),apply(q,x))))]]) ).
cnf(refute_0_65,plain,
( apply(apply(w,apply(q,apply(q,q))),apply(q,x)) != apply(apply(q,x),apply(apply(q,q),apply(q,x)))
| apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) = apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))) ),
inference(resolve,[$cnf( $equal(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) = apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),apply(apply(q,x),apply(apply(q,q),apply(q,x)))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),
introduced(tautology,[refl,[$fot(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y))]]) ).
cnf(refute_0_68,plain,
( apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) != apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)
| apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) != apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x))))
| apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)) ),[1,0],$fot(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))))]]) ).
cnf(refute_0_69,plain,
( apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) != apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x))))
| apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) ),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),
inference(resolve,[$cnf( $equal(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x))))) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) != apply(apply(w,q),apply(x,y))
| apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) != apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y)
| apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,q),apply(x,y)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y))),bind(Y0,$fot(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y))),bind(Z0,$fot(apply(apply(w,q),apply(x,y))))]]) ).
cnf(refute_0_72,plain,
( apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) != apply(apply(w,q),apply(x,y))
| apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,q),apply(x,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,q),apply(x,y)),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),apply(apply(w,q),apply(x,y))) )],[refute_0_56,refute_0_72]) ).
cnf(refute_0_74,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),
introduced(tautology,[refl,[$fot(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z))]]) ).
cnf(refute_0_75,plain,
( apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z)
| apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) != apply(apply(w,q),apply(x,y))
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(apply(w,q),apply(x,y)),z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z)) ),[1,0],$fot(apply(apply(w,q),apply(x,y)))]]) ).
cnf(refute_0_76,plain,
( apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) != apply(apply(w,q),apply(x,y))
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(apply(w,q),apply(x,y)),z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(apply(w,q),apply(x,y)),z),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),apply(apply(w,q),apply(x,y))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(apply(w,q),apply(x,y)),z)
| apply(apply(apply(w,q),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z))),bind(Y0,$fot(apply(apply(apply(w,q),apply(x,y)),z))),bind(Z0,$fot(apply(apply(x,y),apply(apply(x,y),z))))]]) ).
cnf(refute_0_79,plain,
( apply(apply(apply(w,q),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),apply(apply(apply(w,q),apply(x,y)),z)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,q),apply(x,y)),z),apply(apply(x,y),apply(apply(x,y),z))) )],[refute_0_34,refute_0_79]) ).
cnf(refute_0_81,plain,
( apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),apply(apply(x,y),apply(apply(x,y),z))) ),[0],$fot(apply(apply(x,y),apply(apply(x,y),z)))]]) ).
cnf(refute_0_82,plain,
( apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z))
| apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(x,y),apply(apply(x,y),z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),apply(apply(x,y),apply(apply(x,y),z))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),apply(apply(x,y),apply(apply(x,y),z))) )],[refute_0_82,refute_0_26]) ).
cnf(refute_0_84,plain,
apply(apply(x,y),apply(apply(x,y),z)) = apply(apply(x,y),apply(apply(x,y),z)),
introduced(tautology,[refl,[$fot(apply(apply(x,y),apply(apply(x,y),z)))]]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(x,y),apply(apply(x,y),z)),apply(apply(x,y),apply(apply(x,y),z))) )],[refute_0_84,refute_0_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL066-3 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 05:24:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42
% 0.19/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------