TSTP Solution File: COL003-15 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL003-15 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 00:36:11 EDT 2022
% Result : Unsatisfiable 208.66s 208.82s
% Output : CNFRefutation 208.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of clauses : 113 ( 59 unt; 0 nHn; 61 RR)
% Number of literals : 190 ( 189 equ; 79 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(w_definition,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y) ).
cnf(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ).
cnf(refute_0_0,plain,
apply(apply(apply(b,X),apply(X_12,X_12)),Z) = apply(X,apply(apply(X_12,X_12),Z)),
inference(subst,[],[b_definition:[bind(Y,$fot(apply(X_12,X_12)))]]) ).
cnf(refute_0_1,plain,
apply(apply(w,apply(b,X_7)),Y) = apply(apply(apply(b,X_7),Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(apply(b,X_7)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(b,X_7),Y),Y) = apply(X_7,apply(Y,Y)),
inference(subst,[],[b_definition:[bind(X,$fot(X_7)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(b,X_7),Y),Y) != apply(X_7,apply(Y,Y))
| apply(apply(w,apply(b,X_7)),Y) != apply(apply(apply(b,X_7),Y),Y)
| apply(apply(w,apply(b,X_7)),Y) = apply(X_7,apply(Y,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(b,X_7)),Y),apply(apply(apply(b,X_7),Y),Y)) ),[1],$fot(apply(X_7,apply(Y,Y)))]]) ).
cnf(refute_0_4,plain,
( apply(apply(w,apply(b,X_7)),Y) != apply(apply(apply(b,X_7),Y),Y)
| apply(apply(w,apply(b,X_7)),Y) = apply(X_7,apply(Y,Y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_7),Y),Y),apply(X_7,apply(Y,Y))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(apply(w,apply(b,X_7)),Y) = apply(X_7,apply(Y,Y)),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(b,X_7)),Y),apply(apply(apply(b,X_7),Y),Y)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
apply(apply(w,apply(b,apply(b,X))),X_12) = apply(apply(b,X),apply(X_12,X_12)),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_12)),bind(X_7,$fot(apply(b,X)))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( apply(apply(w,apply(b,apply(b,X))),X_12) != apply(apply(b,X),apply(X_12,X_12))
| apply(apply(b,X),apply(X_12,X_12)) = apply(apply(w,apply(b,apply(b,X))),X_12) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(apply(w,apply(b,apply(b,X))),X_12))),bind(Y0,$fot(apply(apply(b,X),apply(X_12,X_12))))]]) ).
cnf(refute_0_11,plain,
apply(apply(b,X),apply(X_12,X_12)) = apply(apply(w,apply(b,apply(b,X))),X_12),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(b,apply(b,X))),X_12),apply(apply(b,X),apply(X_12,X_12))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( apply(apply(apply(b,X),apply(X_12,X_12)),Z) != apply(X,apply(apply(X_12,X_12),Z))
| apply(apply(b,X),apply(X_12,X_12)) != apply(apply(w,apply(b,apply(b,X))),X_12)
| apply(apply(apply(w,apply(b,apply(b,X))),X_12),Z) = apply(X,apply(apply(X_12,X_12),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),apply(X_12,X_12)),Z),apply(X,apply(apply(X_12,X_12),Z))) ),[0,0],$fot(apply(apply(w,apply(b,apply(b,X))),X_12))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(b,X),apply(X_12,X_12)),Z) != apply(X,apply(apply(X_12,X_12),Z))
| apply(apply(apply(w,apply(b,apply(b,X))),X_12),Z) = apply(X,apply(apply(X_12,X_12),Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(b,X),apply(X_12,X_12)),apply(apply(w,apply(b,apply(b,X))),X_12)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(w,apply(b,apply(b,X))),X_12),Z) = apply(X,apply(apply(X_12,X_12),Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(X_12,X_12)),Z),apply(X,apply(apply(X_12,X_12),Z))) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) = apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_158)),bind(Z,$fot(apply(w,apply(b,apply(b,X_158))))),bind(X_12,$fot(apply(w,apply(b,apply(b,X_158)))))]]) ).
cnf(refute_0_16,plain,
apply(apply(w,w),Y) = apply(apply(w,Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(w))]]) ).
cnf(refute_0_17,plain,
apply(apply(w,Y),Y) = apply(apply(Y,Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(Y))]]) ).
cnf(refute_0_18,plain,
( apply(apply(w,Y),Y) != apply(apply(Y,Y),Y)
| apply(apply(w,w),Y) != apply(apply(w,Y),Y)
| apply(apply(w,w),Y) = apply(apply(Y,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,w),Y),apply(apply(w,Y),Y)) ),[1],$fot(apply(apply(Y,Y),Y))]]) ).
cnf(refute_0_19,plain,
( apply(apply(w,w),Y) != apply(apply(w,Y),Y)
| apply(apply(w,w),Y) = apply(apply(Y,Y),Y) ),
inference(resolve,[$cnf( $equal(apply(apply(w,Y),Y),apply(apply(Y,Y),Y)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
apply(apply(w,w),Y) = apply(apply(Y,Y),Y),
inference(resolve,[$cnf( $equal(apply(apply(w,w),Y),apply(apply(w,Y),Y)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) = apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))),
inference(subst,[],[refute_0_20:[bind(Y,$fot(apply(w,apply(b,apply(b,X_158)))))]]) ).
cnf(refute_0_22,plain,
( apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))
| apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))),bind(Y0,$fot(apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))))]]) ).
cnf(refute_0_23,plain,
apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))),
inference(resolve,[$cnf( $equal(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))),apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) != apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))
| apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) = apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))),apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))) ),[0],$fot(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))]]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) = apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))),apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) = apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))),apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))) )],[refute_0_15,refute_0_25]) ).
cnf(refute_0_27,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),X_9) = apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(apply(b,apply(w,w)),w))),bind(Y,$fot(apply(apply(b,b),b))),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_28,plain,
( strong_fixed_point != apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b))
| apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)) = strong_fixed_point ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(strong_fixed_point)),bind(Y0,$fot(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b))))]]) ).
cnf(refute_0_29,plain,
apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)) = strong_fixed_point,
inference(resolve,[$cnf( $equal(strong_fixed_point,apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b))) )],[strong_fixed_point,refute_0_28]) ).
cnf(refute_0_30,plain,
( apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),X_9) != apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))
| apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)) != strong_fixed_point
| apply(strong_fixed_point,X_9) = apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),X_9),apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))) ),[0,0],$fot(strong_fixed_point)]]) ).
cnf(refute_0_31,plain,
( apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),X_9) != apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))
| apply(strong_fixed_point,X_9) = apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) ),
inference(resolve,[$cnf( $equal(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),strong_fixed_point) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
apply(strong_fixed_point,X_9) = apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b)),X_9),apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
apply(apply(apply(b,b),b),X_9) = apply(b,apply(b,X_9)),
inference(subst,[],[b_definition:[bind(X,$fot(b)),bind(Y,$fot(b)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_34,plain,
apply(w,apply(apply(apply(b,b),b),X_9)) = apply(w,apply(apply(apply(b,b),b),X_9)),
introduced(tautology,[refl,[$fot(apply(w,apply(apply(apply(b,b),b),X_9)))]]) ).
cnf(refute_0_35,plain,
( apply(apply(apply(b,b),b),X_9) != apply(b,apply(b,X_9))
| apply(w,apply(apply(apply(b,b),b),X_9)) != apply(w,apply(apply(apply(b,b),b),X_9))
| apply(w,apply(apply(apply(b,b),b),X_9)) = apply(w,apply(b,apply(b,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(w,apply(apply(apply(b,b),b),X_9)),apply(w,apply(apply(apply(b,b),b),X_9))) ),[1,1],$fot(apply(b,apply(b,X_9)))]]) ).
cnf(refute_0_36,plain,
( apply(apply(apply(b,b),b),X_9) != apply(b,apply(b,X_9))
| apply(w,apply(apply(apply(b,b),b),X_9)) = apply(w,apply(b,apply(b,X_9))) ),
inference(resolve,[$cnf( $equal(apply(w,apply(apply(apply(b,b),b),X_9)),apply(w,apply(apply(apply(b,b),b),X_9))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
apply(w,apply(apply(apply(b,b),b),X_9)) = apply(w,apply(b,apply(b,X_9))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,b),b),X_9),apply(b,apply(b,X_9))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) = apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))),
introduced(tautology,[refl,[$fot(apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))))]]) ).
cnf(refute_0_39,plain,
( apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) != apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9)))
| apply(w,apply(apply(apply(b,b),b),X_9)) != apply(w,apply(b,apply(b,X_9)))
| apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))),apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9)))) ),[1,1],$fot(apply(w,apply(b,apply(b,X_9))))]]) ).
cnf(refute_0_40,plain,
( apply(w,apply(apply(apply(b,b),b),X_9)) != apply(w,apply(b,apply(b,X_9)))
| apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) ),
inference(resolve,[$cnf( $equal(apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))),apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))),
inference(resolve,[$cnf( $equal(apply(w,apply(apply(apply(b,b),b),X_9)),apply(w,apply(b,apply(b,X_9)))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) = apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(w,w))),bind(Y,$fot(w)),bind(Z,$fot(apply(apply(apply(b,b),b),X_9)))]]) ).
cnf(refute_0_43,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_44,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_43]) ).
cnf(refute_0_45,plain,
( apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) != apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9)))
| apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) != apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))
| apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)))),bind(Y0,$fot(apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))))),bind(Z0,$fot(apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))))]]) ).
cnf(refute_0_46,plain,
( apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))) != apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))
| apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)),apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9)))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))),
inference(resolve,[$cnf( $equal(apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X_9))),apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
( apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)) != apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))
| apply(strong_fixed_point,X_9) != apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))
| apply(strong_fixed_point,X_9) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(strong_fixed_point,X_9),apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))) ),[1],$fot(apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))))]]) ).
cnf(refute_0_49,plain,
( apply(strong_fixed_point,X_9) != apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))
| apply(strong_fixed_point,X_9) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9)),apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
apply(strong_fixed_point,X_9) = apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))),
inference(resolve,[$cnf( $equal(apply(strong_fixed_point,X_9),apply(apply(apply(b,apply(w,w)),w),apply(apply(apply(b,b),b),X_9))) )],[refute_0_32,refute_0_49]) ).
cnf(refute_0_51,plain,
( apply(strong_fixed_point,X_9) != apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))
| apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) = apply(strong_fixed_point,X_9) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(strong_fixed_point,X_9))),bind(Y0,$fot(apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))))]]) ).
cnf(refute_0_52,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,X_9)))) = apply(strong_fixed_point,X_9),
inference(resolve,[$cnf( $equal(apply(strong_fixed_point,X_9),apply(apply(w,w),apply(w,apply(b,apply(b,X_9))))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) = apply(strong_fixed_point,X_158),
inference(subst,[],[refute_0_52:[bind(X_9,$fot(X_158))]]) ).
cnf(refute_0_54,plain,
( apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(strong_fixed_point,X_158)
| apply(strong_fixed_point,X_158) = apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))),apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))) ),[0],$fot(apply(strong_fixed_point,X_158))]]) ).
cnf(refute_0_55,plain,
( apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(strong_fixed_point,X_158) = apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) ),
inference(resolve,[$cnf( $equal(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))),apply(strong_fixed_point,X_158)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))),
introduced(tautology,[refl,[$fot(apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))))]]) ).
cnf(refute_0_57,plain,
( apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) != apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))
| apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(strong_fixed_point,X_158)
| apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(strong_fixed_point,X_158)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))),apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))) ),[1,1],$fot(apply(strong_fixed_point,X_158))]]) ).
cnf(refute_0_58,plain,
( apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(strong_fixed_point,X_158)
| apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(strong_fixed_point,X_158)) ),
inference(resolve,[$cnf( $equal(apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))),apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(strong_fixed_point,X_158)),
inference(resolve,[$cnf( $equal(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))),apply(strong_fixed_point,X_158)) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
apply(apply(apply(b,X_7),apply(w,w)),X_9) = apply(X_7,apply(apply(w,w),X_9)),
inference(subst,[],[b_definition:[bind(X,$fot(X_7)),bind(Y,$fot(apply(w,w))),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_61,plain,
apply(apply(w,w),X_9) = apply(apply(X_9,X_9),X_9),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_9))]]) ).
cnf(refute_0_62,plain,
( apply(apply(apply(b,X_7),apply(w,w)),X_9) != apply(X_7,apply(apply(w,w),X_9))
| apply(apply(w,w),X_9) != apply(apply(X_9,X_9),X_9)
| apply(apply(apply(b,X_7),apply(w,w)),X_9) = apply(X_7,apply(apply(X_9,X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X_7),apply(w,w)),X_9),apply(X_7,apply(apply(w,w),X_9))) ),[1,1],$fot(apply(apply(X_9,X_9),X_9))]]) ).
cnf(refute_0_63,plain,
( apply(apply(apply(b,X_7),apply(w,w)),X_9) != apply(X_7,apply(apply(w,w),X_9))
| apply(apply(apply(b,X_7),apply(w,w)),X_9) = apply(X_7,apply(apply(X_9,X_9),X_9)) ),
inference(resolve,[$cnf( $equal(apply(apply(w,w),X_9),apply(apply(X_9,X_9),X_9)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
apply(apply(apply(b,X_7),apply(w,w)),X_9) = apply(X_7,apply(apply(X_9,X_9),X_9)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_7),apply(w,w)),X_9),apply(X_7,apply(apply(w,w),X_9))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( apply(apply(apply(b,X_7),apply(w,w)),X_9) != apply(X_7,apply(apply(X_9,X_9),X_9))
| apply(apply(apply(b,X_7),apply(w,w)),X_9) != apply(X_7,apply(apply(w,w),X_9))
| apply(X_7,apply(apply(w,w),X_9)) = apply(X_7,apply(apply(X_9,X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X_7),apply(w,w)),X_9),apply(X_7,apply(apply(X_9,X_9),X_9))) ),[0],$fot(apply(X_7,apply(apply(w,w),X_9)))]]) ).
cnf(refute_0_66,plain,
( apply(apply(apply(b,X_7),apply(w,w)),X_9) != apply(X_7,apply(apply(X_9,X_9),X_9))
| apply(X_7,apply(apply(w,w),X_9)) = apply(X_7,apply(apply(X_9,X_9),X_9)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_7),apply(w,w)),X_9),apply(X_7,apply(apply(w,w),X_9))) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
apply(X_7,apply(apply(w,w),X_9)) = apply(X_7,apply(apply(X_9,X_9),X_9)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_7),apply(w,w)),X_9),apply(X_7,apply(apply(X_9,X_9),X_9))) )],[refute_0_64,refute_0_66]) ).
cnf(refute_0_68,plain,
apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) = apply(X_7,apply(apply(X_9,X_9),X_9)),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_7)),bind(Z,$fot(X_9)),bind(X_12,$fot(X_9))]]) ).
cnf(refute_0_69,plain,
( apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) != apply(X_7,apply(apply(X_9,X_9),X_9))
| apply(X_7,apply(apply(X_9,X_9),X_9)) = apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9))),bind(Y0,$fot(apply(X_7,apply(apply(X_9,X_9),X_9))))]]) ).
cnf(refute_0_70,plain,
apply(X_7,apply(apply(X_9,X_9),X_9)) = apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9),apply(X_7,apply(apply(X_9,X_9),X_9))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( apply(X_7,apply(apply(X_9,X_9),X_9)) != apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9)
| apply(X_7,apply(apply(w,w),X_9)) != apply(X_7,apply(apply(X_9,X_9),X_9))
| apply(X_7,apply(apply(w,w),X_9)) = apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(apply(X_7,apply(apply(w,w),X_9)),apply(X_7,apply(apply(X_9,X_9),X_9))) ),[1],$fot(apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9))]]) ).
cnf(refute_0_72,plain,
( apply(X_7,apply(apply(w,w),X_9)) != apply(X_7,apply(apply(X_9,X_9),X_9))
| apply(X_7,apply(apply(w,w),X_9)) = apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) ),
inference(resolve,[$cnf( $equal(apply(X_7,apply(apply(X_9,X_9),X_9)),apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
apply(X_7,apply(apply(w,w),X_9)) = apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9),
inference(resolve,[$cnf( $equal(apply(X_7,apply(apply(w,w),X_9)),apply(X_7,apply(apply(X_9,X_9),X_9))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
( apply(apply(w,X),Y) != apply(apply(X,Y),Y)
| apply(apply(X,Y),Y) = apply(apply(w,X),Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(apply(w,X),Y))),bind(Y0,$fot(apply(apply(X,Y),Y)))]]) ).
cnf(refute_0_75,plain,
apply(apply(X,Y),Y) = apply(apply(w,X),Y),
inference(resolve,[$cnf( $equal(apply(apply(w,X),Y),apply(apply(X,Y),Y)) )],[w_definition,refute_0_74]) ).
cnf(refute_0_76,plain,
apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) = apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9),
inference(subst,[],[refute_0_75:[bind(X,$fot(apply(w,apply(b,apply(b,X_7))))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_77,plain,
( apply(X_7,apply(apply(w,w),X_9)) != apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9)
| apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9) != apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9)
| apply(X_7,apply(apply(w,w),X_9)) = apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_7,apply(apply(w,w),X_9)),apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9)) ),[0],$fot(apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9))]]) ).
cnf(refute_0_78,plain,
( apply(X_7,apply(apply(w,w),X_9)) != apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9)
| apply(X_7,apply(apply(w,w),X_9)) = apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9),apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
apply(X_7,apply(apply(w,w),X_9)) = apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9),
inference(resolve,[$cnf( $equal(apply(X_7,apply(apply(w,w),X_9)),apply(apply(apply(w,apply(b,apply(b,X_7))),X_9),X_9)) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
( apply(X_7,apply(apply(w,w),X_9)) != apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9)
| apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9) = apply(X_7,apply(apply(w,w),X_9)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(X_7,apply(apply(w,w),X_9)))),bind(Y0,$fot(apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9)))]]) ).
cnf(refute_0_81,plain,
apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9) = apply(X_7,apply(apply(w,w),X_9)),
inference(resolve,[$cnf( $equal(apply(X_7,apply(apply(w,w),X_9)),apply(apply(w,apply(w,apply(b,apply(b,X_7)))),X_9)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) = apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))),
inference(subst,[],[refute_0_81:[bind(X_7,$fot(X_158)),bind(X_9,$fot(apply(w,apply(b,apply(b,X_158)))))]]) ).
cnf(refute_0_83,plain,
apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) = apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y),
inference(subst,[],[w_definition:[bind(X,$fot(apply(w,apply(b,apply(b,X_158)))))]]) ).
cnf(refute_0_84,plain,
apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y) = apply(X_158,apply(apply(Y,Y),Y)),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_158)),bind(Z,$fot(Y)),bind(X_12,$fot(Y))]]) ).
cnf(refute_0_85,plain,
( apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y) != apply(X_158,apply(apply(Y,Y),Y))
| apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) != apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y)
| apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) = apply(X_158,apply(apply(Y,Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y),apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y)) ),[1],$fot(apply(X_158,apply(apply(Y,Y),Y)))]]) ).
cnf(refute_0_86,plain,
( apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) != apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y)
| apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) = apply(X_158,apply(apply(Y,Y),Y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y),apply(X_158,apply(apply(Y,Y),Y))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) = apply(X_158,apply(apply(Y,Y),Y)),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y),apply(apply(apply(w,apply(b,apply(b,X_158))),Y),Y)) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
( apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) != apply(X_158,apply(apply(Y,Y),Y))
| apply(X_158,apply(apply(Y,Y),Y)) = apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y))),bind(Y0,$fot(apply(X_158,apply(apply(Y,Y),Y))))]]) ).
cnf(refute_0_89,plain,
apply(X_158,apply(apply(Y,Y),Y)) = apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(w,apply(b,apply(b,X_158)))),Y),apply(X_158,apply(apply(Y,Y),Y))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))),
inference(subst,[],[refute_0_89:[bind(Y,$fot(apply(w,apply(b,apply(b,X_158)))))]]) ).
cnf(refute_0_91,plain,
( apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) != apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))
| apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))
| apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))))),bind(Y0,$fot(apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))),bind(Z0,$fot(apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))))]]) ).
cnf(refute_0_92,plain,
( apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))
| apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) ),
inference(resolve,[$cnf( $equal(apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))),apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))),
inference(resolve,[$cnf( $equal(apply(apply(w,apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))),apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))) )],[refute_0_82,refute_0_92]) ).
cnf(refute_0_94,plain,
( apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) != apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))
| apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) != apply(X_158,apply(strong_fixed_point,X_158))
| apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(strong_fixed_point,X_158)) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))))),bind(Y0,$fot(apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))))),bind(Z0,$fot(apply(X_158,apply(strong_fixed_point,X_158))))]]) ).
cnf(refute_0_95,plain,
( apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))) != apply(X_158,apply(strong_fixed_point,X_158))
| apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(strong_fixed_point,X_158)) ),
inference(resolve,[$cnf( $equal(apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))),apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) = apply(X_158,apply(strong_fixed_point,X_158)),
inference(resolve,[$cnf( $equal(apply(X_158,apply(apply(w,w),apply(w,apply(b,apply(b,X_158))))),apply(X_158,apply(strong_fixed_point,X_158))) )],[refute_0_59,refute_0_95]) ).
cnf(refute_0_97,plain,
( apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))) != apply(X_158,apply(strong_fixed_point,X_158))
| apply(strong_fixed_point,X_158) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(strong_fixed_point,X_158) = apply(X_158,apply(strong_fixed_point,X_158)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(strong_fixed_point,X_158),apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))) ),[1],$fot(apply(X_158,apply(strong_fixed_point,X_158)))]]) ).
cnf(refute_0_98,plain,
( apply(strong_fixed_point,X_158) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(strong_fixed_point,X_158) = apply(X_158,apply(strong_fixed_point,X_158)) ),
inference(resolve,[$cnf( $equal(apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158))))),apply(X_158,apply(strong_fixed_point,X_158))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))) != apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))
| apply(strong_fixed_point,X_158) = apply(X_158,apply(strong_fixed_point,X_158)) ),
inference(resolve,[$cnf( $equal(apply(strong_fixed_point,X_158),apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))) )],[refute_0_55,refute_0_98]) ).
cnf(refute_0_100,plain,
apply(strong_fixed_point,X_158) = apply(X_158,apply(strong_fixed_point,X_158)),
inference(resolve,[$cnf( $equal(apply(apply(w,w),apply(w,apply(b,apply(b,X_158)))),apply(X_158,apply(apply(apply(w,apply(b,apply(b,X_158))),apply(w,apply(b,apply(b,X_158)))),apply(w,apply(b,apply(b,X_158)))))) )],[refute_0_26,refute_0_99]) ).
cnf(refute_0_101,plain,
( apply(strong_fixed_point,X_158) != apply(X_158,apply(strong_fixed_point,X_158))
| apply(X_158,apply(strong_fixed_point,X_158)) = apply(strong_fixed_point,X_158) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(strong_fixed_point,X_158))),bind(Y0,$fot(apply(X_158,apply(strong_fixed_point,X_158))))]]) ).
cnf(refute_0_102,plain,
apply(X_158,apply(strong_fixed_point,X_158)) = apply(strong_fixed_point,X_158),
inference(resolve,[$cnf( $equal(apply(strong_fixed_point,X_158),apply(X_158,apply(strong_fixed_point,X_158))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt),
inference(subst,[],[refute_0_102:[bind(X_158,$fot(fixed_pt))]]) ).
cnf(refute_0_104,plain,
( apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt)
| apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt)
| apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(strong_fixed_point,fixed_pt),apply(fixed_pt,apply(strong_fixed_point,fixed_pt))) ),[1],$fot(apply(strong_fixed_point,fixed_pt))]]) ).
cnf(refute_0_105,plain,
( apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt)
| apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
inference(resolve,[$cnf( $equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(resolve,[$cnf( $equal(apply(strong_fixed_point,fixed_pt),apply(fixed_pt,apply(strong_fixed_point,fixed_pt))) )],[refute_0_105,prove_strong_fixed_point]) ).
cnf(refute_0_107,plain,
apply(strong_fixed_point,fixed_pt) = apply(strong_fixed_point,fixed_pt),
introduced(tautology,[refl,[$fot(apply(strong_fixed_point,fixed_pt))]]) ).
cnf(refute_0_108,plain,
$false,
inference(resolve,[$cnf( $equal(apply(strong_fixed_point,fixed_pt),apply(strong_fixed_point,fixed_pt)) )],[refute_0_107,refute_0_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL003-15 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 06:07:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 208.66/208.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 208.66/208.82
% 208.66/208.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 208.66/208.83
%------------------------------------------------------------------------------