TSTP Solution File: COL019-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL019-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 00:36:14 EDT 2022
% Result : Unsatisfiable 127.58s 127.80s
% Output : CNFRefutation 127.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of clauses : 65 ( 39 unt; 0 nHn; 32 RR)
% Number of literals : 100 ( 99 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 111 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
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_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(X_124,apply(apply(b,combinator),X_124)) != apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(X_124,apply(apply(b,combinator),X_124))))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(b,X),Y),apply(X_7,Y)) = apply(X,apply(Y,apply(X_7,Y))),
inference(subst,[],[b_definition:[bind(Z,$fot(apply(X_7,Y)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(s,apply(b,X)),X_7),Y) = apply(apply(apply(b,X),Y),apply(X_7,Y)),
inference(subst,[],[s_definition:[bind(X,$fot(apply(b,X))),bind(Y,$fot(X_7)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( apply(apply(apply(s,apply(b,X)),X_7),Y) != apply(apply(apply(b,X),Y),apply(X_7,Y))
| apply(apply(apply(b,X),Y),apply(X_7,Y)) = apply(apply(apply(s,apply(b,X)),X_7),Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,apply(b,X)),X_7),Y))),bind(Y0,$fot(apply(apply(apply(b,X),Y),apply(X_7,Y))))]]) ).
cnf(refute_0_7,plain,
apply(apply(apply(b,X),Y),apply(X_7,Y)) = apply(apply(apply(s,apply(b,X)),X_7),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X)),X_7),Y),apply(apply(apply(b,X),Y),apply(X_7,Y))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(b,X),Y),apply(X_7,Y)) != apply(X,apply(Y,apply(X_7,Y)))
| apply(apply(apply(b,X),Y),apply(X_7,Y)) != apply(apply(apply(s,apply(b,X)),X_7),Y)
| apply(apply(apply(s,apply(b,X)),X_7),Y) = apply(X,apply(Y,apply(X_7,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),Y),apply(X_7,Y)),apply(X,apply(Y,apply(X_7,Y)))) ),[0],$fot(apply(apply(apply(s,apply(b,X)),X_7),Y))]]) ).
cnf(refute_0_9,plain,
( apply(apply(apply(b,X),Y),apply(X_7,Y)) != apply(X,apply(Y,apply(X_7,Y)))
| apply(apply(apply(s,apply(b,X)),X_7),Y) = apply(X,apply(Y,apply(X_7,Y))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),apply(X_7,Y)),apply(apply(apply(s,apply(b,X)),X_7),Y)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
apply(apply(apply(s,apply(b,X)),X_7),Y) = apply(X,apply(Y,apply(X_7,Y))),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),Y),apply(X_7,Y)),apply(X,apply(Y,apply(X_7,Y)))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(apply(s,apply(b,X_17)),apply(b,X_17)),X_18) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_17)),bind(Y,$fot(X_18)),bind(X_7,$fot(apply(b,X_17)))]]) ).
cnf(refute_0_12,plain,
apply(apply(t,X),apply(X_7,X)) = apply(apply(X_7,X),X),
inference(subst,[],[t_definition:[bind(Y,$fot(apply(X_7,X)))]]) ).
cnf(refute_0_13,plain,
apply(apply(apply(s,t),X_7),X) = apply(apply(t,X),apply(X_7,X)),
inference(subst,[],[s_definition:[bind(X,$fot(t)),bind(Y,$fot(X_7)),bind(Z,$fot(X))]]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(s,t),X_7),X) != apply(apply(t,X),apply(X_7,X))
| apply(apply(t,X),apply(X_7,X)) = apply(apply(apply(s,t),X_7),X) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,t),X_7),X))),bind(Y0,$fot(apply(apply(t,X),apply(X_7,X))))]]) ).
cnf(refute_0_15,plain,
apply(apply(t,X),apply(X_7,X)) = apply(apply(apply(s,t),X_7),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),X_7),X),apply(apply(t,X),apply(X_7,X))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( apply(apply(t,X),apply(X_7,X)) != apply(apply(X_7,X),X)
| apply(apply(t,X),apply(X_7,X)) != apply(apply(apply(s,t),X_7),X)
| apply(apply(apply(s,t),X_7),X) = apply(apply(X_7,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,X),apply(X_7,X)),apply(apply(X_7,X),X)) ),[0],$fot(apply(apply(apply(s,t),X_7),X))]]) ).
cnf(refute_0_17,plain,
( apply(apply(t,X),apply(X_7,X)) != apply(apply(X_7,X),X)
| apply(apply(apply(s,t),X_7),X) = apply(apply(X_7,X),X) ),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_7,X)),apply(apply(apply(s,t),X_7),X)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
apply(apply(apply(s,t),X_7),X) = apply(apply(X_7,X),X),
inference(resolve,[$cnf( $equal(apply(apply(t,X),apply(X_7,X)),apply(apply(X_7,X),X)) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(s,t),s),apply(b,X_17)) = apply(apply(s,apply(b,X_17)),apply(b,X_17)),
inference(subst,[],[refute_0_18:[bind(X,$fot(apply(b,X_17))),bind(X_7,$fot(s))]]) ).
cnf(refute_0_20,plain,
( apply(apply(apply(s,t),s),apply(b,X_17)) != apply(apply(s,apply(b,X_17)),apply(b,X_17))
| apply(apply(s,apply(b,X_17)),apply(b,X_17)) = apply(apply(apply(s,t),s),apply(b,X_17)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,t),s),apply(b,X_17)))),bind(Y0,$fot(apply(apply(s,apply(b,X_17)),apply(b,X_17))))]]) ).
cnf(refute_0_21,plain,
apply(apply(s,apply(b,X_17)),apply(b,X_17)) = apply(apply(apply(s,t),s),apply(b,X_17)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),s),apply(b,X_17)),apply(apply(s,apply(b,X_17)),apply(b,X_17))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(s,apply(b,X_17)),apply(b,X_17)),X_18) != apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))
| apply(apply(s,apply(b,X_17)),apply(b,X_17)) != apply(apply(apply(s,t),s),apply(b,X_17))
| apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,apply(b,X_17)),apply(b,X_17)),X_18),apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))) ),[0,0],$fot(apply(apply(apply(s,t),s),apply(b,X_17)))]]) ).
cnf(refute_0_23,plain,
( apply(apply(apply(s,apply(b,X_17)),apply(b,X_17)),X_18) != apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))
| apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))) ),
inference(resolve,[$cnf( $equal(apply(apply(s,apply(b,X_17)),apply(b,X_17)),apply(apply(apply(s,t),s),apply(b,X_17))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(b,X_17)),apply(b,X_17)),X_18),apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))) )],[refute_0_11,refute_0_23]) ).
cnf(refute_0_25,plain,
apply(apply(t,Y),Y) = apply(Y,Y),
inference(subst,[],[t_definition:[bind(X,$fot(Y))]]) ).
cnf(refute_0_26,plain,
apply(apply(apply(s,t),t),Y) = apply(apply(t,Y),Y),
inference(subst,[],[refute_0_18:[bind(X,$fot(Y)),bind(X_7,$fot(t))]]) ).
cnf(refute_0_27,plain,
( apply(apply(apply(s,t),t),Y) != apply(apply(t,Y),Y)
| apply(apply(t,Y),Y) = apply(apply(apply(s,t),t),Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,t),t),Y))),bind(Y0,$fot(apply(apply(t,Y),Y)))]]) ).
cnf(refute_0_28,plain,
apply(apply(t,Y),Y) = apply(apply(apply(s,t),t),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),t),Y),apply(apply(t,Y),Y)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( apply(apply(t,Y),Y) != apply(Y,Y)
| apply(apply(t,Y),Y) != apply(apply(apply(s,t),t),Y)
| apply(apply(apply(s,t),t),Y) = apply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(t,Y),Y),apply(Y,Y)) ),[0],$fot(apply(apply(apply(s,t),t),Y))]]) ).
cnf(refute_0_30,plain,
( apply(apply(t,Y),Y) != apply(Y,Y)
| apply(apply(apply(s,t),t),Y) = apply(Y,Y) ),
inference(resolve,[$cnf( $equal(apply(apply(t,Y),Y),apply(apply(apply(s,t),t),Y)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
apply(apply(apply(s,t),t),Y) = apply(Y,Y),
inference(resolve,[$cnf( $equal(apply(apply(t,Y),Y),apply(Y,Y)) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
apply(apply(apply(s,t),t),apply(X_37,X_38)) = apply(apply(X_37,X_38),apply(X_37,X_38)),
inference(subst,[],[refute_0_31:[bind(Y,$fot(apply(X_37,X_38)))]]) ).
cnf(refute_0_33,plain,
apply(apply(apply(s,Y),Y),Z) = apply(apply(Y,Z),apply(Y,Z)),
inference(subst,[],[s_definition:[bind(X,$fot(Y))]]) ).
cnf(refute_0_34,plain,
apply(apply(apply(s,t),s),Y) = apply(apply(s,Y),Y),
inference(subst,[],[refute_0_18:[bind(X,$fot(Y)),bind(X_7,$fot(s))]]) ).
cnf(refute_0_35,plain,
( apply(apply(apply(s,t),s),Y) != apply(apply(s,Y),Y)
| apply(apply(s,Y),Y) = apply(apply(apply(s,t),s),Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,t),s),Y))),bind(Y0,$fot(apply(apply(s,Y),Y)))]]) ).
cnf(refute_0_36,plain,
apply(apply(s,Y),Y) = apply(apply(apply(s,t),s),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),s),Y),apply(apply(s,Y),Y)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(s,Y),Y),Z) != apply(apply(Y,Z),apply(Y,Z))
| apply(apply(s,Y),Y) != apply(apply(apply(s,t),s),Y)
| apply(apply(apply(apply(s,t),s),Y),Z) = apply(apply(Y,Z),apply(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,Y),Y),Z),apply(apply(Y,Z),apply(Y,Z))) ),[0,0],$fot(apply(apply(apply(s,t),s),Y))]]) ).
cnf(refute_0_38,plain,
( apply(apply(apply(s,Y),Y),Z) != apply(apply(Y,Z),apply(Y,Z))
| apply(apply(apply(apply(s,t),s),Y),Z) = apply(apply(Y,Z),apply(Y,Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(s,Y),Y),apply(apply(apply(s,t),s),Y)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
apply(apply(apply(apply(s,t),s),Y),Z) = apply(apply(Y,Z),apply(Y,Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,Y),Y),Z),apply(apply(Y,Z),apply(Y,Z))) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
apply(apply(apply(apply(s,t),s),X_37),X_38) = apply(apply(X_37,X_38),apply(X_37,X_38)),
inference(subst,[],[refute_0_39:[bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_41,plain,
( apply(apply(apply(apply(s,t),s),X_37),X_38) != apply(apply(X_37,X_38),apply(X_37,X_38))
| apply(apply(X_37,X_38),apply(X_37,X_38)) = apply(apply(apply(apply(s,t),s),X_37),X_38) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(apply(s,t),s),X_37),X_38))),bind(Y0,$fot(apply(apply(X_37,X_38),apply(X_37,X_38))))]]) ).
cnf(refute_0_42,plain,
apply(apply(X_37,X_38),apply(X_37,X_38)) = apply(apply(apply(apply(s,t),s),X_37),X_38),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,t),s),X_37),X_38),apply(apply(X_37,X_38),apply(X_37,X_38))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( apply(apply(X_37,X_38),apply(X_37,X_38)) != apply(apply(apply(apply(s,t),s),X_37),X_38)
| apply(apply(apply(s,t),t),apply(X_37,X_38)) != apply(apply(X_37,X_38),apply(X_37,X_38))
| apply(apply(apply(s,t),t),apply(X_37,X_38)) = apply(apply(apply(apply(s,t),s),X_37),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(s,t),t),apply(X_37,X_38)),apply(apply(X_37,X_38),apply(X_37,X_38))) ),[1],$fot(apply(apply(apply(apply(s,t),s),X_37),X_38))]]) ).
cnf(refute_0_44,plain,
( apply(apply(apply(s,t),t),apply(X_37,X_38)) != apply(apply(X_37,X_38),apply(X_37,X_38))
| apply(apply(apply(s,t),t),apply(X_37,X_38)) = apply(apply(apply(apply(s,t),s),X_37),X_38) ),
inference(resolve,[$cnf( $equal(apply(apply(X_37,X_38),apply(X_37,X_38)),apply(apply(apply(apply(s,t),s),X_37),X_38)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
apply(apply(apply(s,t),t),apply(X_37,X_38)) = apply(apply(apply(apply(s,t),s),X_37),X_38),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),t),apply(X_37,X_38)),apply(apply(X_37,X_38),apply(X_37,X_38))) )],[refute_0_32,refute_0_44]) ).
cnf(refute_0_46,plain,
( apply(apply(apply(s,t),t),apply(X_37,X_38)) != apply(apply(apply(apply(s,t),s),X_37),X_38)
| apply(apply(apply(apply(s,t),s),X_37),X_38) = apply(apply(apply(s,t),t),apply(X_37,X_38)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,t),t),apply(X_37,X_38)))),bind(Y0,$fot(apply(apply(apply(apply(s,t),s),X_37),X_38)))]]) ).
cnf(refute_0_47,plain,
apply(apply(apply(apply(s,t),s),X_37),X_38) = apply(apply(apply(s,t),t),apply(X_37,X_38)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),t),apply(X_37,X_38)),apply(apply(apply(apply(s,t),s),X_37),X_38)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) = apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18)),
inference(subst,[],[refute_0_47:[bind(X_37,$fot(apply(b,X_17))),bind(X_38,$fot(X_18))]]) ).
cnf(refute_0_49,plain,
( apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) != apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))
| apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) != apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18))
| apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18)) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18),apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))) ),[0],$fot(apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18)))]]) ).
cnf(refute_0_50,plain,
( apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18) != apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))
| apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18)) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18),apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
apply(apply(apply(s,t),t),apply(apply(b,X_17),X_18)) = apply(X_17,apply(X_18,apply(apply(b,X_17),X_18))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,t),s),apply(b,X_17)),X_18),apply(X_17,apply(X_18,apply(apply(b,X_17),X_18)))) )],[refute_0_24,refute_0_50]) ).
cnf(refute_0_52,plain,
apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)) = apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))),
inference(subst,[],[refute_0_51:[bind(X_17,$fot(combinator)),bind(X_18,$fot(X_124))]]) ).
cnf(refute_0_53,plain,
( apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)) != apply(combinator,apply(X_124,apply(apply(b,combinator),X_124)))
| apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))) = apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)))),bind(Y0,$fot(apply(combinator,apply(X_124,apply(apply(b,combinator),X_124)))))]]) ).
cnf(refute_0_54,plain,
apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))) = apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)),apply(combinator,apply(X_124,apply(apply(b,combinator),X_124)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( apply(X_124,apply(apply(b,combinator),X_124)) != apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124))
| apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))) != apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124))
| apply(X_124,apply(apply(b,combinator),X_124)) = apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_124,apply(apply(b,combinator),X_124)),apply(combinator,apply(X_124,apply(apply(b,combinator),X_124)))) ),[1],$fot(apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)))]]) ).
cnf(refute_0_56,plain,
( apply(X_124,apply(apply(b,combinator),X_124)) != apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124))
| apply(X_124,apply(apply(b,combinator),X_124)) = apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(X_124,apply(apply(b,combinator),X_124))),apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
apply(X_124,apply(apply(b,combinator),X_124)) != apply(apply(apply(s,t),t),apply(apply(b,combinator),X_124)),
inference(resolve,[$cnf( $equal(apply(X_124,apply(apply(b,combinator),X_124)),apply(combinator,apply(X_124,apply(apply(b,combinator),X_124)))) )],[refute_0_56,refute_0_0]) ).
cnf(refute_0_58,plain,
apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t))) != apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t))),
inference(subst,[],[refute_0_57:[bind(X_124,$fot(apply(apply(s,t),t)))]]) ).
cnf(refute_0_59,plain,
apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t))) = apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t))),
introduced(tautology,[refl,[$fot(apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t))))]]) ).
cnf(refute_0_60,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t))),apply(apply(apply(s,t),t),apply(apply(b,combinator),apply(apply(s,t),t)))) )],[refute_0_59,refute_0_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL019-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 14:06:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 127.58/127.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 127.58/127.80
% 127.58/127.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 127.58/127.80
%------------------------------------------------------------------------------