TSTP Solution File: COL081-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL081-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 00:36:27 EDT 2022
% Result : Unsatisfiable 39.37s 39.57s
% Output : CNFRefutation 39.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 18
% Syntax : Number of clauses : 69 ( 35 unt; 0 nHn; 36 RR)
% Number of literals : 113 ( 112 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 142 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(k(X),Y) = X ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ).
cnf(extensionality2,axiom,
( X = Y
| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ).
cnf(prove_TRC2c,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))) ).
cnf(refute_0_0,plain,
( apply(k(X),n(k(X),X_32)) != apply(X_32,n(k(X),X_32))
| k(X) = X_32 ),
inference(subst,[],[extensionality2:[bind(X,$fot(k(X))),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_1,plain,
apply(k(X),n(k(X),X_32)) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(n(k(X),X_32)))]]) ).
cnf(refute_0_2,plain,
( X != apply(X_32,n(k(X),X_32))
| apply(k(X),n(k(X),X_32)) != X
| apply(k(X),n(k(X),X_32)) = apply(X_32,n(k(X),X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(k(X),n(k(X),X_32)),X) ),[1],$fot(apply(X_32,n(k(X),X_32)))]]) ).
cnf(refute_0_3,plain,
( X != apply(X_32,n(k(X),X_32))
| apply(k(X),n(k(X),X_32)) = apply(X_32,n(k(X),X_32)) ),
inference(resolve,[$cnf( $equal(apply(k(X),n(k(X),X_32)),X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( X != apply(X_32,n(k(X),X_32))
| k(X) = X_32 ),
inference(resolve,[$cnf( $equal(apply(k(X),n(k(X),X_32)),apply(X_32,n(k(X),X_32))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( X != apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219)))))
| k(X) = apply(abstraction,k(k(X_219))) ),
inference(subst,[],[refute_0_4:[bind(X_32,$fot(apply(abstraction,k(k(X_219)))))]]) ).
cnf(refute_0_6,plain,
apply(apply(apply(abstraction,X_3),k(X)),X_5) = apply(apply(X_3,k(X_5)),apply(k(X),X_5)),
inference(subst,[],[abstraction:[bind(X,$fot(X_3)),bind(Y,$fot(k(X))),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_7,plain,
apply(k(X),X_5) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(X_5))]]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(abstraction,X_3),k(X)),X_5) != apply(apply(X_3,k(X_5)),apply(k(X),X_5))
| apply(k(X),X_5) != X
| apply(apply(apply(abstraction,X_3),k(X)),X_5) = apply(apply(X_3,k(X_5)),X) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,X_3),k(X)),X_5),apply(apply(X_3,k(X_5)),apply(k(X),X_5))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_9,plain,
( apply(apply(apply(abstraction,X_3),k(X)),X_5) != apply(apply(X_3,k(X_5)),apply(k(X),X_5))
| apply(apply(apply(abstraction,X_3),k(X)),X_5) = apply(apply(X_3,k(X_5)),X) ),
inference(resolve,[$cnf( $equal(apply(k(X),X_5),X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
apply(apply(apply(abstraction,X_3),k(X)),X_5) = apply(apply(X_3,k(X_5)),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X_3),k(X)),X_5),apply(apply(X_3,k(X_5)),apply(k(X),X_5))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)) = apply(apply(abstraction,k(k(X_214))),X),
inference(subst,[],[refute_0_10:[bind(X_3,$fot(abstraction)),bind(X_5,$fot(k(X_214)))]]) ).
cnf(refute_0_12,plain,
( X_208 != apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X))))
| k(X_208) = apply(apply(apply(abstraction,abstraction),X_87),k(X)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_208)),bind(X_32,$fot(apply(apply(apply(abstraction,abstraction),X_87),k(X))))]]) ).
cnf(refute_0_13,plain,
apply(k(X),apply(apply(X_87,k(X)),X_89)) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(apply(apply(X_87,k(X)),X_89)))]]) ).
cnf(refute_0_14,plain,
apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(apply(k(X),k(X_5)),apply(X_4,X_5)),
inference(subst,[],[abstraction:[bind(X,$fot(k(X))),bind(Y,$fot(X_4)),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_15,plain,
apply(k(X),k(X_5)) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(k(X_5)))]]) ).
cnf(refute_0_16,plain,
( apply(apply(apply(abstraction,k(X)),X_4),X_5) != apply(apply(k(X),k(X_5)),apply(X_4,X_5))
| apply(k(X),k(X_5)) != X
| apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(X,apply(X_4,X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,k(X)),X_4),X_5),apply(apply(k(X),k(X_5)),apply(X_4,X_5))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(abstraction,k(X)),X_4),X_5) != apply(apply(k(X),k(X_5)),apply(X_4,X_5))
| apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(X,apply(X_4,X_5)) ),
inference(resolve,[$cnf( $equal(apply(k(X),k(X_5)),X) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(X,apply(X_4,X_5)),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,k(X)),X_4),X_5),apply(apply(k(X),k(X_5)),apply(X_4,X_5))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(abstraction,k(X_22)),apply(Y,X_22)),X_24) = apply(X_22,apply(apply(Y,X_22),X_24)),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_22)),bind(X_4,$fot(apply(Y,X_22))),bind(X_5,$fot(X_24))]]) ).
cnf(refute_0_20,plain,
apply(apply(apply(abstraction,abstraction),Y),X_22) = apply(apply(abstraction,k(X_22)),apply(Y,X_22)),
inference(subst,[],[abstraction:[bind(X,$fot(abstraction)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_21,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( apply(apply(apply(abstraction,abstraction),Y),X_22) != apply(apply(abstraction,k(X_22)),apply(Y,X_22))
| apply(apply(abstraction,k(X_22)),apply(Y,X_22)) = apply(apply(apply(abstraction,abstraction),Y),X_22) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(apply(apply(apply(abstraction,abstraction),Y),X_22))),bind(Y0,$fot(apply(apply(abstraction,k(X_22)),apply(Y,X_22))))]]) ).
cnf(refute_0_25,plain,
apply(apply(abstraction,k(X_22)),apply(Y,X_22)) = apply(apply(apply(abstraction,abstraction),Y),X_22),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,abstraction),Y),X_22),apply(apply(abstraction,k(X_22)),apply(Y,X_22))) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( apply(apply(apply(abstraction,k(X_22)),apply(Y,X_22)),X_24) != apply(X_22,apply(apply(Y,X_22),X_24))
| apply(apply(abstraction,k(X_22)),apply(Y,X_22)) != apply(apply(apply(abstraction,abstraction),Y),X_22)
| apply(apply(apply(apply(abstraction,abstraction),Y),X_22),X_24) = apply(X_22,apply(apply(Y,X_22),X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,k(X_22)),apply(Y,X_22)),X_24),apply(X_22,apply(apply(Y,X_22),X_24))) ),[0,0],$fot(apply(apply(apply(abstraction,abstraction),Y),X_22))]]) ).
cnf(refute_0_27,plain,
( apply(apply(apply(abstraction,k(X_22)),apply(Y,X_22)),X_24) != apply(X_22,apply(apply(Y,X_22),X_24))
| apply(apply(apply(apply(abstraction,abstraction),Y),X_22),X_24) = apply(X_22,apply(apply(Y,X_22),X_24)) ),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,k(X_22)),apply(Y,X_22)),apply(apply(apply(abstraction,abstraction),Y),X_22)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
apply(apply(apply(apply(abstraction,abstraction),Y),X_22),X_24) = apply(X_22,apply(apply(Y,X_22),X_24)),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,k(X_22)),apply(Y,X_22)),X_24),apply(X_22,apply(apply(Y,X_22),X_24))) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89) = apply(k(X),apply(apply(X_87,k(X)),X_89)),
inference(subst,[],[refute_0_28:[bind(Y,$fot(X_87)),bind(X_22,$fot(k(X))),bind(X_24,$fot(X_89))]]) ).
cnf(refute_0_30,plain,
( apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89) != apply(k(X),apply(apply(X_87,k(X)),X_89))
| apply(k(X),apply(apply(X_87,k(X)),X_89)) = apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89))),bind(Y0,$fot(apply(k(X),apply(apply(X_87,k(X)),X_89))))]]) ).
cnf(refute_0_31,plain,
apply(k(X),apply(apply(X_87,k(X)),X_89)) = apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89),apply(k(X),apply(apply(X_87,k(X)),X_89))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( apply(k(X),apply(apply(X_87,k(X)),X_89)) != X
| apply(k(X),apply(apply(X_87,k(X)),X_89)) != apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89)
| apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89) = X ),
introduced(tautology,[equality,[$cnf( $equal(apply(k(X),apply(apply(X_87,k(X)),X_89)),X) ),[0],$fot(apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89))]]) ).
cnf(refute_0_33,plain,
( apply(k(X),apply(apply(X_87,k(X)),X_89)) != X
| apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89) = X ),
inference(resolve,[$cnf( $equal(apply(k(X),apply(apply(X_87,k(X)),X_89)),apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),X_89) = X,
inference(resolve,[$cnf( $equal(apply(k(X),apply(apply(X_87,k(X)),X_89)),X) )],[refute_0_13,refute_0_33]) ).
cnf(refute_0_35,plain,
apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X)))) = X,
inference(subst,[],[refute_0_34:[bind(X_89,$fot(n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X)))))]]) ).
cnf(refute_0_36,plain,
( X_208 != X
| apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X)))) != X
| X_208 = apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_208,apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X))))) ),[1],$fot(X)]]) ).
cnf(refute_0_37,plain,
( X_208 != X
| X_208 = apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X)))),X) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_208 != X
| k(X_208) = apply(apply(apply(abstraction,abstraction),X_87),k(X)) ),
inference(resolve,[$cnf( $equal(X_208,apply(apply(apply(apply(abstraction,abstraction),X_87),k(X)),n(k(X_208),apply(apply(apply(abstraction,abstraction),X_87),k(X))))) )],[refute_0_37,refute_0_12]) ).
cnf(refute_0_39,plain,
( X != X
| k(X) = apply(apply(apply(abstraction,abstraction),X_87),k(X)) ),
inference(subst,[],[refute_0_38:[bind(X_208,$fot(X))]]) ).
cnf(refute_0_40,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_41,plain,
k(X) = apply(apply(apply(abstraction,abstraction),X_87),k(X)),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
k(X_214) = apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)),
inference(subst,[],[refute_0_41:[bind(X,$fot(X_214)),bind(X_87,$fot(k(X)))]]) ).
cnf(refute_0_43,plain,
( k(X_214) != apply(apply(apply(abstraction,abstraction),k(X)),k(X_214))
| apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)) = k(X_214) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(k(X_214))),bind(Y0,$fot(apply(apply(apply(abstraction,abstraction),k(X)),k(X_214))))]]) ).
cnf(refute_0_44,plain,
apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)) = k(X_214),
inference(resolve,[$cnf( $equal(k(X_214),apply(apply(apply(abstraction,abstraction),k(X)),k(X_214))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)) != apply(apply(abstraction,k(k(X_214))),X)
| apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)) != k(X_214)
| k(X_214) = apply(apply(abstraction,k(k(X_214))),X) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)),apply(apply(abstraction,k(k(X_214))),X)) ),[0],$fot(k(X_214))]]) ).
cnf(refute_0_46,plain,
( apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)) != apply(apply(abstraction,k(k(X_214))),X)
| k(X_214) = apply(apply(abstraction,k(k(X_214))),X) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)),k(X_214)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
k(X_214) = apply(apply(abstraction,k(k(X_214))),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,abstraction),k(X)),k(X_214)),apply(apply(abstraction,k(k(X_214))),X)) )],[refute_0_11,refute_0_46]) ).
cnf(refute_0_48,plain,
k(X_219) = apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))),
inference(subst,[],[refute_0_47:[bind(X,$fot(n(k(X),apply(abstraction,k(k(X_219)))))),bind(X_214,$fot(X_219))]]) ).
cnf(refute_0_49,plain,
( k(X_219) != apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219)))))
| apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))) = k(X_219) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(k(X_219))),bind(Y0,$fot(apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219)))))))]]) ).
cnf(refute_0_50,plain,
apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))) = k(X_219),
inference(resolve,[$cnf( $equal(k(X_219),apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219)))))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( X != k(X_219)
| apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))) != k(X_219)
| X = apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219)))))) ),[1],$fot(k(X_219))]]) ).
cnf(refute_0_52,plain,
( X != k(X_219)
| X = apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))) ),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219))))),k(X_219)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( X != k(X_219)
| k(X) = apply(abstraction,k(k(X_219))) ),
inference(resolve,[$cnf( $equal(X,apply(apply(abstraction,k(k(X_219))),n(k(X),apply(abstraction,k(k(X_219)))))) )],[refute_0_52,refute_0_5]) ).
cnf(refute_0_54,plain,
( k(X_219) != k(X_219)
| k(k(X_219)) = apply(abstraction,k(k(X_219))) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(k(X_219)))]]) ).
cnf(refute_0_55,plain,
k(X_219) = k(X_219),
introduced(tautology,[refl,[$fot(k(X_219))]]) ).
cnf(refute_0_56,plain,
k(k(X_219)) = apply(abstraction,k(k(X_219))),
inference(resolve,[$cnf( $equal(k(X_219),k(X_219)) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( k(k(X_219)) != apply(abstraction,k(k(X_219)))
| apply(abstraction,k(k(X_219))) = k(k(X_219)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(k(k(X_219)))),bind(Y0,$fot(apply(abstraction,k(k(X_219)))))]]) ).
cnf(refute_0_58,plain,
apply(abstraction,k(k(X_219))) = k(k(X_219)),
inference(resolve,[$cnf( $equal(k(k(X_219)),apply(abstraction,k(k(X_219)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
apply(abstraction,k(k(b))) = k(k(b)),
inference(subst,[],[refute_0_58:[bind(X_219,$fot(b))]]) ).
cnf(refute_0_60,plain,
( apply(abstraction,k(k(b))) != k(k(b))
| k(k(b)) != k(k(b))
| k(k(b)) = apply(abstraction,k(k(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(k(k(b)),apply(abstraction,k(k(b)))) ),[1],$fot(k(k(b)))]]) ).
cnf(refute_0_61,plain,
( k(k(b)) != k(k(b))
| k(k(b)) = apply(abstraction,k(k(b))) ),
inference(resolve,[$cnf( $equal(apply(abstraction,k(k(b))),k(k(b))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
k(k(b)) != k(k(b)),
inference(resolve,[$cnf( $equal(k(k(b)),apply(abstraction,k(k(b)))) )],[refute_0_61,prove_TRC2c]) ).
cnf(refute_0_63,plain,
k(k(b)) = k(k(b)),
introduced(tautology,[refl,[$fot(k(k(b)))]]) ).
cnf(refute_0_64,plain,
$false,
inference(resolve,[$cnf( $equal(k(k(b)),k(k(b))) )],[refute_0_63,refute_0_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : COL081-2 : TPTP v8.1.0. Released v1.2.0.
% 0.09/0.11 % Command : metis --show proof --show saturation %s
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Tue May 31 05:44:58 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 39.37/39.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.37/39.57
% 39.37/39.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.37/39.57
%------------------------------------------------------------------------------