TSTP Solution File: COL079-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL079-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 1.95s 2.20s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of clauses : 66 ( 33 unt; 0 nHn; 38 RR)
% Number of literals : 111 ( 110 equ; 47 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; 2 con; 0-2 aty)
% Number of variables : 150 ( 2 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_TRC2a,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b) ).
cnf(refute_0_0,plain,
( apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| X = apply(abstraction,apply(abstraction,apply(abstraction,X_87))) ),
inference(subst,[],[extensionality2:[bind(Y,$fot(apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))]]) ).
cnf(refute_0_1,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) != apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))
| X = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86) ),
inference(subst,[],[extensionality2:[bind(Y,$fot(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)),
inference(subst,[],[abstraction:[bind(Y,$fot(k(apply(X_13,Z))))]]) ).
cnf(refute_0_3,plain,
apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z) = apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z)),
inference(subst,[],[abstraction:[bind(X,$fot(apply(abstraction,X_6)))]]) ).
cnf(refute_0_4,plain,
apply(apply(apply(abstraction,X_2),k(X)),X_4) = apply(apply(X_2,k(X_4)),apply(k(X),X_4)),
inference(subst,[],[abstraction:[bind(X,$fot(X_2)),bind(Y,$fot(k(X))),bind(Z,$fot(X_4))]]) ).
cnf(refute_0_5,plain,
apply(k(X),X_4) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(X_4))]]) ).
cnf(refute_0_6,plain,
( apply(apply(apply(abstraction,X_2),k(X)),X_4) != apply(apply(X_2,k(X_4)),apply(k(X),X_4))
| apply(k(X),X_4) != X
| apply(apply(apply(abstraction,X_2),k(X)),X_4) = apply(apply(X_2,k(X_4)),X) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,X_2),k(X)),X_4),apply(apply(X_2,k(X_4)),apply(k(X),X_4))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(abstraction,X_2),k(X)),X_4) != apply(apply(X_2,k(X_4)),apply(k(X),X_4))
| apply(apply(apply(abstraction,X_2),k(X)),X_4) = apply(apply(X_2,k(X_4)),X) ),
inference(resolve,[$cnf( $equal(apply(k(X),X_4),X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
apply(apply(apply(abstraction,X_2),k(X)),X_4) = apply(apply(X_2,k(X_4)),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X_2),k(X)),X_4),apply(apply(X_2,k(X_4)),apply(k(X),X_4))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z)) = apply(apply(X_6,k(apply(Y,Z))),Z),
inference(subst,[],[refute_0_8:[bind(X,$fot(Z)),bind(X_2,$fot(X_6)),bind(X_4,$fot(apply(Y,Z)))]]) ).
cnf(refute_0_10,plain,
( apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z)) != apply(apply(X_6,k(apply(Y,Z))),Z)
| apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z) != apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z))
| apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z) = apply(apply(X_6,k(apply(Y,Z))),Z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z),apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z))) ),[1],$fot(apply(apply(X_6,k(apply(Y,Z))),Z))]]) ).
cnf(refute_0_11,plain,
( apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z) != apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z))
| apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z) = apply(apply(X_6,k(apply(Y,Z))),Z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z)),apply(apply(X_6,k(apply(Y,Z))),Z)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z) = apply(apply(X_6,k(apply(Y,Z))),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,X_6)),Y),Z),apply(apply(apply(abstraction,X_6),k(Z)),apply(Y,Z))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_13)),bind(X_6,$fot(apply(abstraction,X)))]]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) != apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z)
| apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z))),bind(Y0,$fot(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z)))]]) ).
cnf(refute_0_18,plain,
apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z),apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) != apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))
| apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) != apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z)
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))) ),[0],$fot(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z))]]) ).
cnf(refute_0_20,plain,
( apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) != apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))) )],[refute_0_2,refute_0_20]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(abstraction,X),Y),Z) != apply(apply(X,k(Z)),apply(Y,Z))
| apply(apply(X,k(Z)),apply(Y,Z)) = apply(apply(apply(abstraction,X),Y),Z) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(apply(abstraction,X),Y),Z))),bind(Y0,$fot(apply(apply(X,k(Z)),apply(Y,Z))))]]) ).
cnf(refute_0_23,plain,
apply(apply(X,k(Z)),apply(Y,Z)) = apply(apply(apply(abstraction,X),Y),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X),Y),Z),apply(apply(X,k(Z)),apply(Y,Z))) )],[abstraction,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(X,k(Z)),apply(X_13,Z)) = apply(apply(apply(abstraction,X),X_13),Z),
inference(subst,[],[refute_0_23:[bind(Y,$fot(X_13))]]) ).
cnf(refute_0_25,plain,
apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(X,k(Z)),apply(X_13,Z)),
inference(subst,[],[refute_0_8:[bind(X,$fot(apply(X_13,Z))),bind(X_2,$fot(X)),bind(X_4,$fot(Z))]]) ).
cnf(refute_0_26,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_16,refute_0_26]) ).
cnf(refute_0_28,plain,
( apply(apply(X,k(Z)),apply(X_13,Z)) != apply(apply(apply(abstraction,X),X_13),Z)
| apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) != apply(apply(X,k(Z)),apply(X_13,Z))
| apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(apply(abstraction,X),X_13),Z) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z))),bind(Y0,$fot(apply(apply(X,k(Z)),apply(X_13,Z)))),bind(Z0,$fot(apply(apply(apply(abstraction,X),X_13),Z)))]]) ).
cnf(refute_0_29,plain,
( apply(apply(X,k(Z)),apply(X_13,Z)) != apply(apply(apply(abstraction,X),X_13),Z)
| apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(apply(abstraction,X),X_13),Z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),apply(apply(X,k(Z)),apply(X_13,Z))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) = apply(apply(apply(abstraction,X),X_13),Z),
inference(resolve,[$cnf( $equal(apply(apply(X,k(Z)),apply(X_13,Z)),apply(apply(apply(abstraction,X),X_13),Z)) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) = apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),
inference(subst,[],[refute_0_23:[bind(Y,$fot(k(apply(X_13,Z))))]]) ).
cnf(refute_0_32,plain,
( apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) != apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z)
| apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) != apply(apply(apply(abstraction,X),X_13),Z)
| apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) = apply(apply(apply(abstraction,X),X_13),Z) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)))),bind(Y0,$fot(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z))),bind(Z0,$fot(apply(apply(apply(abstraction,X),X_13),Z)))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z) != apply(apply(apply(abstraction,X),X_13),Z)
| apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) = apply(apply(apply(abstraction,X),X_13),Z) ),
inference(resolve,[$cnf( $equal(apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)),apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) = apply(apply(apply(abstraction,X),X_13),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X),k(apply(X_13,Z))),Z),apply(apply(apply(abstraction,X),X_13),Z)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)) != apply(apply(apply(abstraction,X),X_13),Z)
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) != apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(apply(abstraction,X),X_13),Z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z),apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))) ),[1],$fot(apply(apply(apply(abstraction,X),X_13),Z))]]) ).
cnf(refute_0_36,plain,
( apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) != apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(apply(abstraction,X),X_13),Z) ),
inference(resolve,[$cnf( $equal(apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z)),apply(apply(apply(abstraction,X),X_13),Z)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z) = apply(apply(apply(abstraction,X),X_13),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X))),X_13),Z),apply(apply(X,k(Z)),apply(k(apply(X_13,Z)),Z))) )],[refute_0_21,refute_0_36]) ).
cnf(refute_0_38,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) = apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_84)),bind(Z,$fot(n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))),bind(X_13,$fot(X_86))]]) ).
cnf(refute_0_39,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) != apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) != apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))
| apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) = apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))),apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))) ),[1],$fot(apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))))]]) ).
cnf(refute_0_40,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) != apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))
| apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) = apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))),apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) != apply(apply(apply(abstraction,X_84),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))
| X = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86) ),
inference(resolve,[$cnf( $equal(apply(X,n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))),apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),n(X,apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))) )],[refute_0_40,refute_0_1]) ).
cnf(refute_0_42,plain,
( apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) != apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))
| apply(apply(abstraction,X_84),X_86) = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(apply(apply(abstraction,X_84),X_86)))]]) ).
cnf(refute_0_43,plain,
apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))) = apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))),
introduced(tautology,[refl,[$fot(apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))))]]) ).
cnf(refute_0_44,plain,
apply(apply(abstraction,X_84),X_86) = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86))),apply(apply(apply(abstraction,X_84),X_86),n(apply(apply(abstraction,X_84),X_86),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_84))),X_86)))) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),
inference(subst,[],[refute_0_44:[bind(X_84,$fot(X_87)),bind(X_86,$fot(n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))))]]) ).
cnf(refute_0_46,plain,
( apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) = apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))))),bind(Y0,$fot(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))))]]) ).
cnf(refute_0_47,plain,
apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) = apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))) ),[1],$fot(apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))))]]) ).
cnf(refute_0_49,plain,
( apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) = apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) ),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,X_87),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| X = apply(abstraction,apply(abstraction,apply(abstraction,X_87))) ),
inference(resolve,[$cnf( $equal(apply(X,n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),apply(apply(abstraction,apply(abstraction,apply(abstraction,X_87))),n(X,apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))) )],[refute_0_49,refute_0_0]) ).
cnf(refute_0_51,plain,
( apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) != apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))
| apply(abstraction,X_87) = apply(abstraction,apply(abstraction,apply(abstraction,X_87))) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(apply(abstraction,X_87)))]]) ).
cnf(refute_0_52,plain,
apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87))))) = apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),
introduced(tautology,[refl,[$fot(apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87))))))]]) ).
cnf(refute_0_53,plain,
apply(abstraction,X_87) = apply(abstraction,apply(abstraction,apply(abstraction,X_87))),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87))))),apply(apply(abstraction,X_87),n(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
( apply(abstraction,X_87) != apply(abstraction,apply(abstraction,apply(abstraction,X_87)))
| apply(abstraction,apply(abstraction,apply(abstraction,X_87))) = apply(abstraction,X_87) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(apply(abstraction,X_87))),bind(Y0,$fot(apply(abstraction,apply(abstraction,apply(abstraction,X_87)))))]]) ).
cnf(refute_0_55,plain,
apply(abstraction,apply(abstraction,apply(abstraction,X_87))) = apply(abstraction,X_87),
inference(resolve,[$cnf( $equal(apply(abstraction,X_87),apply(abstraction,apply(abstraction,apply(abstraction,X_87)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) = apply(abstraction,b),
inference(subst,[],[refute_0_55:[bind(X_87,$fot(b))]]) ).
cnf(refute_0_57,plain,
( apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b)
| apply(abstraction,b) != apply(abstraction,b)
| apply(abstraction,apply(abstraction,apply(abstraction,b))) = apply(abstraction,b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)) ),[0],$fot(apply(abstraction,b))]]) ).
cnf(refute_0_58,plain,
( apply(abstraction,b) != apply(abstraction,b)
| apply(abstraction,apply(abstraction,apply(abstraction,b))) = apply(abstraction,b) ),
inference(resolve,[$cnf( $equal(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
apply(abstraction,b) != apply(abstraction,b),
inference(resolve,[$cnf( $equal(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)) )],[refute_0_58,prove_TRC2a]) ).
cnf(refute_0_60,plain,
apply(abstraction,b) = apply(abstraction,b),
introduced(tautology,[refl,[$fot(apply(abstraction,b))]]) ).
cnf(refute_0_61,plain,
$false,
inference(resolve,[$cnf( $equal(apply(abstraction,b),apply(abstraction,b)) )],[refute_0_60,refute_0_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL079-2 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 14:17:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.95/2.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.95/2.20
% 1.95/2.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.95/2.20
%------------------------------------------------------------------------------