TSTP Solution File: COL080-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL080-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 36.17s 36.39s
% Output : CNFRefutation 36.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of clauses : 56 ( 27 unt; 0 nHn; 33 RR)
% Number of literals : 94 ( 93 equ; 40 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 : 114 ( 9 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_TRC2b,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,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( $equal(apply(k(X),n(k(X),X_32)),apply(X_32,n(k(X),X_32))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( X_193 != apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58)))))
| k(X_193) = apply(abstraction,apply(abstraction,k(X_58))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_193)),bind(X_32,$fot(apply(abstraction,apply(abstraction,k(X_58)))))]]) ).
cnf(refute_0_6,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) != apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))
| X = apply(apply(abstraction,apply(abstraction,k(X_58))),X_56) ),
inference(subst,[],[extensionality2:[bind(Y,$fot(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))]]) ).
cnf(refute_0_7,plain,
apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z)),
inference(subst,[],[abstraction:[bind(X,$fot(apply(abstraction,k(X_12))))]]) ).
cnf(refute_0_8,plain,
apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(apply(k(X),k(X_5)),apply(X_4,X_5)),
inference(subst,[],[abstraction:[bind(X,$fot(k(X))),bind(Y,$fot(X_4)),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_9,plain,
apply(k(X),k(X_5)) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(k(X_5)))]]) ).
cnf(refute_0_10,plain,
( apply(apply(apply(abstraction,k(X)),X_4),X_5) != apply(apply(k(X),k(X_5)),apply(X_4,X_5))
| apply(k(X),k(X_5)) != X
| apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(X,apply(X_4,X_5)) ),
introduced(tautology,[equality,[$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_11,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( $equal(apply(k(X),k(X_5)),X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
apply(apply(apply(abstraction,k(X)),X_4),X_5) = apply(X,apply(X_4,X_5)),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,k(X)),X_4),X_5),apply(apply(k(X),k(X_5)),apply(X_4,X_5))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z)) = apply(X_12,apply(k(Z),apply(Y,Z))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_12)),bind(X_4,$fot(k(Z))),bind(X_5,$fot(apply(Y,Z)))]]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) != apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z))
| apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z)) != apply(X_12,apply(k(Z),apply(Y,Z)))
| apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(X_12,apply(k(Z),apply(Y,Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z),apply(X_12,apply(k(Z),apply(Y,Z)))) ),[0],$fot(apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z)))]]) ).
cnf(refute_0_15,plain,
( apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) != apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z))
| apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(X_12,apply(k(Z),apply(Y,Z))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z)),apply(X_12,apply(k(Z),apply(Y,Z)))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(X_12,apply(k(Z),apply(Y,Z))),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z),apply(apply(apply(abstraction,k(X_12)),k(Z)),apply(Y,Z))) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
apply(k(Z),apply(Y,Z)) = Z,
inference(subst,[],[k_definition:[bind(X,$fot(Z)),bind(Y,$fot(apply(Y,Z)))]]) ).
cnf(refute_0_18,plain,
apply(X_12,apply(k(Z),apply(Y,Z))) = apply(X_12,apply(k(Z),apply(Y,Z))),
introduced(tautology,[refl,[$fot(apply(X_12,apply(k(Z),apply(Y,Z))))]]) ).
cnf(refute_0_19,plain,
( apply(X_12,apply(k(Z),apply(Y,Z))) != apply(X_12,apply(k(Z),apply(Y,Z)))
| apply(k(Z),apply(Y,Z)) != Z
| apply(X_12,apply(k(Z),apply(Y,Z))) = apply(X_12,Z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(X_12,apply(k(Z),apply(Y,Z))),apply(X_12,apply(k(Z),apply(Y,Z)))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_20,plain,
( apply(k(Z),apply(Y,Z)) != Z
| apply(X_12,apply(k(Z),apply(Y,Z))) = apply(X_12,Z) ),
inference(resolve,[$cnf( $equal(apply(X_12,apply(k(Z),apply(Y,Z))),apply(X_12,apply(k(Z),apply(Y,Z)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
apply(X_12,apply(k(Z),apply(Y,Z))) = apply(X_12,Z),
inference(resolve,[$cnf( $equal(apply(k(Z),apply(Y,Z)),Z) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( apply(X_12,apply(k(Z),apply(Y,Z))) != apply(X_12,Z)
| apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) != apply(X_12,apply(k(Z),apply(Y,Z)))
| apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(X_12,Z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z),apply(X_12,apply(k(Z),apply(Y,Z)))) ),[1],$fot(apply(X_12,Z))]]) ).
cnf(refute_0_23,plain,
( apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) != apply(X_12,apply(k(Z),apply(Y,Z)))
| apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(X_12,Z) ),
inference(resolve,[$cnf( $equal(apply(X_12,apply(k(Z),apply(Y,Z))),apply(X_12,Z)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z) = apply(X_12,Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,k(X_12))),Y),Z),apply(X_12,apply(k(Z),apply(Y,Z)))) )],[refute_0_16,refute_0_23]) ).
cnf(refute_0_25,plain,
apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) = apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))),
inference(subst,[],[refute_0_24:[bind(Y,$fot(X_56)),bind(Z,$fot(n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))),bind(X_12,$fot(X_58))]]) ).
cnf(refute_0_26,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) != apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))
| apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) != apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))
| apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) = apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))),apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))) ),[1],$fot(apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))))]]) ).
cnf(refute_0_27,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) != apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))
| apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) = apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))),apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) != apply(X_58,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))
| X = apply(apply(abstraction,apply(abstraction,k(X_58))),X_56) ),
inference(resolve,[$cnf( $equal(apply(X,n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))),apply(apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),n(X,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))) )],[refute_0_27,refute_0_6]) ).
cnf(refute_0_29,plain,
( apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) != apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))
| X_58 = apply(apply(abstraction,apply(abstraction,k(X_58))),X_56) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(X_58))]]) ).
cnf(refute_0_30,plain,
apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))) = apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))),
introduced(tautology,[refl,[$fot(apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))))]]) ).
cnf(refute_0_31,plain,
X_58 = apply(apply(abstraction,apply(abstraction,k(X_58))),X_56),
inference(resolve,[$cnf( $equal(apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56))),apply(X_58,n(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),X_56)))) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
X_58 = apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))),
inference(subst,[],[refute_0_31:[bind(X_56,$fot(n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))))]]) ).
cnf(refute_0_33,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_34,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_35,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( X_58 != apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58)))))
| apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))) = X_58 ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(X_58)),bind(Y0,$fot(apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58)))))))]]) ).
cnf(refute_0_37,plain,
apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))) = X_58,
inference(resolve,[$cnf( $equal(X_58,apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58)))))) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_193 != X_58
| apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))) != X_58
| X_193 = apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_193,apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58)))))) ),[1],$fot(X_58)]]) ).
cnf(refute_0_39,plain,
( X_193 != X_58
| X_193 = apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))) ),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58))))),X_58) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( X_193 != X_58
| k(X_193) = apply(abstraction,apply(abstraction,k(X_58))) ),
inference(resolve,[$cnf( $equal(X_193,apply(apply(abstraction,apply(abstraction,k(X_58))),n(k(X_193),apply(abstraction,apply(abstraction,k(X_58)))))) )],[refute_0_39,refute_0_5]) ).
cnf(refute_0_41,plain,
( X_58 != X_58
| k(X_58) = apply(abstraction,apply(abstraction,k(X_58))) ),
inference(subst,[],[refute_0_40:[bind(X_193,$fot(X_58))]]) ).
cnf(refute_0_42,plain,
X_58 = X_58,
introduced(tautology,[refl,[$fot(X_58)]]) ).
cnf(refute_0_43,plain,
k(X_58) = apply(abstraction,apply(abstraction,k(X_58))),
inference(resolve,[$cnf( $equal(X_58,X_58) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
( k(X_58) != apply(abstraction,apply(abstraction,k(X_58)))
| apply(abstraction,apply(abstraction,k(X_58))) = k(X_58) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(k(X_58))),bind(Y0,$fot(apply(abstraction,apply(abstraction,k(X_58)))))]]) ).
cnf(refute_0_45,plain,
apply(abstraction,apply(abstraction,k(X_58))) = k(X_58),
inference(resolve,[$cnf( $equal(k(X_58),apply(abstraction,apply(abstraction,k(X_58)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
apply(abstraction,apply(abstraction,k(b))) = k(b),
inference(subst,[],[refute_0_45:[bind(X_58,$fot(b))]]) ).
cnf(refute_0_47,plain,
( apply(abstraction,apply(abstraction,k(b))) != k(b)
| k(b) != k(b)
| k(b) = apply(abstraction,apply(abstraction,k(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(k(b),apply(abstraction,apply(abstraction,k(b)))) ),[1],$fot(k(b))]]) ).
cnf(refute_0_48,plain,
( k(b) != k(b)
| k(b) = apply(abstraction,apply(abstraction,k(b))) ),
inference(resolve,[$cnf( $equal(apply(abstraction,apply(abstraction,k(b))),k(b)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
k(b) != k(b),
inference(resolve,[$cnf( $equal(k(b),apply(abstraction,apply(abstraction,k(b)))) )],[refute_0_48,prove_TRC2b]) ).
cnf(refute_0_50,plain,
k(b) = k(b),
introduced(tautology,[refl,[$fot(k(b))]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(k(b),k(b)) )],[refute_0_50,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL080-2 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue May 31 07:12:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 36.17/36.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.17/36.39
% 36.17/36.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.17/36.39
%------------------------------------------------------------------------------