TSTP Solution File: LCL133-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL133-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Sun Jul 17 12:49:49 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of clauses : 105 ( 51 unt; 0 nHn; 56 RR)
% Number of literals : 184 ( 183 equ; 81 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 238 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(lemma_antecedent,negated_conjecture,
implies(X,Y) = implies(Y,X) ).
cnf(prove_wajsberg_lemma,negated_conjecture,
x != y ).
cnf(refute_0_0,plain,
implies(implies(X_7,implies(X,Y)),implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_7)),bind(Y,$fot(implies(X,Y))),bind(Z,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_1,plain,
( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) != truth
| implies(implies(X_7,implies(X,Y)),implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != truth
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z))))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_2,plain,
( implies(implies(X_7,implies(X,Y)),implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != truth
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[wajsberg_2,refute_0_1]) ).
cnf(refute_0_3,plain,
implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z))))),truth) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
implies(truth,implies(X_4,truth)) = implies(X_4,truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_4,truth)))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X,Y) != implies(Y,X)
| implies(Y,X) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(implies(Y,X)))]]) ).
cnf(refute_0_9,plain,
implies(Y,X) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),implies(Y,X)) )],[lemma_antecedent,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(implies(X,Y),Y) = implies(Y,implies(X,Y)),
inference(subst,[],[refute_0_9:[bind(X,$fot(Y)),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_11,plain,
( implies(implies(X,Y),Y) != implies(Y,implies(X,Y))
| implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(Y,implies(X,Y)) = implies(implies(Y,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) ),[0],$fot(implies(Y,implies(X,Y)))]]) ).
cnf(refute_0_12,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(Y,implies(X,Y)) = implies(implies(Y,X),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(Y,implies(X,Y))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(implies(Y,X),X) = implies(X,implies(Y,X)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_14,plain,
( implies(Y,implies(X,Y)) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) != implies(X,implies(Y,X))
| implies(Y,implies(X,Y)) = implies(X,implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(Y,implies(X,Y)),implies(X,implies(Y,X))) ),[0],$fot(implies(implies(Y,X),X))]]) ).
cnf(refute_0_15,plain,
( implies(Y,implies(X,Y)) != implies(implies(Y,X),X)
| implies(Y,implies(X,Y)) = implies(X,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),X),implies(X,implies(Y,X))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(Y,implies(X,Y)) = implies(X,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(X,Y)),implies(implies(Y,X),X)) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
implies(Y,implies(X,Y)) = implies(X,implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(truth,implies(X_4,truth)) = implies(X_4,implies(truth,X_4)),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_4)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_19,plain,
( implies(truth,implies(X_4,truth)) != implies(X_4,implies(truth,X_4))
| implies(truth,implies(X_4,truth)) != implies(X_4,truth)
| implies(X_4,implies(truth,X_4)) = implies(X_4,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_4,truth)),implies(X_4,truth)) ),[0],$fot(implies(X_4,implies(truth,X_4)))]]) ).
cnf(refute_0_20,plain,
( implies(truth,implies(X_4,truth)) != implies(X_4,truth)
| implies(X_4,implies(truth,X_4)) = implies(X_4,truth) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_4,truth)),implies(X_4,implies(truth,X_4))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(X_4,implies(truth,X_4)) = implies(X_4,truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_4,truth)),implies(X_4,truth)) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(truth,X_4) = X_4,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_23,plain,
implies(X_4,implies(truth,X_4)) = implies(X_4,implies(truth,X_4)),
introduced(tautology,[refl,[$fot(implies(X_4,implies(truth,X_4)))]]) ).
cnf(refute_0_24,plain,
( implies(X_4,implies(truth,X_4)) != implies(X_4,implies(truth,X_4))
| implies(truth,X_4) != X_4
| implies(X_4,implies(truth,X_4)) = implies(X_4,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_4,implies(truth,X_4)),implies(X_4,implies(truth,X_4))) ),[1,1],$fot(X_4)]]) ).
cnf(refute_0_25,plain,
( implies(truth,X_4) != X_4
| implies(X_4,implies(truth,X_4)) = implies(X_4,X_4) ),
inference(resolve,[$cnf( $equal(implies(X_4,implies(truth,X_4)),implies(X_4,implies(truth,X_4))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(X_4,implies(truth,X_4)) = implies(X_4,X_4),
inference(resolve,[$cnf( $equal(implies(truth,X_4),X_4) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( implies(X_4,implies(truth,X_4)) != implies(X_4,X_4)
| implies(X_4,implies(truth,X_4)) != implies(X_4,truth)
| implies(X_4,X_4) = implies(X_4,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_4,implies(truth,X_4)),implies(X_4,truth)) ),[0],$fot(implies(X_4,X_4))]]) ).
cnf(refute_0_28,plain,
( implies(X_4,implies(truth,X_4)) != implies(X_4,truth)
| implies(X_4,X_4) = implies(X_4,truth) ),
inference(resolve,[$cnf( $equal(implies(X_4,implies(truth,X_4)),implies(X_4,X_4)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(truth,X) = implies(X,truth),
inference(subst,[],[lemma_antecedent:[bind(X,$fot(truth)),bind(Y,$fot(X))]]) ).
cnf(refute_0_30,plain,
( implies(truth,X) != X
| implies(truth,X) != implies(X,truth)
| implies(X,truth) = X ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,X),X) ),[0],$fot(implies(X,truth))]]) ).
cnf(refute_0_31,plain,
( implies(truth,X) != X
| implies(X,truth) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),implies(X,truth)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(X,truth) = X,
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(X_4,truth) = X_4,
inference(subst,[],[refute_0_32:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_34,plain,
( implies(X_4,X_4) != implies(X_4,truth)
| implies(X_4,truth) != X_4
| implies(X_4,X_4) = X_4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_4,X_4),X_4) ),[0],$fot(implies(X_4,truth))]]) ).
cnf(refute_0_35,plain,
( implies(X_4,X_4) != implies(X_4,truth)
| implies(X_4,X_4) = X_4 ),
inference(resolve,[$cnf( $equal(implies(X_4,truth),X_4) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( implies(X_4,implies(truth,X_4)) != implies(X_4,truth)
| implies(X_4,X_4) = X_4 ),
inference(resolve,[$cnf( $equal(implies(X_4,X_4),implies(X_4,truth)) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(X_4,X_4) = X_4,
inference(resolve,[$cnf( $equal(implies(X_4,implies(truth,X_4)),implies(X_4,truth)) )],[refute_0_21,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(X_7,X_7) = X_7,
inference(subst,[],[refute_0_37:[bind(X_4,$fot(X_7))]]) ).
cnf(refute_0_39,plain,
implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(implies(implies(X_8,X_9),implies(X_7,X_9)))),bind(Y,$fot(implies(X_7,X_8)))]]) ).
cnf(refute_0_40,plain,
implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_41,plain,
( implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))) != truth
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))))
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_42,plain,
( implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))))
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))),truth) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(X_7,X_8),truth) = implies(X_7,X_8),
inference(subst,[],[refute_0_32:[bind(X,$fot(implies(X_7,X_8)))]]) ).
cnf(refute_0_45,plain,
implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) = implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(X_7,X_8))),bind(Y,$fot(implies(implies(X_8,X_9),implies(X_7,X_9))))]]) ).
cnf(refute_0_46,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_47,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_46]) ).
cnf(refute_0_48,plain,
( implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))) != truth
| implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) != implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9)))
| implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) = truth ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)))),bind(Y0,$fot(implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_49,plain,
( implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))) != truth
| implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)),implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9)))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))),truth) )],[refute_0_40,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),
introduced(tautology,[refl,[$fot(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))))]]) ).
cnf(refute_0_52,plain,
( implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)))
| implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) != truth
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(X_7,X_8),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_53,plain,
( implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)) != truth
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(X_7,X_8),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(implies(X_7,X_8),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8)),truth) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(X_7,X_8),truth)
| implies(implies(X_7,X_8),truth) != implies(X_7,X_8)
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(X_7,X_8) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))))),bind(Y0,$fot(implies(implies(X_7,X_8),truth))),bind(Z0,$fot(implies(X_7,X_8)))]]) ).
cnf(refute_0_56,plain,
( implies(implies(X_7,X_8),truth) != implies(X_7,X_8)
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(X_7,X_8) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(X_7,X_8),truth)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) = implies(X_7,X_8),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),truth),implies(X_7,X_8)) )],[refute_0_44,refute_0_56]) ).
cnf(refute_0_58,plain,
( implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(X_7,X_8)
| implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)
| implies(X_7,X_8) = implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)) ),[0],$fot(implies(X_7,X_8))]]) ).
cnf(refute_0_59,plain,
( implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)
| implies(X_7,X_8) = implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(X_7,X_8)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth) = implies(implies(X_8,X_9),implies(X_7,X_9)),
inference(subst,[],[refute_0_32:[bind(X,$fot(implies(implies(X_8,X_9),implies(X_7,X_9))))]]) ).
cnf(refute_0_61,plain,
( implies(X_7,X_8) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)
| implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth) != implies(implies(X_8,X_9),implies(X_7,X_9))
| implies(X_7,X_8) = implies(implies(X_8,X_9),implies(X_7,X_9)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))) ),[0],$fot(implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth))]]) ).
cnf(refute_0_62,plain,
( implies(X_7,X_8) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)
| implies(X_7,X_8) = implies(implies(X_8,X_9),implies(X_7,X_9)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth),implies(implies(X_8,X_9),implies(X_7,X_9))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))) != implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)
| implies(X_7,X_8) = implies(implies(X_8,X_9),implies(X_7,X_9)) ),
inference(resolve,[$cnf( $equal(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(X_7,X_8) = implies(implies(X_8,X_9),implies(X_7,X_9)),
inference(resolve,[$cnf( $equal(implies(implies(X_7,X_8),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),implies(X_7,X_8))),implies(implies(implies(X_8,X_9),implies(X_7,X_9)),truth)) )],[refute_0_43,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(X_7,X_8) != implies(implies(X_8,X_9),implies(X_7,X_9))
| implies(implies(X_8,X_9),implies(X_7,X_9)) = implies(X_7,X_8) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_7,X_8))),bind(Y0,$fot(implies(implies(X_8,X_9),implies(X_7,X_9))))]]) ).
cnf(refute_0_66,plain,
implies(implies(X_8,X_9),implies(X_7,X_9)) = implies(X_7,X_8),
inference(resolve,[$cnf( $equal(implies(X_7,X_8),implies(implies(X_8,X_9),implies(X_7,X_9))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) = implies(X_7,X_7),
inference(subst,[],[refute_0_66:[bind(X_8,$fot(X_7)),bind(X_9,$fot(implies(X,Y)))]]) ).
cnf(refute_0_68,plain,
( implies(X_7,X_7) != X_7
| implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) != implies(X_7,X_7)
| implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) = X_7 ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))))),bind(Y0,$fot(implies(X_7,X_7))),bind(Z0,$fot(X_7))]]) ).
cnf(refute_0_69,plain,
( implies(X_7,X_7) != X_7
| implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) = X_7 ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))),implies(X_7,X_7)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) = X_7,
inference(resolve,[$cnf( $equal(implies(X_7,X_7),X_7) )],[refute_0_38,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(implies(Y,Z),implies(X,Z)) = implies(X,Y),
inference(subst,[],[refute_0_66:[bind(X_7,$fot(X)),bind(X_8,$fot(Y)),bind(X_9,$fot(Z))]]) ).
cnf(refute_0_72,plain,
implies(X_7,implies(implies(Y,Z),implies(X,Z))) = implies(X_7,implies(implies(Y,Z),implies(X,Z))),
introduced(tautology,[refl,[$fot(implies(X_7,implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_73,plain,
( implies(X_7,implies(implies(Y,Z),implies(X,Z))) != implies(X_7,implies(implies(Y,Z),implies(X,Z)))
| implies(implies(Y,Z),implies(X,Z)) != implies(X,Y)
| implies(X_7,implies(implies(Y,Z),implies(X,Z))) = implies(X_7,implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_7,implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z)))) ),[1,1],$fot(implies(X,Y))]]) ).
cnf(refute_0_74,plain,
( implies(implies(Y,Z),implies(X,Z)) != implies(X,Y)
| implies(X_7,implies(implies(Y,Z),implies(X,Z))) = implies(X_7,implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(X_7,implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(implies(Y,Z),implies(X,Z)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
implies(X_7,implies(implies(Y,Z),implies(X,Z))) = implies(X_7,implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(implies(Y,Z),implies(X,Z)),implies(X,Y)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) = implies(X_7,implies(implies(Y,Z),implies(X,Z))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_7,implies(implies(Y,Z),implies(X,Z)))))]]) ).
cnf(refute_0_77,plain,
( implies(X_7,implies(implies(Y,Z),implies(X,Z))) != implies(X_7,implies(X,Y))
| implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) != implies(X_7,implies(implies(Y,Z),implies(X,Z)))
| implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) = implies(X_7,implies(X,Y)) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))))),bind(Y0,$fot(implies(X_7,implies(implies(Y,Z),implies(X,Z))))),bind(Z0,$fot(implies(X_7,implies(X,Y))))]]) ).
cnf(refute_0_78,plain,
( implies(X_7,implies(implies(Y,Z),implies(X,Z))) != implies(X_7,implies(X,Y))
| implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) = implies(X_7,implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))),implies(X_7,implies(implies(Y,Z),implies(X,Z)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) = implies(X_7,implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(X_7,implies(implies(Y,Z),implies(X,Z))),implies(X_7,implies(X,Y))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),
introduced(tautology,[refl,[$fot(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))))]]) ).
cnf(refute_0_81,plain,
( implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))))
| implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) != implies(X_7,implies(X,Y))
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))))) ),[1,1],$fot(implies(X_7,implies(X,Y)))]]) ).
cnf(refute_0_82,plain,
( implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))) != implies(X_7,implies(X,Y))
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z)))),implies(X_7,implies(X,Y))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) != X_7
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y)))
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = X_7 ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))))),bind(Y0,$fot(implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))))),bind(Z0,$fot(X_7))]]) ).
cnf(refute_0_85,plain,
( implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))) != X_7
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = X_7 ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) = X_7,
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(X_7,implies(X,Y))),X_7) )],[refute_0_70,refute_0_85]) ).
cnf(refute_0_87,plain,
( implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != X_7
| implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != truth
| X_7 = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),truth) ),[0],$fot(X_7)]]) ).
cnf(refute_0_88,plain,
( implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))) != truth
| X_7 = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),X_7) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
X_7 = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(X,Y)),implies(truth,implies(X_7,implies(implies(Y,Z),implies(X,Z))))),truth) )],[refute_0_3,refute_0_88]) ).
cnf(refute_0_90,plain,
x = truth,
inference(subst,[],[refute_0_89:[bind(X_7,$fot(x))]]) ).
cnf(refute_0_91,plain,
( truth != y
| x != truth
| x = y ),
introduced(tautology,[equality,[$cnf( $equal(x,truth) ),[1],$fot(y)]]) ).
cnf(refute_0_92,plain,
( truth != y
| x = y ),
inference(resolve,[$cnf( $equal(x,truth) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
y = truth,
inference(subst,[],[refute_0_89:[bind(X_7,$fot(y))]]) ).
cnf(refute_0_94,plain,
( truth != truth
| y != truth
| truth = y ),
introduced(tautology,[equality,[$cnf( ~ $equal(truth,y) ),[1],$fot(truth)]]) ).
cnf(refute_0_95,plain,
( truth != truth
| truth = y ),
inference(resolve,[$cnf( $equal(y,truth) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( truth != truth
| x = y ),
inference(resolve,[$cnf( $equal(truth,y) )],[refute_0_95,refute_0_92]) ).
cnf(refute_0_97,plain,
truth != truth,
inference(resolve,[$cnf( $equal(x,y) )],[refute_0_96,prove_wajsberg_lemma]) ).
cnf(refute_0_98,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_99,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_98,refute_0_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL133-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 11:21:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------