TSTP Solution File: LCL174-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL174-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 12:50:12 EDT 2022
% Result : Unsatisfiable 2.01s 2.23s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of clauses : 76 ( 41 unt; 0 nHn; 36 RR)
% Number of literals : 125 ( 66 equ; 50 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43))))
| theorem(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),or(not(X),X_36)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_35)),bind(B,$fot(X_36)),bind(C,$fot(not(X)))]]) ).
cnf(refute_0_2,plain,
implies(X,X_36) = or(not(X),X_36),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_36))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( implies(X,X_36) != or(not(X),X_36)
| or(not(X),X_36) = implies(X,X_36) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_36))),bind(Y0,$fot(or(not(X),X_36)))]]) ).
cnf(refute_0_7,plain,
or(not(X),X_36) = implies(X,X_36),
inference(resolve,[$cnf( $equal(implies(X,X_36),or(not(X),X_36)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( or(not(X),X_36) != implies(X,X_36)
| ~ axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),or(not(X),X_36))))
| axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),or(not(X),X_36)))) ),[0,1,1],$fot(implies(X,X_36))]]) ).
cnf(refute_0_9,plain,
( ~ axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),or(not(X),X_36))))
| axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_36),implies(X,X_36)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),or(not(X),X_36)))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_12,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_11]) ).
cnf(refute_0_13,plain,
or(not(X),X_35) = implies(X,X_35),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_14,plain,
implies(or(not(X),X_35),implies(X,X_36)) = implies(or(not(X),X_35),implies(X,X_36)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_35),implies(X,X_36)))]]) ).
cnf(refute_0_15,plain,
( implies(or(not(X),X_35),implies(X,X_36)) != implies(or(not(X),X_35),implies(X,X_36))
| or(not(X),X_35) != implies(X,X_35)
| implies(or(not(X),X_35),implies(X,X_36)) = implies(implies(X,X_35),implies(X,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_35),implies(X,X_36)),implies(or(not(X),X_35),implies(X,X_36))) ),[1,0],$fot(implies(X,X_35))]]) ).
cnf(refute_0_16,plain,
( or(not(X),X_35) != implies(X,X_35)
| implies(or(not(X),X_35),implies(X,X_36)) = implies(implies(X,X_35),implies(X,X_36)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_35),implies(X,X_36)),implies(or(not(X),X_35),implies(X,X_36))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
implies(or(not(X),X_35),implies(X,X_36)) = implies(implies(X,X_35),implies(X,X_36)),
inference(resolve,[$cnf( $equal(or(not(X),X_35),implies(X,X_35)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))) = implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))),
introduced(tautology,[refl,[$fot(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))))]]) ).
cnf(refute_0_19,plain,
( implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))) != implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))
| implies(or(not(X),X_35),implies(X,X_36)) != implies(implies(X,X_35),implies(X,X_36))
| implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))) = implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))),implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))) ),[1,1],$fot(implies(implies(X,X_35),implies(X,X_36)))]]) ).
cnf(refute_0_20,plain,
( implies(or(not(X),X_35),implies(X,X_36)) != implies(implies(X,X_35),implies(X,X_36))
| implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))) = implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))),implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))) = implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_35),implies(X,X_36)),implies(implies(X,X_35),implies(X,X_36))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))) != implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36)))
| ~ axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))))
| axiom(implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))) ),[0],$fot(implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36))))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))))
| axiom(implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36))),implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
axiom(implies(implies(X_35,X_36),implies(implies(X,X_35),implies(X,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_35,X_36),implies(or(not(X),X_35),implies(X,X_36)))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
axiom(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43)))),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_41)),bind(X_35,$fot(X_42)),bind(X_36,$fot(X_43))]]) ).
cnf(refute_0_26,plain,
theorem(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43)))),
inference(resolve,[$cnf( axiom(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43)))) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
( ~ axiom(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21))))
| theorem(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))))]]) ).
cnf(refute_0_28,plain,
axiom(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_19)),bind(B,$fot(X_20)),bind(C,$fot(X_21))]]) ).
cnf(refute_0_29,plain,
theorem(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))),
inference(resolve,[$cnf( axiom(implies(or(X_19,or(X_20,X_21)),or(X_20,or(X_19,X_21)))) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,or(not(X),X_28)))),
inference(subst,[],[refute_0_29:[bind(X_19,$fot(not(X))),bind(X_20,$fot(X_27)),bind(X_21,$fot(X_28))]]) ).
cnf(refute_0_31,plain,
implies(X,X_28) = or(not(X),X_28),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_28))]]) ).
cnf(refute_0_32,plain,
( implies(X,X_28) != or(not(X),X_28)
| or(not(X),X_28) = implies(X,X_28) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_28))),bind(Y0,$fot(or(not(X),X_28)))]]) ).
cnf(refute_0_33,plain,
or(not(X),X_28) = implies(X,X_28),
inference(resolve,[$cnf( $equal(implies(X,X_28),or(not(X),X_28)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( or(not(X),X_28) != implies(X,X_28)
| ~ theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,or(not(X),X_28))))
| theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,or(not(X),X_28)))) ),[0,1,1],$fot(implies(X,X_28))]]) ).
cnf(refute_0_35,plain,
( ~ theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,or(not(X),X_28))))
| theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_28),implies(X,X_28)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,or(not(X),X_28)))) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
or(not(X),or(X_27,X_28)) = implies(X,or(X_27,X_28)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(or(X_27,X_28)))]]) ).
cnf(refute_0_38,plain,
implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))) = implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))))]]) ).
cnf(refute_0_39,plain,
( implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))) != implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))
| or(not(X),or(X_27,X_28)) != implies(X,or(X_27,X_28))
| implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))) = implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))),implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))) ),[1,0],$fot(implies(X,or(X_27,X_28)))]]) ).
cnf(refute_0_40,plain,
( or(not(X),or(X_27,X_28)) != implies(X,or(X_27,X_28))
| implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))) = implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))),implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))) = implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_27,X_28)),implies(X,or(X_27,X_28))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))) != implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28)))
| ~ theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))))
| theorem(implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))) ),[0],$fot(implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28))))]]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))))
| theorem(implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28))),implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
theorem(implies(implies(X,or(X_27,X_28)),or(X_27,implies(X,X_28)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),or(X_27,X_28)),or(X_27,implies(X,X_28)))) )],[refute_0_36,refute_0_43]) ).
cnf(refute_0_45,plain,
theorem(implies(implies(X_29,or(not(X),X_31)),or(not(X),implies(X_29,X_31)))),
inference(subst,[],[refute_0_44:[bind(X,$fot(X_29)),bind(X_27,$fot(not(X))),bind(X_28,$fot(X_31))]]) ).
cnf(refute_0_46,plain,
implies(X,implies(X_29,X_31)) = or(not(X),implies(X_29,X_31)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_29,X_31)))]]) ).
cnf(refute_0_47,plain,
( implies(X,implies(X_29,X_31)) != or(not(X),implies(X_29,X_31))
| or(not(X),implies(X_29,X_31)) = implies(X,implies(X_29,X_31)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,implies(X_29,X_31)))),bind(Y0,$fot(or(not(X),implies(X_29,X_31))))]]) ).
cnf(refute_0_48,plain,
or(not(X),implies(X_29,X_31)) = implies(X,implies(X_29,X_31)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_29,X_31)),or(not(X),implies(X_29,X_31))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( or(not(X),implies(X_29,X_31)) != implies(X,implies(X_29,X_31))
| ~ theorem(implies(implies(X_29,or(not(X),X_31)),or(not(X),implies(X_29,X_31))))
| theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_29,or(not(X),X_31)),or(not(X),implies(X_29,X_31)))) ),[0,1],$fot(implies(X,implies(X_29,X_31)))]]) ).
cnf(refute_0_50,plain,
( ~ theorem(implies(implies(X_29,or(not(X),X_31)),or(not(X),implies(X_29,X_31))))
| theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_29,X_31)),implies(X,implies(X_29,X_31))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))),
inference(resolve,[$cnf( theorem(implies(implies(X_29,or(not(X),X_31)),or(not(X),implies(X_29,X_31)))) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
or(not(X),X_31) = implies(X,X_31),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_53,plain,
implies(X_29,or(not(X),X_31)) = implies(X_29,or(not(X),X_31)),
introduced(tautology,[refl,[$fot(implies(X_29,or(not(X),X_31)))]]) ).
cnf(refute_0_54,plain,
( implies(X_29,or(not(X),X_31)) != implies(X_29,or(not(X),X_31))
| or(not(X),X_31) != implies(X,X_31)
| implies(X_29,or(not(X),X_31)) = implies(X_29,implies(X,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,or(not(X),X_31)),implies(X_29,or(not(X),X_31))) ),[1,1],$fot(implies(X,X_31))]]) ).
cnf(refute_0_55,plain,
( or(not(X),X_31) != implies(X,X_31)
| implies(X_29,or(not(X),X_31)) = implies(X_29,implies(X,X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_29,or(not(X),X_31)),implies(X_29,or(not(X),X_31))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(X_29,or(not(X),X_31)) = implies(X_29,implies(X,X_31)),
inference(resolve,[$cnf( $equal(or(not(X),X_31),implies(X,X_31)) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))) = implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))),
introduced(tautology,[refl,[$fot(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))))]]) ).
cnf(refute_0_58,plain,
( implies(X_29,or(not(X),X_31)) != implies(X_29,implies(X,X_31))
| implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))) != implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))
| implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))) = implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))),implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))) ),[1,0],$fot(implies(X_29,implies(X,X_31)))]]) ).
cnf(refute_0_59,plain,
( implies(X_29,or(not(X),X_31)) != implies(X_29,implies(X,X_31))
| implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))) = implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))),implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))) = implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31))),
inference(resolve,[$cnf( $equal(implies(X_29,or(not(X),X_31)),implies(X_29,implies(X,X_31))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))) != implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31)))
| ~ theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))))
| theorem(implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))) ),[0],$fot(implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31))))]]) ).
cnf(refute_0_62,plain,
( ~ theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))))
| theorem(implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31))),implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
theorem(implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31)))),
inference(resolve,[$cnf( theorem(implies(implies(X_29,or(not(X),X_31)),implies(X,implies(X_29,X_31)))) )],[refute_0_51,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ theorem(implies(X_29,implies(X,X_31)))
| ~ theorem(implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31))))
| theorem(implies(X,implies(X_29,X_31))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X,implies(X_29,X_31)))),bind(Y,$fot(implies(X_29,implies(X,X_31))))]]) ).
cnf(refute_0_65,plain,
( ~ theorem(implies(X_29,implies(X,X_31)))
| theorem(implies(X,implies(X_29,X_31))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_29,implies(X,X_31)),implies(X,implies(X_29,X_31)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ theorem(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43))))
| theorem(implies(implies(X_41,X_42),implies(implies(X_42,X_43),implies(X_41,X_43)))) ),
inference(subst,[],[refute_0_65:[bind(X,$fot(implies(X_41,X_42))),bind(X_29,$fot(implies(X_42,X_43))),bind(X_31,$fot(implies(X_41,X_43)))]]) ).
cnf(refute_0_67,plain,
theorem(implies(implies(X_41,X_42),implies(implies(X_42,X_43),implies(X_41,X_43)))),
inference(resolve,[$cnf( theorem(implies(implies(X_42,X_43),implies(implies(X_41,X_42),implies(X_41,X_43)))) )],[refute_0_26,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
inference(subst,[],[refute_0_67:[bind(X_41,$fot(p)),bind(X_42,$fot(q)),bind(X_43,$fot(r))]]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))) )],[refute_0_68,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL174-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 18:48:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.01/2.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.01/2.23
% 2.01/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.01/2.24
%------------------------------------------------------------------------------