TSTP Solution File: LCL189-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL189-3 : 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 12:50:24 EDT 2022
% Result : Unsatisfiable 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of clauses : 77 ( 42 unt; 0 nHn; 37 RR)
% Number of literals : 125 ( 52 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 176 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
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(or(not(p),implies(implies(p,q),q))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_4,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(p),implies(implies(p,q),q)) = implies(p,implies(implies(p,q),q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(p)),bind(Y,$fot(implies(implies(p,q),q)))]]) ).
cnf(refute_0_6,plain,
( or(not(p),implies(implies(p,q),q)) != implies(p,implies(implies(p,q),q))
| ~ theorem(implies(p,implies(implies(p,q),q)))
| theorem(or(not(p),implies(implies(p,q),q))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(p),implies(implies(p,q),q))) ),[0],$fot(implies(p,implies(implies(p,q),q)))]]) ).
cnf(refute_0_7,plain,
( ~ theorem(implies(p,implies(implies(p,q),q)))
| theorem(or(not(p),implies(implies(p,q),q))) ),
inference(resolve,[$cnf( $equal(or(not(p),implies(implies(p,q),q)),implies(p,implies(implies(p,q),q))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
~ theorem(implies(p,implies(implies(p,q),q))),
inference(resolve,[$cnf( theorem(or(not(p),implies(implies(p,q),q))) )],[refute_0_7,prove_this]) ).
cnf(refute_0_9,plain,
( ~ theorem(implies(X_76,implies(X_75,X_77)))
| ~ theorem(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77))))
| theorem(implies(X_75,implies(X_76,X_77))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_75,implies(X_76,X_77)))),bind(Y,$fot(implies(X_76,implies(X_75,X_77))))]]) ).
cnf(refute_0_10,plain,
( ~ axiom(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74))))
| theorem(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74)))))]]) ).
cnf(refute_0_11,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_12,plain,
implies(X,X_33) = or(not(X),X_33),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_13,plain,
( implies(X,X_33) != or(not(X),X_33)
| or(not(X),X_33) = implies(X,X_33) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_33))),bind(Y0,$fot(or(not(X),X_33)))]]) ).
cnf(refute_0_14,plain,
or(not(X),X_33) = implies(X,X_33),
inference(resolve,[$cnf( $equal(implies(X,X_33),or(not(X),X_33)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( or(not(X),X_33) != implies(X,X_33)
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) ),[0,1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_16,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
or(not(X),or(X_32,X_33)) = implies(X,or(X_32,X_33)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_32,X_33)))]]) ).
cnf(refute_0_19,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_20,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))
| or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[1,0],$fot(implies(X,or(X_32,X_33)))]]) ).
cnf(refute_0_21,plain,
( or(not(X),or(X_32,X_33)) != implies(X,or(X_32,X_33))
| implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_32,X_33)),implies(X,or(X_32,X_33))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[0],$fot(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_24,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
axiom(implies(implies(X_49,or(not(X),X_51)),or(not(X),implies(X_49,X_51)))),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_49)),bind(X_32,$fot(not(X))),bind(X_33,$fot(X_51))]]) ).
cnf(refute_0_27,plain,
implies(X,implies(X_49,X_51)) = or(not(X),implies(X_49,X_51)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_49,X_51)))]]) ).
cnf(refute_0_28,plain,
( implies(X,implies(X_49,X_51)) != or(not(X),implies(X_49,X_51))
| or(not(X),implies(X_49,X_51)) = implies(X,implies(X_49,X_51)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(X_49,X_51)))),bind(Y0,$fot(or(not(X),implies(X_49,X_51))))]]) ).
cnf(refute_0_29,plain,
or(not(X),implies(X_49,X_51)) = implies(X,implies(X_49,X_51)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_49,X_51)),or(not(X),implies(X_49,X_51))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( or(not(X),implies(X_49,X_51)) != implies(X,implies(X_49,X_51))
| ~ axiom(implies(implies(X_49,or(not(X),X_51)),or(not(X),implies(X_49,X_51))))
| axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_49,or(not(X),X_51)),or(not(X),implies(X_49,X_51)))) ),[0,1],$fot(implies(X,implies(X_49,X_51)))]]) ).
cnf(refute_0_31,plain,
( ~ axiom(implies(implies(X_49,or(not(X),X_51)),or(not(X),implies(X_49,X_51))))
| axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_49,X_51)),implies(X,implies(X_49,X_51))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))),
inference(resolve,[$cnf( axiom(implies(implies(X_49,or(not(X),X_51)),or(not(X),implies(X_49,X_51)))) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
or(not(X),X_51) = implies(X,X_51),
inference(subst,[],[refute_0_4:[bind(Y,$fot(X_51))]]) ).
cnf(refute_0_34,plain,
implies(X_49,or(not(X),X_51)) = implies(X_49,or(not(X),X_51)),
introduced(tautology,[refl,[$fot(implies(X_49,or(not(X),X_51)))]]) ).
cnf(refute_0_35,plain,
( implies(X_49,or(not(X),X_51)) != implies(X_49,or(not(X),X_51))
| or(not(X),X_51) != implies(X,X_51)
| implies(X_49,or(not(X),X_51)) = implies(X_49,implies(X,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_49,or(not(X),X_51)),implies(X_49,or(not(X),X_51))) ),[1,1],$fot(implies(X,X_51))]]) ).
cnf(refute_0_36,plain,
( or(not(X),X_51) != implies(X,X_51)
| implies(X_49,or(not(X),X_51)) = implies(X_49,implies(X,X_51)) ),
inference(resolve,[$cnf( $equal(implies(X_49,or(not(X),X_51)),implies(X_49,or(not(X),X_51))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(X_49,or(not(X),X_51)) = implies(X_49,implies(X,X_51)),
inference(resolve,[$cnf( $equal(or(not(X),X_51),implies(X,X_51)) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))) = implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))),
introduced(tautology,[refl,[$fot(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))))]]) ).
cnf(refute_0_39,plain,
( implies(X_49,or(not(X),X_51)) != implies(X_49,implies(X,X_51))
| implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))) != implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))
| implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))) = implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))),implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))) ),[1,0],$fot(implies(X_49,implies(X,X_51)))]]) ).
cnf(refute_0_40,plain,
( implies(X_49,or(not(X),X_51)) != implies(X_49,implies(X,X_51))
| implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))) = implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))),implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))) = implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51))),
inference(resolve,[$cnf( $equal(implies(X_49,or(not(X),X_51)),implies(X_49,implies(X,X_51))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))) != implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51)))
| ~ axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))))
| axiom(implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))) ),[0],$fot(implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51))))]]) ).
cnf(refute_0_43,plain,
( ~ axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))))
| axiom(implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51))),implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
axiom(implies(implies(X_49,implies(X,X_51)),implies(X,implies(X_49,X_51)))),
inference(resolve,[$cnf( axiom(implies(implies(X_49,or(not(X),X_51)),implies(X,implies(X_49,X_51)))) )],[refute_0_32,refute_0_43]) ).
cnf(refute_0_45,plain,
axiom(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74)))),
inference(subst,[],[refute_0_44:[bind(X,$fot(X_72)),bind(X_49,$fot(X_73)),bind(X_51,$fot(X_74))]]) ).
cnf(refute_0_46,plain,
theorem(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74)))),
inference(resolve,[$cnf( axiom(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74)))) )],[refute_0_45,refute_0_10]) ).
cnf(refute_0_47,plain,
theorem(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))),
inference(subst,[],[refute_0_46:[bind(X_72,$fot(X_75)),bind(X_73,$fot(X_76)),bind(X_74,$fot(X_77))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(implies(X_76,implies(X_75,X_77)))
| theorem(implies(X_75,implies(X_76,X_77))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_76,implies(X_75,X_77)),implies(X_75,implies(X_76,X_77)))) )],[refute_0_47,refute_0_9]) ).
cnf(refute_0_49,plain,
( ~ theorem(implies(implies(X_75,X_77),implies(X_75,X_77)))
| theorem(implies(X_75,implies(implies(X_75,X_77),X_77))) ),
inference(subst,[],[refute_0_48:[bind(X_76,$fot(implies(X_75,X_77)))]]) ).
cnf(refute_0_50,plain,
( ~ theorem(X_478)
| ~ theorem(implies(X_478,implies(X_479,X_479)))
| theorem(implies(X_479,X_479)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_479,X_479))),bind(Y,$fot(X_478))]]) ).
cnf(refute_0_51,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_52,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_51]) ).
cnf(refute_0_53,plain,
theorem(implies(A,or(not(X_7),A))),
inference(subst,[],[refute_0_52:[bind(B,$fot(not(X_7)))]]) ).
cnf(refute_0_54,plain,
implies(X_7,A) = or(not(X_7),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_7)),bind(Y,$fot(A))]]) ).
cnf(refute_0_55,plain,
( implies(X_7,A) != or(not(X_7),A)
| or(not(X_7),A) = implies(X_7,A) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_7,A))),bind(Y0,$fot(or(not(X_7),A)))]]) ).
cnf(refute_0_56,plain,
or(not(X_7),A) = implies(X_7,A),
inference(resolve,[$cnf( $equal(implies(X_7,A),or(not(X_7),A)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( or(not(X_7),A) != implies(X_7,A)
| ~ theorem(implies(A,or(not(X_7),A)))
| theorem(implies(A,implies(X_7,A))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(A,or(not(X_7),A))) ),[0,1],$fot(implies(X_7,A))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(implies(A,or(not(X_7),A)))
| theorem(implies(A,implies(X_7,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),A),implies(X_7,A)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
theorem(implies(A,implies(X_7,A))),
inference(resolve,[$cnf( theorem(implies(A,or(not(X_7),A))) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
theorem(implies(X_477,implies(X_475,X_477))),
inference(subst,[],[refute_0_59:[bind(A,$fot(X_477)),bind(X_7,$fot(X_475))]]) ).
cnf(refute_0_61,plain,
( ~ theorem(implies(X_477,implies(X_475,X_477)))
| theorem(implies(X_475,implies(X_477,X_477))) ),
inference(subst,[],[refute_0_48:[bind(X_75,$fot(X_475)),bind(X_76,$fot(X_477)),bind(X_77,$fot(X_477))]]) ).
cnf(refute_0_62,plain,
theorem(implies(X_475,implies(X_477,X_477))),
inference(resolve,[$cnf( theorem(implies(X_477,implies(X_475,X_477))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
theorem(implies(X_478,implies(X_479,X_479))),
inference(subst,[],[refute_0_62:[bind(X_475,$fot(X_478)),bind(X_477,$fot(X_479))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(X_478)
| theorem(implies(X_479,X_479)) ),
inference(resolve,[$cnf( theorem(implies(X_478,implies(X_479,X_479))) )],[refute_0_63,refute_0_50]) ).
cnf(refute_0_65,plain,
( ~ theorem(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74))))
| theorem(implies(X_494,X_494)) ),
inference(subst,[],[refute_0_64:[bind(X_478,$fot(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74))))),bind(X_479,$fot(X_494))]]) ).
cnf(refute_0_66,plain,
theorem(implies(X_494,X_494)),
inference(resolve,[$cnf( theorem(implies(implies(X_73,implies(X_72,X_74)),implies(X_72,implies(X_73,X_74)))) )],[refute_0_46,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(implies(implies(X_75,X_77),implies(X_75,X_77))),
inference(subst,[],[refute_0_66:[bind(X_494,$fot(implies(X_75,X_77)))]]) ).
cnf(refute_0_68,plain,
theorem(implies(X_75,implies(implies(X_75,X_77),X_77))),
inference(resolve,[$cnf( theorem(implies(implies(X_75,X_77),implies(X_75,X_77))) )],[refute_0_67,refute_0_49]) ).
cnf(refute_0_69,plain,
theorem(implies(p,implies(implies(p,q),q))),
inference(subst,[],[refute_0_68:[bind(X_75,$fot(p)),bind(X_77,$fot(q))]]) ).
cnf(refute_0_70,plain,
$false,
inference(resolve,[$cnf( theorem(implies(p,implies(implies(p,q),q))) )],[refute_0_69,refute_0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL189-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n016.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 : Sun Jul 3 20:17:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.50
%------------------------------------------------------------------------------