TSTP Solution File: LCL203-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL203-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 12:50:34 EDT 2022
% Result : Unsatisfiable 58.33s 58.48s
% Output : CNFRefutation 58.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of clauses : 135 ( 73 unt; 0 nHn; 65 RR)
% Number of literals : 217 ( 55 equ; 84 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 : 274 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
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(not(or(p,q)),or(not(p),not(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( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(p),not(q)) = implies(p,not(q)),
inference(subst,[],[refute_0_4:[bind(X,$fot(p)),bind(Y,$fot(not(q)))]]) ).
cnf(refute_0_6,plain,
implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),or(not(p),not(q))),
introduced(tautology,[refl,[$fot(implies(not(or(p,q)),or(not(p),not(q))))]]) ).
cnf(refute_0_7,plain,
( implies(not(or(p,q)),or(not(p),not(q))) != implies(not(or(p,q)),or(not(p),not(q)))
| or(not(p),not(q)) != implies(p,not(q))
| implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),implies(p,not(q))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(or(p,q)),or(not(p),not(q))),implies(not(or(p,q)),or(not(p),not(q)))) ),[1,1],$fot(implies(p,not(q)))]]) ).
cnf(refute_0_8,plain,
( or(not(p),not(q)) != implies(p,not(q))
| implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),implies(p,not(q))) ),
inference(resolve,[$cnf( $equal(implies(not(or(p,q)),or(not(p),not(q))),implies(not(or(p,q)),or(not(p),not(q)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(not(or(p,q)),or(not(p),not(q))) = implies(not(or(p,q)),implies(p,not(q))),
inference(resolve,[$cnf( $equal(or(not(p),not(q)),implies(p,not(q))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(not(or(p,q)),or(not(p),not(q))) != implies(not(or(p,q)),implies(p,not(q)))
| ~ theorem(implies(not(or(p,q)),implies(p,not(q))))
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(implies(not(or(p,q)),or(not(p),not(q)))) ),[0],$fot(implies(not(or(p,q)),implies(p,not(q))))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(not(or(p,q)),implies(p,not(q))))
| theorem(implies(not(or(p,q)),or(not(p),not(q)))) ),
inference(resolve,[$cnf( $equal(implies(not(or(p,q)),or(not(p),not(q))),implies(not(or(p,q)),implies(p,not(q)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
~ theorem(implies(not(or(p,q)),implies(p,not(q)))),
inference(resolve,[$cnf( theorem(implies(not(or(p,q)),or(not(p),not(q)))) )],[refute_0_11,prove_this]) ).
cnf(refute_0_13,plain,
( ~ axiom(implies(or(X_15,X_16),or(X_16,X_15)))
| theorem(implies(or(X_15,X_16),or(X_16,X_15))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_15,X_16),or(X_16,X_15))))]]) ).
cnf(refute_0_14,plain,
axiom(implies(or(X_15,X_16),or(X_16,X_15))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_15)),bind(B,$fot(X_16))]]) ).
cnf(refute_0_15,plain,
theorem(implies(or(X_15,X_16),or(X_16,X_15))),
inference(resolve,[$cnf( axiom(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( ~ theorem(implies(or(X_15,X_16),or(X_16,X_15)))
| ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_16,X_15))),bind(Y,$fot(or(X_15,X_16)))]]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(X_15,X_16))
| theorem(or(X_16,X_15)) ),
inference(resolve,[$cnf( theorem(implies(or(X_15,X_16),or(X_16,X_15))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ theorem(or(implies(X_54433,not(X_54432)),not(not(or(X_54431,X_54432)))))
| theorem(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432)))) ),
inference(subst,[],[refute_0_17:[bind(X_15,$fot(implies(X_54433,not(X_54432)))),bind(X_16,$fot(not(not(or(X_54431,X_54432)))))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(or(X_671,X_672),implies(X_673,not(X_672))))
| theorem(or(implies(X_673,not(X_672)),or(X_671,X_672))) ),
inference(subst,[],[refute_0_17:[bind(X_15,$fot(or(X_671,X_672))),bind(X_16,$fot(implies(X_673,not(X_672))))]]) ).
cnf(refute_0_20,plain,
( ~ axiom(implies(X_7,implies(X_8,X_7)))
| theorem(implies(X_7,implies(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_7,implies(X_8,X_7))))]]) ).
cnf(refute_0_21,plain,
axiom(implies(A,or(not(X_5),A))),
inference(subst,[],[axiom_1_3:[bind(B,$fot(not(X_5)))]]) ).
cnf(refute_0_22,plain,
implies(X_5,A) = or(not(X_5),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_5)),bind(Y,$fot(A))]]) ).
cnf(refute_0_23,plain,
( implies(X_5,A) != or(not(X_5),A)
| or(not(X_5),A) = implies(X_5,A) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_5,A))),bind(Y0,$fot(or(not(X_5),A)))]]) ).
cnf(refute_0_24,plain,
or(not(X_5),A) = implies(X_5,A),
inference(resolve,[$cnf( $equal(implies(X_5,A),or(not(X_5),A)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( or(not(X_5),A) != implies(X_5,A)
| ~ axiom(implies(A,or(not(X_5),A)))
| axiom(implies(A,implies(X_5,A))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(A,or(not(X_5),A))) ),[0,1],$fot(implies(X_5,A))]]) ).
cnf(refute_0_26,plain,
( ~ axiom(implies(A,or(not(X_5),A)))
| axiom(implies(A,implies(X_5,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),A),implies(X_5,A)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
axiom(implies(A,implies(X_5,A))),
inference(resolve,[$cnf( axiom(implies(A,or(not(X_5),A))) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
axiom(implies(X_7,implies(X_8,X_7))),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_7)),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_29,plain,
theorem(implies(X_7,implies(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(X_7,implies(X_8,X_7))) )],[refute_0_28,refute_0_20]) ).
cnf(refute_0_30,plain,
theorem(implies(X_68,implies(X_8,X_68))),
inference(subst,[],[refute_0_29:[bind(X_7,$fot(X_68))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,implies(X_8,X_68)))
| theorem(implies(X_8,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_8,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(X_68)
| theorem(implies(X_8,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,implies(X_8,X_68))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ theorem(or(or(X_120,X_121),not(X_121)))
| theorem(implies(X_8,or(or(X_120,X_121),not(X_121)))) ),
inference(subst,[],[refute_0_32:[bind(X_68,$fot(or(or(X_120,X_121),not(X_121))))]]) ).
cnf(refute_0_34,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_35,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_34]) ).
cnf(refute_0_36,plain,
theorem(implies(X_115,or(B,X_115))),
inference(subst,[],[refute_0_35:[bind(A,$fot(X_115))]]) ).
cnf(refute_0_37,plain,
theorem(implies(or(not(X),X_18),or(X_18,not(X)))),
inference(subst,[],[refute_0_15:[bind(X_15,$fot(not(X))),bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_38,plain,
implies(X,X_18) = or(not(X),X_18),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_18))]]) ).
cnf(refute_0_39,plain,
( implies(X,X_18) != or(not(X),X_18)
| or(not(X),X_18) = implies(X,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_18))),bind(Y0,$fot(or(not(X),X_18)))]]) ).
cnf(refute_0_40,plain,
or(not(X),X_18) = implies(X,X_18),
inference(resolve,[$cnf( $equal(implies(X,X_18),or(not(X),X_18)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( or(not(X),X_18) != implies(X,X_18)
| ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) ),[0,0],$fot(implies(X,X_18))]]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(or(not(X),X_18),or(X_18,not(X))))
| theorem(implies(implies(X,X_18),or(X_18,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_18),implies(X,X_18)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
theorem(implies(implies(X,X_18),or(X_18,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_18),or(X_18,not(X)))) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ theorem(implies(X,X_18))
| ~ theorem(implies(implies(X,X_18),or(X_18,not(X))))
| theorem(or(X_18,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_18,not(X)))),bind(Y,$fot(implies(X,X_18)))]]) ).
cnf(refute_0_45,plain,
( ~ theorem(implies(X,X_18))
| theorem(or(X_18,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_18),or(X_18,not(X)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ theorem(implies(X_115,or(B,X_115)))
| theorem(or(or(B,X_115),not(X_115))) ),
inference(subst,[],[refute_0_45:[bind(X,$fot(X_115)),bind(X_18,$fot(or(B,X_115)))]]) ).
cnf(refute_0_47,plain,
theorem(or(or(B,X_115),not(X_115))),
inference(resolve,[$cnf( theorem(implies(X_115,or(B,X_115))) )],[refute_0_36,refute_0_46]) ).
cnf(refute_0_48,plain,
theorem(or(or(X_120,X_121),not(X_121))),
inference(subst,[],[refute_0_47:[bind(B,$fot(X_120)),bind(X_115,$fot(X_121))]]) ).
cnf(refute_0_49,plain,
theorem(implies(X_8,or(or(X_120,X_121),not(X_121)))),
inference(resolve,[$cnf( theorem(or(or(X_120,X_121),not(X_121))) )],[refute_0_48,refute_0_33]) ).
cnf(refute_0_50,plain,
theorem(implies(X_640,or(or(X_120,X_121),not(X_121)))),
inference(subst,[],[refute_0_49:[bind(X_8,$fot(X_640))]]) ).
cnf(refute_0_51,plain,
( ~ axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
| theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))))]]) ).
cnf(refute_0_52,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_53,plain,
implies(X,X_33) = or(not(X),X_33),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_54,plain,
( implies(X,X_33) != or(not(X),X_33)
| or(not(X),X_33) = implies(X,X_33) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_33))),bind(Y0,$fot(or(not(X),X_33)))]]) ).
cnf(refute_0_55,plain,
or(not(X),X_33) = implies(X,X_33),
inference(resolve,[$cnf( $equal(implies(X,X_33),or(not(X),X_33)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( or(not(X),X_33) != implies(X,X_33)
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) ),[0,1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_57,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33))))
| axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,or(not(X),X_33)))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
or(not(X),or(X_32,X_33)) = implies(X,or(X_32,X_33)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_32,X_33)))]]) ).
cnf(refute_0_60,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_61,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_62,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( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) = implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_32,X_33)),implies(X,or(X_32,X_33))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))) != implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))
| ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),[0],$fot(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33))))]]) ).
cnf(refute_0_65,plain,
( ~ axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))))
| axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33))),implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
axiom(implies(implies(X,or(X_32,X_33)),or(X_32,implies(X,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_32,X_33)),or(X_32,implies(X,X_33)))) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_34)),bind(X_32,$fot(X_35)),bind(X_33,$fot(X_36))]]) ).
cnf(refute_0_68,plain,
theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))),
inference(resolve,[$cnf( axiom(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_67,refute_0_51]) ).
cnf(refute_0_69,plain,
( ~ theorem(implies(X_34,or(X_35,X_36)))
| ~ theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36))))
| theorem(or(X_35,implies(X_34,X_36))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_35,implies(X_34,X_36)))),bind(Y,$fot(implies(X_34,or(X_35,X_36))))]]) ).
cnf(refute_0_70,plain,
( ~ theorem(implies(X_34,or(X_35,X_36)))
| theorem(or(X_35,implies(X_34,X_36))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_34,or(X_35,X_36)),or(X_35,implies(X_34,X_36)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ theorem(implies(X_640,or(or(X_120,X_121),not(X_121))))
| theorem(or(or(X_120,X_121),implies(X_640,not(X_121)))) ),
inference(subst,[],[refute_0_70:[bind(X_34,$fot(X_640)),bind(X_35,$fot(or(X_120,X_121))),bind(X_36,$fot(not(X_121)))]]) ).
cnf(refute_0_72,plain,
theorem(or(or(X_120,X_121),implies(X_640,not(X_121)))),
inference(resolve,[$cnf( theorem(implies(X_640,or(or(X_120,X_121),not(X_121)))) )],[refute_0_50,refute_0_71]) ).
cnf(refute_0_73,plain,
theorem(or(or(X_671,X_672),implies(X_673,not(X_672)))),
inference(subst,[],[refute_0_72:[bind(X_120,$fot(X_671)),bind(X_121,$fot(X_672)),bind(X_640,$fot(X_673))]]) ).
cnf(refute_0_74,plain,
theorem(or(implies(X_673,not(X_672)),or(X_671,X_672))),
inference(resolve,[$cnf( theorem(or(or(X_671,X_672),implies(X_673,not(X_672)))) )],[refute_0_73,refute_0_19]) ).
cnf(refute_0_75,plain,
( ~ theorem(implies(or(X_2042,X_2041),or(X_2042,not(not(X_2041)))))
| ~ theorem(or(X_2042,X_2041))
| theorem(or(X_2042,not(not(X_2041)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_2042,not(not(X_2041))))),bind(Y,$fot(or(X_2042,X_2041)))]]) ).
cnf(refute_0_76,plain,
theorem(implies(or(X_17,not(X)),or(not(X),X_17))),
inference(subst,[],[refute_0_15:[bind(X_15,$fot(X_17)),bind(X_16,$fot(not(X)))]]) ).
cnf(refute_0_77,plain,
implies(X,X_17) = or(not(X),X_17),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_17))]]) ).
cnf(refute_0_78,plain,
( implies(X,X_17) != or(not(X),X_17)
| or(not(X),X_17) = implies(X,X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_17))),bind(Y0,$fot(or(not(X),X_17)))]]) ).
cnf(refute_0_79,plain,
or(not(X),X_17) = implies(X,X_17),
inference(resolve,[$cnf( $equal(implies(X,X_17),or(not(X),X_17)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( or(not(X),X_17) != implies(X,X_17)
| ~ theorem(implies(or(X_17,not(X)),or(not(X),X_17)))
| theorem(implies(or(X_17,not(X)),implies(X,X_17))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_17,not(X)),or(not(X),X_17))) ),[0,1],$fot(implies(X,X_17))]]) ).
cnf(refute_0_81,plain,
( ~ theorem(implies(or(X_17,not(X)),or(not(X),X_17)))
| theorem(implies(or(X_17,not(X)),implies(X,X_17))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_17),implies(X,X_17)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
theorem(implies(or(X_17,not(X)),implies(X,X_17))),
inference(resolve,[$cnf( theorem(implies(or(X_17,not(X)),or(not(X),X_17))) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
theorem(implies(or(not(X),not(X_19)),implies(X_19,not(X)))),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_19)),bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_84,plain,
implies(X,not(X_19)) = or(not(X),not(X_19)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_19)))]]) ).
cnf(refute_0_85,plain,
( implies(X,not(X_19)) != or(not(X),not(X_19))
| or(not(X),not(X_19)) = implies(X,not(X_19)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(X_19)))),bind(Y0,$fot(or(not(X),not(X_19))))]]) ).
cnf(refute_0_86,plain,
or(not(X),not(X_19)) = implies(X,not(X_19)),
inference(resolve,[$cnf( $equal(implies(X,not(X_19)),or(not(X),not(X_19))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( or(not(X),not(X_19)) != implies(X,not(X_19))
| ~ theorem(implies(or(not(X),not(X_19)),implies(X_19,not(X))))
| theorem(implies(implies(X,not(X_19)),implies(X_19,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),not(X_19)),implies(X_19,not(X)))) ),[0,0],$fot(implies(X,not(X_19)))]]) ).
cnf(refute_0_88,plain,
( ~ theorem(implies(or(not(X),not(X_19)),implies(X_19,not(X))))
| theorem(implies(implies(X,not(X_19)),implies(X_19,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_19)),implies(X,not(X_19))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
theorem(implies(implies(X,not(X_19)),implies(X_19,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),not(X_19)),implies(X_19,not(X)))) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ theorem(implies(X,not(X_19)))
| ~ theorem(implies(implies(X,not(X_19)),implies(X_19,not(X))))
| theorem(implies(X_19,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_19,not(X)))),bind(Y,$fot(implies(X,not(X_19))))]]) ).
cnf(refute_0_91,plain,
( ~ theorem(implies(X,not(X_19)))
| theorem(implies(X_19,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,not(X_19)),implies(X_19,not(X)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ theorem(implies(not(X_19),not(X_19)))
| theorem(implies(X_19,not(not(X_19)))) ),
inference(subst,[],[refute_0_91:[bind(X,$fot(not(X_19)))]]) ).
cnf(refute_0_93,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_94,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_93]) ).
cnf(refute_0_95,plain,
theorem(implies(or(X_67,X_67),X_67)),
inference(subst,[],[refute_0_94:[bind(A,$fot(X_67))]]) ).
cnf(refute_0_96,plain,
( ~ theorem(implies(or(X_67,X_67),X_67))
| ~ theorem(or(X_67,X_67))
| theorem(X_67) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_67)),bind(Y,$fot(or(X_67,X_67)))]]) ).
cnf(refute_0_97,plain,
( ~ theorem(or(X_67,X_67))
| theorem(X_67) ),
inference(resolve,[$cnf( theorem(implies(or(X_67,X_67),X_67)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ theorem(or(implies(X_646,X_646),implies(X_646,X_646)))
| theorem(implies(X_646,X_646)) ),
inference(subst,[],[refute_0_97:[bind(X_67,$fot(implies(X_646,X_646)))]]) ).
cnf(refute_0_99,plain,
theorem(implies(X_642,or(X_641,X_642))),
inference(subst,[],[refute_0_35:[bind(A,$fot(X_642)),bind(B,$fot(X_641))]]) ).
cnf(refute_0_100,plain,
( ~ theorem(implies(X_642,or(X_641,X_642)))
| theorem(or(X_641,implies(X_642,X_642))) ),
inference(subst,[],[refute_0_70:[bind(X_34,$fot(X_642)),bind(X_35,$fot(X_641)),bind(X_36,$fot(X_642))]]) ).
cnf(refute_0_101,plain,
theorem(or(X_641,implies(X_642,X_642))),
inference(resolve,[$cnf( theorem(implies(X_642,or(X_641,X_642))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
theorem(or(implies(X_646,X_646),implies(X_646,X_646))),
inference(subst,[],[refute_0_101:[bind(X_641,$fot(implies(X_646,X_646))),bind(X_642,$fot(X_646))]]) ).
cnf(refute_0_103,plain,
theorem(implies(X_646,X_646)),
inference(resolve,[$cnf( theorem(or(implies(X_646,X_646),implies(X_646,X_646))) )],[refute_0_102,refute_0_98]) ).
cnf(refute_0_104,plain,
theorem(implies(not(X_19),not(X_19))),
inference(subst,[],[refute_0_103:[bind(X_646,$fot(not(X_19)))]]) ).
cnf(refute_0_105,plain,
theorem(implies(X_19,not(not(X_19)))),
inference(resolve,[$cnf( theorem(implies(not(X_19),not(X_19))) )],[refute_0_104,refute_0_92]) ).
cnf(refute_0_106,plain,
theorem(implies(X_2038,not(not(X_2038)))),
inference(subst,[],[refute_0_105:[bind(X_19,$fot(X_2038))]]) ).
cnf(refute_0_107,plain,
( ~ axiom(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38))))
| theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))))]]) ).
cnf(refute_0_108,plain,
axiom(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_37)),bind(B,$fot(X_38)),bind(C,$fot(X_39))]]) ).
cnf(refute_0_109,plain,
theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))),
inference(resolve,[$cnf( axiom(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))) )],[refute_0_108,refute_0_107]) ).
cnf(refute_0_110,plain,
( ~ theorem(implies(X_37,X_38))
| ~ theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38))))
| theorem(implies(or(X_39,X_37),or(X_39,X_38))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_39,X_37),or(X_39,X_38)))),bind(Y,$fot(implies(X_37,X_38)))]]) ).
cnf(refute_0_111,plain,
( ~ theorem(implies(X_37,X_38))
| theorem(implies(or(X_39,X_37),or(X_39,X_38))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_37,X_38),implies(or(X_39,X_37),or(X_39,X_38)))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( ~ theorem(implies(X_2038,not(not(X_2038))))
| theorem(implies(or(X_2040,X_2038),or(X_2040,not(not(X_2038))))) ),
inference(subst,[],[refute_0_111:[bind(X_37,$fot(X_2038)),bind(X_38,$fot(not(not(X_2038)))),bind(X_39,$fot(X_2040))]]) ).
cnf(refute_0_113,plain,
theorem(implies(or(X_2040,X_2038),or(X_2040,not(not(X_2038))))),
inference(resolve,[$cnf( theorem(implies(X_2038,not(not(X_2038)))) )],[refute_0_106,refute_0_112]) ).
cnf(refute_0_114,plain,
theorem(implies(or(X_2042,X_2041),or(X_2042,not(not(X_2041))))),
inference(subst,[],[refute_0_113:[bind(X_2038,$fot(X_2041)),bind(X_2040,$fot(X_2042))]]) ).
cnf(refute_0_115,plain,
( ~ theorem(or(X_2042,X_2041))
| theorem(or(X_2042,not(not(X_2041)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_2042,X_2041),or(X_2042,not(not(X_2041))))) )],[refute_0_114,refute_0_75]) ).
cnf(refute_0_116,plain,
( ~ theorem(or(implies(X_673,not(X_672)),or(X_671,X_672)))
| theorem(or(implies(X_673,not(X_672)),not(not(or(X_671,X_672))))) ),
inference(subst,[],[refute_0_115:[bind(X_2041,$fot(or(X_671,X_672))),bind(X_2042,$fot(implies(X_673,not(X_672))))]]) ).
cnf(refute_0_117,plain,
theorem(or(implies(X_673,not(X_672)),not(not(or(X_671,X_672))))),
inference(resolve,[$cnf( theorem(or(implies(X_673,not(X_672)),or(X_671,X_672))) )],[refute_0_74,refute_0_116]) ).
cnf(refute_0_118,plain,
theorem(or(implies(X_54433,not(X_54432)),not(not(or(X_54431,X_54432))))),
inference(subst,[],[refute_0_117:[bind(X_671,$fot(X_54431)),bind(X_672,$fot(X_54432)),bind(X_673,$fot(X_54433))]]) ).
cnf(refute_0_119,plain,
theorem(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432)))),
inference(resolve,[$cnf( theorem(or(implies(X_54433,not(X_54432)),not(not(or(X_54431,X_54432))))) )],[refute_0_118,refute_0_18]) ).
cnf(refute_0_120,plain,
or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432))) = implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432))),
inference(subst,[],[refute_0_4:[bind(X,$fot(not(or(X_54431,X_54432)))),bind(Y,$fot(implies(X_54433,not(X_54432))))]]) ).
cnf(refute_0_121,plain,
( or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432))) != implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432)))
| ~ theorem(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432))))
| theorem(implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432)))) ),[0],$fot(implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432))))]]) ).
cnf(refute_0_122,plain,
( ~ theorem(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432))))
| theorem(implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432)))) ),
inference(resolve,[$cnf( $equal(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432))),implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432)))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
theorem(implies(not(or(X_54431,X_54432)),implies(X_54433,not(X_54432)))),
inference(resolve,[$cnf( theorem(or(not(not(or(X_54431,X_54432))),implies(X_54433,not(X_54432)))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
theorem(implies(not(or(p,q)),implies(p,not(q)))),
inference(subst,[],[refute_0_123:[bind(X_54431,$fot(p)),bind(X_54432,$fot(q)),bind(X_54433,$fot(p))]]) ).
cnf(refute_0_125,plain,
$false,
inference(resolve,[$cnf( theorem(implies(not(or(p,q)),implies(p,not(q)))) )],[refute_0_124,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL203-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 02:17:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 58.33/58.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.33/58.48
% 58.33/58.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.33/58.49
%------------------------------------------------------------------------------