TSTP Solution File: LCL176-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL176-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:50:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of clauses : 80 ( 46 unt; 0 nHn; 35 RR)
% Number of literals : 123 ( 17 equ; 44 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 154 ( 28 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(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(p,p)) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_417,not(X_417)))
| theorem(or(not(X_417),X_417)) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(X_417)),bind(X_8,$fot(not(X_417)))]]) ).
cnf(refute_0_6,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_7,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_6]) ).
cnf(refute_0_8,plain,
theorem(implies(or(X_49,X_49),X_49)),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_49))]]) ).
cnf(refute_0_9,plain,
( ~ theorem(implies(or(X_49,X_49),X_49))
| ~ theorem(or(X_49,X_49))
| theorem(X_49) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_49)),bind(Y,$fot(or(X_49,X_49)))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(X_49,X_49))
| theorem(X_49) ),
inference(resolve,[$cnf( theorem(implies(or(X_49,X_49),X_49)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ theorem(or(or(X_415,not(X_415)),or(X_415,not(X_415))))
| theorem(or(X_415,not(X_415))) ),
inference(subst,[],[refute_0_10:[bind(X_49,$fot(or(X_415,not(X_415))))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(implies(or(X_53,or(X_54,X_55)),or(X_54,or(X_53,X_55))))
| ~ theorem(or(X_53,or(X_54,X_55)))
| theorem(or(X_54,or(X_53,X_55))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_54,or(X_53,X_55)))),bind(Y,$fot(or(X_53,or(X_54,X_55))))]]) ).
cnf(refute_0_13,plain,
( ~ axiom(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31))))
| theorem(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))))]]) ).
cnf(refute_0_14,plain,
axiom(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_29)),bind(B,$fot(X_30)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_15,plain,
theorem(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))),
inference(resolve,[$cnf( axiom(implies(or(X_29,or(X_30,X_31)),or(X_30,or(X_29,X_31)))) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
theorem(implies(or(X_53,or(X_54,X_55)),or(X_54,or(X_53,X_55)))),
inference(subst,[],[refute_0_15:[bind(X_29,$fot(X_53)),bind(X_30,$fot(X_54)),bind(X_31,$fot(X_55))]]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(X_53,or(X_54,X_55)))
| theorem(or(X_54,or(X_53,X_55))) ),
inference(resolve,[$cnf( theorem(implies(or(X_53,or(X_54,X_55)),or(X_54,or(X_53,X_55)))) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( ~ theorem(or(X_411,or(X_412,not(X_411))))
| theorem(or(X_412,or(X_411,not(X_411)))) ),
inference(subst,[],[refute_0_17:[bind(X_53,$fot(X_411)),bind(X_54,$fot(X_412)),bind(X_55,$fot(not(X_411)))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(or(X_410,not(X_409)),X_409))
| theorem(or(X_409,or(X_410,not(X_409)))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(or(X_410,not(X_409)))),bind(X_8,$fot(X_409))]]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(or(or(X_408,not(X_406)),X_406),or(or(X_408,not(X_406)),X_406)))
| theorem(or(or(X_408,not(X_406)),X_406)) ),
inference(subst,[],[refute_0_10:[bind(X_49,$fot(or(or(X_408,not(X_406)),X_406)))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(or(or(X_371,not(X_369)),or(X_370,X_369)))
| theorem(or(X_370,or(or(X_371,not(X_369)),X_369))) ),
inference(subst,[],[refute_0_17:[bind(X_53,$fot(or(X_371,not(X_369)))),bind(X_54,$fot(X_370)),bind(X_55,$fot(X_369))]]) ).
cnf(refute_0_22,plain,
( ~ theorem(or(or(X_355,X_354),or(X_356,not(X_354))))
| theorem(or(or(X_356,not(X_354)),or(X_355,X_354))) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(or(X_355,X_354))),bind(X_8,$fot(or(X_356,not(X_354))))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_24,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_25,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
theorem(implies(X_50,or(X_4,X_50))),
inference(subst,[],[refute_0_25:[bind(X_3,$fot(X_50))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(X_50)
| ~ theorem(implies(X_50,or(X_4,X_50)))
| theorem(or(X_4,X_50)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_50))),bind(Y,$fot(X_50))]]) ).
cnf(refute_0_28,plain,
( ~ theorem(X_50)
| theorem(or(X_4,X_50)) ),
inference(resolve,[$cnf( theorem(implies(X_50,or(X_4,X_50))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ theorem(or(or(X_108,X_107),not(X_107)))
| theorem(or(X_4,or(or(X_108,X_107),not(X_107)))) ),
inference(subst,[],[refute_0_28:[bind(X_50,$fot(or(or(X_108,X_107),not(X_107))))]]) ).
cnf(refute_0_30,plain,
theorem(implies(X_101,or(X_4,X_101))),
inference(subst,[],[refute_0_25:[bind(X_3,$fot(X_101))]]) ).
cnf(refute_0_31,plain,
theorem(implies(or(not(X),X_12),or(X_12,not(X)))),
inference(subst,[],[refute_0_2:[bind(X_7,$fot(not(X))),bind(X_8,$fot(X_12))]]) ).
cnf(refute_0_32,plain,
implies(X,X_12) = or(not(X),X_12),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_12))]]) ).
cnf(refute_0_33,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_34,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_35,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( implies(X,X_12) != or(not(X),X_12)
| or(not(X),X_12) = implies(X,X_12) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(implies(X,X_12))),bind(Y0,$fot(or(not(X),X_12)))]]) ).
cnf(refute_0_37,plain,
or(not(X),X_12) = implies(X,X_12),
inference(resolve,[$cnf( $equal(implies(X,X_12),or(not(X),X_12)) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( or(not(X),X_12) != implies(X,X_12)
| ~ theorem(implies(or(not(X),X_12),or(X_12,not(X))))
| theorem(implies(implies(X,X_12),or(X_12,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_12),or(X_12,not(X)))) ),[0,0],$fot(implies(X,X_12))]]) ).
cnf(refute_0_39,plain,
( ~ theorem(implies(or(not(X),X_12),or(X_12,not(X))))
| theorem(implies(implies(X,X_12),or(X_12,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_12),implies(X,X_12)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
theorem(implies(implies(X,X_12),or(X_12,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_12),or(X_12,not(X)))) )],[refute_0_31,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ theorem(implies(X,X_12))
| ~ theorem(implies(implies(X,X_12),or(X_12,not(X))))
| theorem(or(X_12,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_12,not(X)))),bind(Y,$fot(implies(X,X_12)))]]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X,X_12))
| theorem(or(X_12,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_12),or(X_12,not(X)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ theorem(implies(X_101,or(X_4,X_101)))
| theorem(or(or(X_4,X_101),not(X_101))) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_101)),bind(X_12,$fot(or(X_4,X_101)))]]) ).
cnf(refute_0_44,plain,
theorem(or(or(X_4,X_101),not(X_101))),
inference(resolve,[$cnf( theorem(implies(X_101,or(X_4,X_101))) )],[refute_0_30,refute_0_43]) ).
cnf(refute_0_45,plain,
theorem(or(or(X_108,X_107),not(X_107))),
inference(subst,[],[refute_0_44:[bind(X_101,$fot(X_107)),bind(X_4,$fot(X_108))]]) ).
cnf(refute_0_46,plain,
theorem(or(X_4,or(or(X_108,X_107),not(X_107)))),
inference(resolve,[$cnf( theorem(or(or(X_108,X_107),not(X_107))) )],[refute_0_45,refute_0_29]) ).
cnf(refute_0_47,plain,
theorem(or(X_342,or(or(X_108,X_107),not(X_107)))),
inference(subst,[],[refute_0_46:[bind(X_4,$fot(X_342))]]) ).
cnf(refute_0_48,plain,
( ~ theorem(or(X_342,or(or(X_108,X_107),not(X_107))))
| theorem(or(or(X_108,X_107),or(X_342,not(X_107)))) ),
inference(subst,[],[refute_0_17:[bind(X_53,$fot(X_342)),bind(X_54,$fot(or(X_108,X_107))),bind(X_55,$fot(not(X_107)))]]) ).
cnf(refute_0_49,plain,
theorem(or(or(X_108,X_107),or(X_342,not(X_107)))),
inference(resolve,[$cnf( theorem(or(X_342,or(or(X_108,X_107),not(X_107)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
theorem(or(or(X_355,X_354),or(X_356,not(X_354)))),
inference(subst,[],[refute_0_49:[bind(X_107,$fot(X_354)),bind(X_108,$fot(X_355)),bind(X_342,$fot(X_356))]]) ).
cnf(refute_0_51,plain,
theorem(or(or(X_356,not(X_354)),or(X_355,X_354))),
inference(resolve,[$cnf( theorem(or(or(X_355,X_354),or(X_356,not(X_354)))) )],[refute_0_50,refute_0_22]) ).
cnf(refute_0_52,plain,
theorem(or(or(X_371,not(X_369)),or(X_370,X_369))),
inference(subst,[],[refute_0_51:[bind(X_354,$fot(X_369)),bind(X_355,$fot(X_370)),bind(X_356,$fot(X_371))]]) ).
cnf(refute_0_53,plain,
theorem(or(X_370,or(or(X_371,not(X_369)),X_369))),
inference(resolve,[$cnf( theorem(or(or(X_371,not(X_369)),or(X_370,X_369))) )],[refute_0_52,refute_0_21]) ).
cnf(refute_0_54,plain,
theorem(or(or(or(X_408,not(X_406)),X_406),or(or(X_408,not(X_406)),X_406))),
inference(subst,[],[refute_0_53:[bind(X_369,$fot(X_406)),bind(X_370,$fot(or(or(X_408,not(X_406)),X_406))),bind(X_371,$fot(X_408))]]) ).
cnf(refute_0_55,plain,
theorem(or(or(X_408,not(X_406)),X_406)),
inference(resolve,[$cnf( theorem(or(or(or(X_408,not(X_406)),X_406),or(or(X_408,not(X_406)),X_406))) )],[refute_0_54,refute_0_20]) ).
cnf(refute_0_56,plain,
theorem(or(or(X_410,not(X_409)),X_409)),
inference(subst,[],[refute_0_55:[bind(X_406,$fot(X_409)),bind(X_408,$fot(X_410))]]) ).
cnf(refute_0_57,plain,
theorem(or(X_409,or(X_410,not(X_409)))),
inference(resolve,[$cnf( theorem(or(or(X_410,not(X_409)),X_409)) )],[refute_0_56,refute_0_19]) ).
cnf(refute_0_58,plain,
theorem(or(X_411,or(X_412,not(X_411)))),
inference(subst,[],[refute_0_57:[bind(X_409,$fot(X_411)),bind(X_410,$fot(X_412))]]) ).
cnf(refute_0_59,plain,
theorem(or(X_412,or(X_411,not(X_411)))),
inference(resolve,[$cnf( theorem(or(X_411,or(X_412,not(X_411)))) )],[refute_0_58,refute_0_18]) ).
cnf(refute_0_60,plain,
theorem(or(or(X_415,not(X_415)),or(X_415,not(X_415)))),
inference(subst,[],[refute_0_59:[bind(X_411,$fot(X_415)),bind(X_412,$fot(or(X_415,not(X_415))))]]) ).
cnf(refute_0_61,plain,
theorem(or(X_415,not(X_415))),
inference(resolve,[$cnf( theorem(or(or(X_415,not(X_415)),or(X_415,not(X_415)))) )],[refute_0_60,refute_0_11]) ).
cnf(refute_0_62,plain,
theorem(or(X_417,not(X_417))),
inference(subst,[],[refute_0_61:[bind(X_415,$fot(X_417))]]) ).
cnf(refute_0_63,plain,
theorem(or(not(X_417),X_417)),
inference(resolve,[$cnf( theorem(or(X_417,not(X_417))) )],[refute_0_62,refute_0_5]) ).
cnf(refute_0_64,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_65,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_64]) ).
cnf(refute_0_66,plain,
or(not(X_417),X_417) = implies(X_417,X_417),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_417)),bind(Y,$fot(X_417))]]) ).
cnf(refute_0_67,plain,
( or(not(X_417),X_417) != implies(X_417,X_417)
| ~ theorem(or(not(X_417),X_417))
| theorem(implies(X_417,X_417)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X_417),X_417)) ),[0],$fot(implies(X_417,X_417))]]) ).
cnf(refute_0_68,plain,
( ~ theorem(or(not(X_417),X_417))
| theorem(implies(X_417,X_417)) ),
inference(resolve,[$cnf( $equal(or(not(X_417),X_417),implies(X_417,X_417)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
theorem(implies(X_417,X_417)),
inference(resolve,[$cnf( theorem(or(not(X_417),X_417)) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
theorem(implies(p,p)),
inference(subst,[],[refute_0_69:[bind(X_417,$fot(p))]]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( theorem(implies(p,p)) )],[refute_0_70,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL176-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 05:09:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48
%------------------------------------------------------------------------------