TSTP Solution File: LCL076-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL076-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:49:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 46 ( 26 unt; 0 nHn; 20 RR)
% Number of literals : 72 ( 0 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 97 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(prove_cn_40,negated_conjecture,
~ is_a_theorem(implies(a,not(not(a)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(not(not(not(Y))),not(Y)))
| is_a_theorem(implies(Y,not(not(Y)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(implies(X_7,implies(Y,X_7))),
inference(subst,[],[cn_18:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(X_7)
| ~ is_a_theorem(implies(X_7,implies(Y,X_7)))
| is_a_theorem(implies(Y,X_7)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_7)),bind(Y,$fot(implies(Y,X_7)))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X_7)
| is_a_theorem(implies(Y,X_7)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_7,implies(Y,X_7))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))
| is_a_theorem(implies(Y,implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))) ),
inference(subst,[],[refute_0_5:[bind(X_7,$fot(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(not(X_30),not(X_29)),implies(X_29,X_30))),
inference(subst,[],[cn_49:[bind(X,$fot(X_30)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| ~ is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z))))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,implies(Y,Z)))),bind(Y,$fot(implies(implies(X,Y),implies(X,Z))))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X,implies(Y,Z)))
| is_a_theorem(implies(implies(X,Y),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) )],[cn_35,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X_30),not(X_29)),implies(X_29,X_30)))
| is_a_theorem(implies(implies(implies(not(X_30),not(X_29)),X_29),implies(implies(not(X_30),not(X_29)),X_30))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(not(X_30),not(X_29)))),bind(Y,$fot(X_29)),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(not(X_30),not(X_29)),X_29),implies(implies(not(X_30),not(X_29)),X_30))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_30),not(X_29)),implies(X_29,X_30))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))),
inference(subst,[],[refute_0_11:[bind(X_29,$fot(X_41)),bind(X_30,$fot(X_42))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(Y,implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))) )],[refute_0_12,refute_0_6]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(not(not(X_529)),implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))),
inference(subst,[],[refute_0_13:[bind(Y,$fot(not(not(X_529))))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(not(not(X_420)),X_421),implies(not(not(X_420)),X_420)))
| ~ is_a_theorem(implies(not(not(X_420)),X_421))
| is_a_theorem(implies(not(not(X_420)),X_420)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(not(X_420)),X_421))),bind(Y,$fot(implies(not(not(X_420)),X_420)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(not(not(X_395)),implies(X_396,X_395)))
| is_a_theorem(implies(implies(not(not(X_395)),X_396),implies(not(not(X_395)),X_395))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(not(not(X_395)))),bind(Y,$fot(X_396)),bind(Z,$fot(X_395))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(X_53,implies(not(X_51),not(X_52))))
| ~ is_a_theorem(implies(implies(X_53,implies(not(X_51),not(X_52))),implies(X_53,implies(X_52,X_51))))
| is_a_theorem(implies(X_53,implies(X_52,X_51))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_53,implies(not(X_51),not(X_52))))),bind(Y,$fot(implies(X_53,implies(X_52,X_51))))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(X_9,implies(implies(not(X),not(Y)),implies(Y,X)))) ),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_9)),bind(X_7,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(X_9,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_18]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_28,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(subst,[],[refute_0_19:[bind(X_9,$fot(X_28))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(X_28,implies(implies(not(X),not(Y)),implies(Y,X))))
| is_a_theorem(implies(implies(X_28,implies(not(X),not(Y))),implies(X_28,implies(Y,X)))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_28)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(implies(Y,X)))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_28,implies(not(X),not(Y))),implies(X_28,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_28,implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(X_53,implies(not(X_51),not(X_52))),implies(X_53,implies(X_52,X_51)))),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(X_28,$fot(X_53))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(X_53,implies(not(X_51),not(X_52))))
| is_a_theorem(implies(X_53,implies(X_52,X_51))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_53,implies(not(X_51),not(X_52))),implies(X_53,implies(X_52,X_51)))) )],[refute_0_23,refute_0_17]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(not(not(X_51)),implies(not(X_51),not(X_52))))
| is_a_theorem(implies(not(not(X_51)),implies(X_52,X_51))) ),
inference(subst,[],[refute_0_24:[bind(X_53,$fot(not(not(X_51))))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(not(X_389),implies(not(X_388),not(X_389)))),
inference(subst,[],[cn_18:[bind(X,$fot(not(X_389))),bind(Y,$fot(not(X_388)))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(not(X_389),implies(not(X_388),not(X_389))))
| is_a_theorem(implies(not(X_389),implies(X_389,X_388))) ),
inference(subst,[],[refute_0_24:[bind(X_51,$fot(X_388)),bind(X_52,$fot(X_389)),bind(X_53,$fot(not(X_389)))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(not(X_389),implies(X_389,X_388))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_389),implies(not(X_388),not(X_389)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(not(not(X_51)),implies(not(X_51),not(X_52)))),
inference(subst,[],[refute_0_28:[bind(X_388,$fot(not(X_52))),bind(X_389,$fot(not(X_51)))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(not(not(X_51)),implies(X_52,X_51))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_51)),implies(not(X_51),not(X_52)))) )],[refute_0_29,refute_0_25]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(not(not(X_395)),implies(X_396,X_395))),
inference(subst,[],[refute_0_30:[bind(X_51,$fot(X_395)),bind(X_52,$fot(X_396))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(not(not(X_395)),X_396),implies(not(not(X_395)),X_395))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_395)),implies(X_396,X_395))) )],[refute_0_31,refute_0_16]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(not(not(X_420)),X_421),implies(not(not(X_420)),X_420))),
inference(subst,[],[refute_0_32:[bind(X_395,$fot(X_420)),bind(X_396,$fot(X_421))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(not(not(X_420)),X_421))
| is_a_theorem(implies(not(not(X_420)),X_420)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_420)),X_421),implies(not(not(X_420)),X_420))) )],[refute_0_33,refute_0_15]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(not(not(X_529)),implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))))
| is_a_theorem(implies(not(not(X_529)),X_529)) ),
inference(subst,[],[refute_0_34:[bind(X_420,$fot(X_529)),bind(X_421,$fot(implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42))))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(not(not(X_529)),X_529)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_529)),implies(implies(implies(not(X_42),not(X_41)),X_41),implies(implies(not(X_42),not(X_41)),X_42)))) )],[refute_0_14,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(not(not(not(Y))),not(Y))),
inference(subst,[],[refute_0_36:[bind(X_529,$fot(not(Y)))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(Y,not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(Y))),not(Y))) )],[refute_0_37,refute_0_2]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(a,not(not(a)))),
inference(subst,[],[refute_0_38:[bind(Y,$fot(a))]]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_39,prove_cn_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL076-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Sun Jul 3 15:06:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------