TSTP Solution File: LCL126-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL126-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:49:46 EDT 2022
% Result : Unsatisfiable 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of clauses : 37 ( 21 unt; 0 nHn; 16 RR)
% Number of literals : 58 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(q_3,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))) ).
cnf(q_4,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))) ).
cnf(prove_q_2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(X_22,equivalent(equivalent(X_22,equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_25,X_26)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_22,equivalent(equivalent(X_22,equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_25,X_26)),equivalent(X_26,X_25)))
| is_a_theorem(equivalent(X_26,X_25)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_22,equivalent(equivalent(X_22,equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_25,X_26)))),bind(Y,$fot(equivalent(X_26,X_25)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(equivalent(X_6,equivalent(equivalent(X_6,equivalent(Y,Z)),equivalent(Z,Y)))),
inference(subst,[],[q_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(equivalent(X_6,equivalent(equivalent(X_6,equivalent(Y,Z)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(X_6,equivalent(Y,Z)),equivalent(Z,Y))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(equivalent(equivalent(X_6,equivalent(Y,Z)),equivalent(Z,Y))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(equivalent(equivalent(X_6,equivalent(Y,Z)),equivalent(Z,Y))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_6,equivalent(equivalent(X_6,equivalent(Y,Z)),equivalent(Z,Y)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))),equivalent(X_19,X_20)),equivalent(X_20,X_19))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_19)),bind(Z,$fot(X_20)),bind(X_6,$fot(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))),equivalent(X_19,X_20)),equivalent(X_20,X_19))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))) )],[q_3,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_22,equivalent(equivalent(X_22,equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_25,X_26)),equivalent(X_26,X_25))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(Z,$fot(X_24)),bind(X_19,$fot(X_25)),bind(X_20,$fot(X_26))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(equivalent(X_22,equivalent(equivalent(X_22,equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_25,X_26)))
| is_a_theorem(equivalent(X_26,X_25)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_22,equivalent(equivalent(X_22,equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_25,X_26)),equivalent(X_26,X_25))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(equivalent(X_469,X_470),equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(X_469,X_470))) ),
inference(subst,[],[refute_0_7:[bind(X_22,$fot(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)))),bind(X_25,$fot(equivalent(X_469,X_470))),bind(X_26,$fot(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23))))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_459,X_460),equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461))),equivalent(equivalent(equivalent(X_459,X_460),Z),equivalent(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461)),Z)))),
inference(subst,[],[q_4:[bind(X,$fot(equivalent(X_459,X_460))),bind(Y,$fot(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461))))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_43,X_44),equivalent(equivalent(X_43,X_45),equivalent(X_44,X_45))),equivalent(X_46,X_47)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_43,X_44),equivalent(equivalent(X_43,X_45),equivalent(X_44,X_45))),equivalent(X_46,X_47)),equivalent(X_47,X_46)))
| is_a_theorem(equivalent(X_47,X_46)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_43,X_44),equivalent(equivalent(X_43,X_45),equivalent(X_44,X_45))),equivalent(X_46,X_47)))),bind(Y,$fot(equivalent(X_47,X_46)))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))),equivalent(X_19,X_20)),equivalent(X_20,X_19))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_19)),bind(Z,$fot(X_20)),bind(X_6,$fot(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))),equivalent(X_19,X_20)),equivalent(X_20,X_19))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))) )],[q_4,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_43,X_44),equivalent(equivalent(X_43,X_45),equivalent(X_44,X_45))),equivalent(X_46,X_47)),equivalent(X_47,X_46))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_43)),bind(Y,$fot(X_44)),bind(Z,$fot(X_45)),bind(X_19,$fot(X_46)),bind(X_20,$fot(X_47))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_43,X_44),equivalent(equivalent(X_43,X_45),equivalent(X_44,X_45))),equivalent(X_46,X_47)))
| is_a_theorem(equivalent(X_47,X_46)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_43,X_44),equivalent(equivalent(X_43,X_45),equivalent(X_44,X_45))),equivalent(X_46,X_47)),equivalent(X_47,X_46))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_459,X_460),equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461))),equivalent(equivalent(equivalent(X_459,X_460),Z),equivalent(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461)),Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461)),Z),equivalent(equivalent(X_459,X_460),Z))) ),
inference(subst,[],[refute_0_14:[bind(X_43,$fot(X_459)),bind(X_44,$fot(X_460)),bind(X_45,$fot(X_461)),bind(X_46,$fot(equivalent(equivalent(X_459,X_460),Z))),bind(X_47,$fot(equivalent(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461)),Z)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461)),Z),equivalent(equivalent(X_459,X_460),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_459,X_460),equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461))),equivalent(equivalent(equivalent(X_459,X_460),Z),equivalent(equivalent(equivalent(X_459,X_461),equivalent(X_460,X_461)),Z)))) )],[refute_0_9,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(equivalent(X_469,X_470),equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23))))),
inference(subst,[],[refute_0_16:[bind(Z,$fot(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23)))),bind(X_459,$fot(X_469)),bind(X_460,$fot(X_470)),bind(X_461,$fot(X_471))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(X_469,X_470))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(equivalent(X_469,X_470),equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(X_23,X_24)),equivalent(X_24,X_23))))) )],[refute_0_17,refute_0_8]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_560,X_471),equivalent(X_559,X_471)),equivalent(X_560,X_559)),equivalent(X_559,X_560)),equivalent(X_560,X_559))),
inference(subst,[],[refute_0_18:[bind(X_23,$fot(X_560)),bind(X_24,$fot(X_559)),bind(X_469,$fot(X_560)),bind(X_470,$fot(X_559))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(X_499,equivalent(X_497,X_498)),equivalent(X_498,X_497)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_499,equivalent(X_497,X_498)),equivalent(X_498,X_497)),X_499))
| is_a_theorem(X_499) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_499,equivalent(X_497,X_498)),equivalent(X_498,X_497)))),bind(Y,$fot(X_499))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_494,equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),X_494)) ),
inference(subst,[],[refute_0_7:[bind(X_22,$fot(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)))),bind(X_25,$fot(X_494)),bind(X_26,$fot(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23))))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45))),equivalent(equivalent(X_469,X_470),equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45)),equivalent(X_469,X_470))) ),
inference(subst,[],[refute_0_14:[bind(X_43,$fot(equivalent(X_469,X_471))),bind(X_44,$fot(equivalent(X_470,X_471))),bind(X_46,$fot(equivalent(X_469,X_470))),bind(X_47,$fot(equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45))))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45))),equivalent(equivalent(X_469,X_470),equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45))))),
inference(subst,[],[refute_0_16:[bind(Z,$fot(equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45)))),bind(X_459,$fot(X_469)),bind(X_460,$fot(X_470)),bind(X_461,$fot(X_471))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45)),equivalent(X_469,X_470))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_469,X_471),equivalent(X_470,X_471)),equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45))),equivalent(equivalent(X_469,X_470),equivalent(equivalent(equivalent(X_469,X_471),X_45),equivalent(equivalent(X_470,X_471),X_45))))) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_494,equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23))))),
inference(subst,[],[refute_0_24:[bind(X_45,$fot(equivalent(X_24,X_23))),bind(X_469,$fot(X_494)),bind(X_470,$fot(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)))),bind(X_471,$fot(equivalent(X_23,X_24)))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),X_494)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(equivalent(equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23)),equivalent(X_23,X_24)),equivalent(X_24,X_23))),equivalent(X_494,equivalent(equivalent(X_494,equivalent(X_23,X_24)),equivalent(X_24,X_23))))) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_499,equivalent(X_497,X_498)),equivalent(X_498,X_497)),X_499)),
inference(subst,[],[refute_0_26:[bind(X_23,$fot(X_497)),bind(X_24,$fot(X_498)),bind(X_494,$fot(X_499))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(equivalent(equivalent(X_499,equivalent(X_497,X_498)),equivalent(X_498,X_497)))
| is_a_theorem(X_499) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_499,equivalent(X_497,X_498)),equivalent(X_498,X_497)),X_499)) )],[refute_0_27,refute_0_20]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_560,X_471),equivalent(X_559,X_471)),equivalent(X_560,X_559)),equivalent(X_559,X_560)),equivalent(X_560,X_559)))
| is_a_theorem(equivalent(equivalent(equivalent(X_560,X_471),equivalent(X_559,X_471)),equivalent(X_560,X_559))) ),
inference(subst,[],[refute_0_28:[bind(X_497,$fot(X_559)),bind(X_498,$fot(X_560)),bind(X_499,$fot(equivalent(equivalent(equivalent(X_560,X_471),equivalent(X_559,X_471)),equivalent(X_560,X_559))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_560,X_471),equivalent(X_559,X_471)),equivalent(X_560,X_559))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_560,X_471),equivalent(X_559,X_471)),equivalent(X_560,X_559)),equivalent(X_559,X_560)),equivalent(X_560,X_559))) )],[refute_0_19,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
inference(subst,[],[refute_0_30:[bind(X_471,$fot(b)),bind(X_559,$fot(c)),bind(X_560,$fot(a))]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))) )],[refute_0_31,prove_q_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL126-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 01:47:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.53
% 0.18/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.54
%------------------------------------------------------------------------------