%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:41:56 PM UTC 2026
% Result : Unsatisfiable 1.68s 2.00s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 29 ( 16 unt; 0 nHn; 12 RR)
% Number of literals : 46 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(qyf,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))) ).
cnf(prove_xgj,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Z)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y)))
| is_a_theorem(equivalent(Z,Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X,Y),equivalent(X,Z)))),bind(Y,$fot(equivalent(Z,Y)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Z)))
| is_a_theorem(equivalent(Z,Y)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))) )],[qyf,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(equivalent(X_1458,equivalent(equivalent(X_1459,equivalent(X_1458,Z)),equivalent(X_1459,X_1458))),equivalent(X_1458,Z)))
| is_a_theorem(equivalent(Z,equivalent(equivalent(X_1459,equivalent(X_1458,Z)),equivalent(X_1459,X_1458)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_1458)),bind(Y,$fot(equivalent(equivalent(X_1459,equivalent(X_1458,Z)),equivalent(X_1459,X_1458))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(X_1454,X_1456),equivalent(X_1454,equivalent(X_1454,equivalent(equivalent(X_1455,X_1456),equivalent(X_1455,X_1454))))))
| is_a_theorem(equivalent(equivalent(X_1454,equivalent(equivalent(X_1455,X_1456),equivalent(X_1455,X_1454))),X_1456)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_1454)),bind(Y,$fot(X_1456)),bind(Z,$fot(equivalent(X_1454,equivalent(equivalent(X_1455,X_1456),equivalent(X_1455,X_1454)))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)),equivalent(X_918,equivalent(X_918,equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921))))),equivalent(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)),equivalent(X_921,X_920))))
| is_a_theorem(equivalent(equivalent(X_921,X_920),equivalent(X_918,equivalent(X_918,equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)))))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)))),bind(Y,$fot(equivalent(X_918,equivalent(X_918,equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)))))),bind(Z,$fot(equivalent(X_921,X_920)))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,X_7),equivalent(X,equivalent(X,X_7))),equivalent(equivalent(X,X_7),X_7))),
inference(subst,[],[qyf:[bind(Y,$fot(X_7)),bind(Z,$fot(equivalent(X,X_7)))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,X_7),equivalent(X,equivalent(X,X_7))),equivalent(equivalent(X,X_7),X_7)))
| is_a_theorem(equivalent(X_7,equivalent(X,equivalent(X,X_7)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X,X_7))),bind(Y,$fot(equivalent(X,equivalent(X,X_7)))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(X_7,equivalent(X,equivalent(X,X_7)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,X_7),equivalent(X,equivalent(X,X_7))),equivalent(equivalent(X,X_7),X_7))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(X_31)
| ~ is_a_theorem(equivalent(X_31,equivalent(X_31,equivalent(equivalent(equivalent(X_28,X_29),equivalent(X_28,X_30)),equivalent(X_30,X_29)))))
| is_a_theorem(equivalent(X_31,equivalent(equivalent(equivalent(X_28,X_29),equivalent(X_28,X_30)),equivalent(X_30,X_29)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_31)),bind(Y,$fot(equivalent(X_31,equivalent(equivalent(equivalent(X_28,X_29),equivalent(X_28,X_30)),equivalent(X_30,X_29)))))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(X_9)
| ~ is_a_theorem(equivalent(X_9,equivalent(X_8,equivalent(X_8,X_9))))
| is_a_theorem(equivalent(X_8,equivalent(X_8,X_9))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_9)),bind(Y,$fot(equivalent(X_8,equivalent(X_8,X_9))))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(X_9,equivalent(X_8,equivalent(X_8,X_9)))),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_8)),bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(X_9)
| is_a_theorem(equivalent(X_8,equivalent(X_8,X_9))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_9,equivalent(X_8,equivalent(X_8,X_9)))) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y)))
| is_a_theorem(equivalent(X_12,equivalent(X_12,equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))))) ),
inference(subst,[],[refute_0_11:[bind(X_8,$fot(X_12)),bind(X_9,$fot(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(X_12,equivalent(X_12,equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))) )],[qyf,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(X_31,equivalent(X_31,equivalent(equivalent(equivalent(X_28,X_29),equivalent(X_28,X_30)),equivalent(X_30,X_29))))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_28)),bind(Y,$fot(X_29)),bind(Z,$fot(X_30)),bind(X_12,$fot(X_31))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(X_31)
| is_a_theorem(equivalent(X_31,equivalent(equivalent(equivalent(X_28,X_29),equivalent(X_28,X_30)),equivalent(X_30,X_29)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_31,equivalent(X_31,equivalent(equivalent(equivalent(X_28,X_29),equivalent(X_28,X_30)),equivalent(X_30,X_29))))) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(X_7,equivalent(X,equivalent(X,X_7))))
| is_a_theorem(equivalent(equivalent(X_7,equivalent(X,equivalent(X,X_7))),equivalent(equivalent(equivalent(X_467,X_468),equivalent(X_467,X_469)),equivalent(X_469,X_468)))) ),
inference(subst,[],[refute_0_15:[bind(X_28,$fot(X_467)),bind(X_29,$fot(X_468)),bind(X_30,$fot(X_469)),bind(X_31,$fot(equivalent(X_7,equivalent(X,equivalent(X,X_7)))))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(X_7,equivalent(X,equivalent(X,X_7))),equivalent(equivalent(equivalent(X_467,X_468),equivalent(X_467,X_469)),equivalent(X_469,X_468)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_7,equivalent(X,equivalent(X,X_7)))) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)),equivalent(X_918,equivalent(X_918,equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921))))),equivalent(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)),equivalent(X_921,X_920)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_918)),bind(X_467,$fot(X_919)),bind(X_468,$fot(X_920)),bind(X_469,$fot(X_921)),bind(X_7,$fot(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921))))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(equivalent(X_921,X_920),equivalent(X_918,equivalent(X_918,equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)),equivalent(X_918,equivalent(X_918,equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921))))),equivalent(equivalent(equivalent(X_919,X_920),equivalent(X_919,X_921)),equivalent(X_921,X_920)))) )],[refute_0_18,refute_0_4]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(X_1454,X_1456),equivalent(X_1454,equivalent(X_1454,equivalent(equivalent(X_1455,X_1456),equivalent(X_1455,X_1454)))))),
inference(subst,[],[refute_0_19:[bind(X_918,$fot(X_1454)),bind(X_919,$fot(X_1455)),bind(X_920,$fot(X_1456)),bind(X_921,$fot(X_1454))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X_1454,equivalent(equivalent(X_1455,X_1456),equivalent(X_1455,X_1454))),X_1456)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_1454,X_1456),equivalent(X_1454,equivalent(X_1454,equivalent(equivalent(X_1455,X_1456),equivalent(X_1455,X_1454)))))) )],[refute_0_20,refute_0_3]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(X_1458,equivalent(equivalent(X_1459,equivalent(X_1458,Z)),equivalent(X_1459,X_1458))),equivalent(X_1458,Z))),
inference(subst,[],[refute_0_21:[bind(X_1454,$fot(X_1458)),bind(X_1455,$fot(X_1459)),bind(X_1456,$fot(equivalent(X_1458,Z)))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(Z,equivalent(equivalent(X_1459,equivalent(X_1458,Z)),equivalent(X_1459,X_1458)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_1458,equivalent(equivalent(X_1459,equivalent(X_1458,Z)),equivalent(X_1459,X_1458))),equivalent(X_1458,Z))) )],[refute_0_22,refute_0_2]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
inference(subst,[],[refute_0_23:[bind(Z,$fot(a)),bind(X_1458,$fot(c)),bind(X_1459,$fot(b))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))) )],[refute_0_24,prove_xgj]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.33 % Computer : n013.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Fri Sep 4 20:41:49 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.68/2.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.68/2.00
% 1.68/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.68/2.02
%------------------------------------------------------------------------------