%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:41:39 PM UTC 2026
% Result : Unsatisfiable 1.05s 1.30s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of clauses : 60 ( 34 unt; 0 nHn; 21 RR)
% Number of literals : 93 ( 0 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 151 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(yql,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
cnf(prove_ec_5,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11)))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))),bind(Y,$fot(equivalent(equivalent(X_8,X_9),X_11)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z)))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(equivalent(X_994,equivalent(X_992,X_9)),equivalent(equivalent(X_992,X_9),equivalent(equivalent(X_994,X_992),X_992))))
| is_a_theorem(equivalent(equivalent(equivalent(X_994,X_992),X_9),equivalent(X_994,equivalent(X_992,X_9)))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_992)),bind(X_11,$fot(equivalent(X_994,equivalent(X_992,X_9)))),bind(X_8,$fot(equivalent(X_994,X_992)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(X_50,X_51))
| ~ is_a_theorem(equivalent(equivalent(X_50,X_51),equivalent(X_51,X_50)))
| is_a_theorem(equivalent(X_51,X_50)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_50,X_51))),bind(Y,$fot(equivalent(X_51,X_50)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(X_49,X_49))
| is_a_theorem(equivalent(equivalent(Z,X_49),equivalent(X_49,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_49)),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(equivalent(X_27,X_26),X_27),equivalent(equivalent(X_26,X_29),equivalent(X_27,X_26)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_26,X_29),X_27),equivalent(equivalent(X_27,X_26),X_29))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(equivalent(X_27,X_26))),bind(X_11,$fot(equivalent(equivalent(X_27,X_26),X_29))),bind(X_8,$fot(equivalent(X_26,X_29))),bind(X_9,$fot(X_27))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_14,X_12),equivalent(equivalent(Z,X_15),equivalent(X_12,Z))),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_12)),bind(Y,$fot(X_15)),bind(X_7,$fot(equivalent(X_14,X_12)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_14,X_12),equivalent(equivalent(Z,X_15),equivalent(X_12,Z))),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12))))
| is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_14,X_12),equivalent(equivalent(Z,X_15),equivalent(X_12,Z))))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_12)),bind(X_11,$fot(equivalent(equivalent(X_14,X_12),equivalent(equivalent(Z,X_15),equivalent(X_12,Z))))),bind(X_8,$fot(X_14)),bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_14,X_12),equivalent(equivalent(Z,X_15),equivalent(X_12,Z))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_14,X_12),equivalent(equivalent(Z,X_15),equivalent(X_12,Z))),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(equivalent(X_27,X_26),X_27),equivalent(equivalent(X_26,X_29),equivalent(X_27,X_26))))),
inference(subst,[],[refute_0_13:[bind(Z,$fot(X_26)),bind(X_12,$fot(X_27)),bind(X_14,$fot(equivalent(X_27,X_26))),bind(X_15,$fot(X_29))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_26,X_29),X_27),equivalent(equivalent(X_27,X_26),X_29))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_27,X_26),X_29),equivalent(equivalent(equivalent(X_27,X_26),X_27),equivalent(equivalent(X_26,X_29),equivalent(X_27,X_26))))) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_29,X_29),X_29),equivalent(equivalent(X_29,X_29),X_29))),
inference(subst,[],[refute_0_15:[bind(X_26,$fot(X_29)),bind(X_27,$fot(X_29))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(equivalent(X_24,X_24))
| ~ is_a_theorem(equivalent(equivalent(X_24,X_24),equivalent(X_25,X_25)))
| is_a_theorem(equivalent(X_25,X_25)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_24,X_24))),bind(Y,$fot(equivalent(X_25,X_25)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(equivalent(equivalent(X_22,X_22),equivalent(equivalent(X_22,X_21),equivalent(X_21,X_22))))
| is_a_theorem(equivalent(equivalent(X_21,X_21),equivalent(X_22,X_22))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_22)),bind(X_11,$fot(equivalent(X_22,X_22))),bind(X_8,$fot(X_21)),bind(X_9,$fot(X_21))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)),equivalent(equivalent(X_19,X_20),equivalent(X_8,X_19))))
| is_a_theorem(equivalent(equivalent(X_8,X_20),equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_19)),bind(X_11,$fot(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)))),bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_17)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_16,X_17)),equivalent(equivalent(X_16,X_17),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X_16,X_17))),bind(Y,$fot(equivalent(X_16,X_17)))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12)))),
inference(subst,[],[yql:[bind(X,$fot(X_14)),bind(Y,$fot(X_15)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12))))
| is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(X_14,X_15))) ),
inference(subst,[],[refute_0_6:[bind(X_10,$fot(X_12)),bind(X_11,$fot(equivalent(X_14,X_15))),bind(X_8,$fot(X_14)),bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(X_14,X_15))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_14,X_15),equivalent(equivalent(X_12,X_15),equivalent(X_14,X_12)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_17))),
inference(subst,[],[refute_0_23:[bind(X_14,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_16,X_17)),equivalent(equivalent(X_16,X_17),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_17))) )],[refute_0_24,refute_0_20]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)),equivalent(equivalent(X_19,X_20),equivalent(X_8,X_19)))),
inference(subst,[],[refute_0_25:[bind(Z,$fot(equivalent(X_8,X_19))),bind(X_16,$fot(X_19)),bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(equivalent(X_8,X_20),equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,X_19),equivalent(X_19,X_20)),equivalent(equivalent(X_19,X_20),equivalent(X_8,X_19)))) )],[refute_0_26,refute_0_19]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(X_22,X_22),equivalent(equivalent(X_22,X_21),equivalent(X_21,X_22)))),
inference(subst,[],[refute_0_27:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22)),bind(X_8,$fot(X_22))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(X_21,X_21),equivalent(X_22,X_22))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_22,X_22),equivalent(equivalent(X_22,X_21),equivalent(X_21,X_22)))) )],[refute_0_28,refute_0_18]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(X_24,X_24),equivalent(X_25,X_25))),
inference(subst,[],[refute_0_29:[bind(X_21,$fot(X_24)),bind(X_22,$fot(X_25))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(equivalent(X_24,X_24))
| is_a_theorem(equivalent(X_25,X_25)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_24,X_24),equivalent(X_25,X_25))) )],[refute_0_30,refute_0_17]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_29,X_29),X_29),equivalent(equivalent(X_29,X_29),X_29)))
| is_a_theorem(equivalent(X_48,X_48)) ),
inference(subst,[],[refute_0_31:[bind(X_24,$fot(equivalent(equivalent(X_29,X_29),X_29))),bind(X_25,$fot(X_48))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(X_48,X_48)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_29,X_29),X_29),equivalent(equivalent(X_29,X_29),X_29))) )],[refute_0_16,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(X_49,X_49)),
inference(subst,[],[refute_0_33:[bind(X_48,$fot(X_49))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(equivalent(equivalent(Z,X_49),equivalent(X_49,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_49,X_49)) )],[refute_0_34,refute_0_9]) ).
cnf(refute_0_36,plain,
is_a_theorem(equivalent(equivalent(X_50,X_51),equivalent(X_51,X_50))),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_50)),bind(X_49,$fot(X_51))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(equivalent(X_50,X_51))
| is_a_theorem(equivalent(X_51,X_50)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_50,X_51),equivalent(X_51,X_50))) )],[refute_0_36,refute_0_8]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_108,X_109),X_109),X_108))
| is_a_theorem(equivalent(X_108,equivalent(equivalent(X_108,X_109),X_109))) ),
inference(subst,[],[refute_0_37:[bind(X_50,$fot(equivalent(equivalent(X_108,X_109),X_109))),bind(X_51,$fot(X_108))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(equivalent(equivalent(X_99,X_101),equivalent(X_101,X_99))),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_99)),bind(X_49,$fot(X_101))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(equivalent(equivalent(X_30,X_32),X_31))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X_30,X_32),X_31),equivalent(equivalent(X_31,X_30),X_32)))
| is_a_theorem(equivalent(equivalent(X_31,X_30),X_32)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_30,X_32),X_31))),bind(Y,$fot(equivalent(equivalent(X_31,X_30),X_32)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_30,X_32),X_31),equivalent(equivalent(X_31,X_30),X_32))),
inference(subst,[],[refute_0_15:[bind(X_26,$fot(X_30)),bind(X_27,$fot(X_31)),bind(X_29,$fot(X_32))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(equivalent(equivalent(X_30,X_32),X_31))
| is_a_theorem(equivalent(equivalent(X_31,X_30),X_32)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_30,X_32),X_31),equivalent(equivalent(X_31,X_30),X_32))) )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(equivalent(equivalent(X_99,X_101),equivalent(X_101,X_99)))
| is_a_theorem(equivalent(equivalent(equivalent(X_101,X_99),X_99),X_101)) ),
inference(subst,[],[refute_0_42:[bind(X_30,$fot(X_99)),bind(X_31,$fot(equivalent(X_101,X_99))),bind(X_32,$fot(X_101))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_101,X_99),X_99),X_101)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_99,X_101),equivalent(X_101,X_99))) )],[refute_0_39,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_108,X_109),X_109),X_108)),
inference(subst,[],[refute_0_44:[bind(X_101,$fot(X_108)),bind(X_99,$fot(X_109))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(X_108,equivalent(equivalent(X_108,X_109),X_109))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_108,X_109),X_109),X_108)) )],[refute_0_45,refute_0_38]) ).
cnf(refute_0_47,plain,
is_a_theorem(equivalent(X_826,equivalent(equivalent(X_826,X_109),X_109))),
inference(subst,[],[refute_0_46:[bind(X_108,$fot(X_826))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(equivalent(X_23,X_22))
| ~ is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))))
| is_a_theorem(equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_23,X_22))),bind(Y,$fot(equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22)))),
inference(subst,[],[refute_0_27:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22)),bind(X_8,$fot(X_23))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(equivalent(X_23,X_22))
| is_a_theorem(equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(equivalent(X_23,X_21),equivalent(X_21,X_22)))) )],[refute_0_49,refute_0_48]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(equivalent(X_826,equivalent(equivalent(X_826,X_109),X_109)))
| is_a_theorem(equivalent(equivalent(X_826,X_824),equivalent(X_824,equivalent(equivalent(X_826,X_109),X_109)))) ),
inference(subst,[],[refute_0_50:[bind(X_21,$fot(X_824)),bind(X_22,$fot(equivalent(equivalent(X_826,X_109),X_109))),bind(X_23,$fot(X_826))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(equivalent(equivalent(X_826,X_824),equivalent(X_824,equivalent(equivalent(X_826,X_109),X_109)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_826,equivalent(equivalent(X_826,X_109),X_109))) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(equivalent(equivalent(X_994,equivalent(X_992,X_9)),equivalent(equivalent(X_992,X_9),equivalent(equivalent(X_994,X_992),X_992)))),
inference(subst,[],[refute_0_52:[bind(X_109,$fot(X_992)),bind(X_824,$fot(equivalent(X_992,X_9))),bind(X_826,$fot(X_994))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_994,X_992),X_9),equivalent(X_994,equivalent(X_992,X_9)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_994,equivalent(X_992,X_9)),equivalent(equivalent(X_992,X_9),equivalent(equivalent(X_994,X_992),X_992)))) )],[refute_0_53,refute_0_7]) ).
cnf(refute_0_55,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(subst,[],[refute_0_54:[bind(X_9,$fot(c)),bind(X_992,$fot(b)),bind(X_994,$fot(a))]]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))) )],[refute_0_55,prove_ec_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 5 03:00:08 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.05/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.05/1.30
% 1.05/1.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.05/1.32
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