%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:41:43 PM UTC 2026
% Result : Unsatisfiable 2.96s 3.29s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 87 ( 49 unt; 0 nHn; 25 RR)
% Number of literals : 135 ( 0 equ; 49 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 228 ( 43 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X),X),X)) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) ).
cnf(prove_cn_18,negated_conjecture,
~ is_a_theorem(implies(a,implies(b,a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_23,implies(not(X_23),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_23,implies(not(X_23),Y)))
| is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_23)),bind(Y,$fot(implies(not(X_23),Y))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(X_23,implies(not(X_23),Y))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_28)),bind(X_23,$fot(X_29)),bind(X_25,$fot(X_30))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(not(X_4707),not(X_4708)),implies(X_4708,X_4707)))
| is_a_theorem(implies(X_4707,implies(X_4708,X_4707))) ),
inference(subst,[],[refute_0_7:[bind(X_28,$fot(not(X_4708))),bind(X_29,$fot(X_4707)),bind(X_30,$fot(implies(X_4708,X_4707)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(X_91,X_92),implies(X_90,X_92)),X_93))
| ~ is_a_theorem(implies(implies(implies(implies(X_91,X_92),implies(X_90,X_92)),X_93),implies(implies(X_90,X_91),X_93)))
| is_a_theorem(implies(implies(X_90,X_91),X_93)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_91,X_92),implies(X_90,X_92)),X_93))),bind(Y,$fot(implies(implies(X_90,X_91),X_93)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(implies(X_91,X_92),implies(X_90,X_92)),X_93),implies(implies(X_90,X_91),X_93))),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_90)),bind(Y,$fot(X_91)),bind(Z,$fot(X_92)),bind(X_25,$fot(X_93))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(X_91,X_92),implies(X_90,X_92)),X_93))
| is_a_theorem(implies(implies(X_90,X_91),X_93)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_91,X_92),implies(X_90,X_92)),X_93),implies(implies(X_90,X_91),X_93))) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_4693),X_4691),implies(not(X_4691),X_4691)),implies(X_4693,X_4691)))
| is_a_theorem(implies(implies(not(X_4691),not(X_4693)),implies(X_4693,X_4691))) ),
inference(subst,[],[refute_0_13:[bind(X_90,$fot(not(X_4691))),bind(X_91,$fot(not(X_4693))),bind(X_92,$fot(X_4691)),bind(X_93,$fot(implies(X_4693,X_4691)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1326)),X_1327),X_1326),X_1326))
| ~ is_a_theorem(implies(implies(not(not(X_1326)),X_1327),X_1326))
| is_a_theorem(X_1326) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_1326)),X_1327),X_1326))),bind(Y,$fot(X_1326))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)),implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)))
| is_a_theorem(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)) ),
inference(subst,[],[refute_0_18:[bind(X_7,$fot(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| is_a_theorem(implies(implies(implies(X_29,X_30),Z),implies(implies(implies(not(X_29),X_28),X_30),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(X_29,X_30),Z),implies(implies(implies(not(X_29),X_28),X_30),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_6,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(not(X_1313),X_1313),X_1313),implies(implies(implies(not(not(X_1313)),X_28),X_1313),X_1313))),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_1313)),bind(X_29,$fot(not(X_1313))),bind(X_30,$fot(X_1313))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_452),X_452),X_452),X_454),implies(X_453,X_454)))
| ~ is_a_theorem(implies(implies(implies(not(X_452),X_452),X_452),X_454))
| is_a_theorem(implies(X_453,X_454)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_452),X_452),X_452),X_454))),bind(Y,$fot(implies(X_453,X_454)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(X_133,implies(not(implies(implies(not(X_131),X_131),X_131)),X_132)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_131),X_131),X_131)),X_132),Z),implies(X_133,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_133)),bind(Y,$fot(implies(not(implies(implies(not(X_131),X_131),X_131)),X_132)))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_28]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24)),
inference(subst,[],[refute_0_29:[bind(X_9,$fot(X_24))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(not(implies(implies(not(X),X),X)),X_25))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(not(implies(implies(not(X),X),X)),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(not(X_106),X_105),implies(not(implies(implies(not(X),X),X)),X_105))),
inference(subst,[],[refute_0_32:[bind(X_24,$fot(not(X_106))),bind(X_25,$fot(X_105))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(not(X_106),X_105),implies(not(implies(implies(not(X),X),X)),X_105)))
| is_a_theorem(implies(X_106,implies(not(implies(implies(not(X),X),X)),X_105))) ),
inference(subst,[],[refute_0_7:[bind(X_28,$fot(X_105)),bind(X_29,$fot(X_106)),bind(X_30,$fot(implies(not(implies(implies(not(X),X),X)),X_105)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(X_106,implies(not(implies(implies(not(X),X),X)),X_105))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_106),X_105),implies(not(implies(implies(not(X),X),X)),X_105))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(X_133,implies(not(implies(implies(not(X_131),X_131),X_131)),X_132))),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_131)),bind(X_105,$fot(X_132)),bind(X_106,$fot(X_133))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_131),X_131),X_131)),X_132),Z),implies(X_133,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_133,implies(not(implies(implies(not(X_131),X_131),X_131)),X_132))) )],[refute_0_36,refute_0_24]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_131),X_131),X_131)),implies(implies(not(X_131),X_131),X_131)),X_451),implies(X_133,X_451))),
inference(subst,[],[refute_0_37:[bind(Z,$fot(X_451)),bind(X_132,$fot(implies(implies(not(X_131),X_131),X_131)))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46)))
| ~ is_a_theorem(implies(implies(implies(not(X_47),X_47),X_48),X_46))
| is_a_theorem(implies(implies(X_47,X_48),X_46)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_47),X_47),X_48),X_46))),bind(Y,$fot(implies(implies(X_47,X_48),X_46)))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27)))
| is_a_theorem(implies(implies(implies(implies(not(X_26),X_26),X_27),Z),implies(implies(X_26,X_27),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_26,X_27))),bind(Y,$fot(implies(implies(not(X_26),X_26),X_27)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(not(X_24),X_24),X_24)),
inference(subst,[],[cn_2:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(not(X_24),X_24),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_24),X_24))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24),X_24),X_24)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))),
inference(subst,[],[refute_0_43:[bind(X_24,$fot(X_26)),bind(X_25,$fot(X_27))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(not(X_26),X_26),X_27),Z),implies(implies(X_26,X_27),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))) )],[refute_0_44,refute_0_40]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46))),
inference(subst,[],[refute_0_45:[bind(Z,$fot(X_46)),bind(X_26,$fot(X_47)),bind(X_27,$fot(X_48))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_47),X_47),X_48),X_46))
| is_a_theorem(implies(implies(X_47,X_48),X_46)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46))) )],[refute_0_46,refute_0_39]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_131),X_131),X_131)),implies(implies(not(X_131),X_131),X_131)),X_451),implies(X_133,X_451)))
| is_a_theorem(implies(implies(implies(implies(not(X_131),X_131),X_131),X_451),implies(X_133,X_451))) ),
inference(subst,[],[refute_0_47:[bind(X_46,$fot(implies(X_133,X_451))),bind(X_47,$fot(implies(implies(not(X_131),X_131),X_131))),bind(X_48,$fot(X_451))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(implies(not(X_131),X_131),X_131),X_451),implies(X_133,X_451))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_131),X_131),X_131)),implies(implies(not(X_131),X_131),X_131)),X_451),implies(X_133,X_451))) )],[refute_0_38,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(implies(not(X_452),X_452),X_452),X_454),implies(X_453,X_454))),
inference(subst,[],[refute_0_49:[bind(X_131,$fot(X_452)),bind(X_133,$fot(X_453)),bind(X_451,$fot(X_454))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_452),X_452),X_452),X_454))
| is_a_theorem(implies(X_453,X_454)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_452),X_452),X_452),X_454),implies(X_453,X_454))) )],[refute_0_50,refute_0_23]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1313),X_1313),X_1313),implies(implies(implies(not(not(X_1313)),X_28),X_1313),X_1313)))
| is_a_theorem(implies(X_1314,implies(implies(implies(not(not(X_1313)),X_28),X_1313),X_1313))) ),
inference(subst,[],[refute_0_51:[bind(X_452,$fot(X_1313)),bind(X_453,$fot(X_1314)),bind(X_454,$fot(implies(implies(implies(not(not(X_1313)),X_28),X_1313),X_1313)))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_1314,implies(implies(implies(not(not(X_1313)),X_28),X_1313),X_1313))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1313),X_1313),X_1313),implies(implies(implies(not(not(X_1313)),X_28),X_1313),X_1313))) )],[refute_0_22,refute_0_52]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(not(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)),implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323))),
inference(subst,[],[refute_0_53:[bind(X_1313,$fot(X_1323)),bind(X_1314,$fot(not(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)))),bind(X_28,$fot(X_1325))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323)),implies(implies(implies(not(not(X_1323)),X_1325),X_1323),X_1323))) )],[refute_0_54,refute_0_19]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(implies(not(not(X_1326)),X_1327),X_1326),X_1326)),
inference(subst,[],[refute_0_55:[bind(X_1323,$fot(X_1326)),bind(X_1325,$fot(X_1327))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(implies(not(not(X_1326)),X_1327),X_1326))
| is_a_theorem(X_1326) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1326)),X_1327),X_1326),X_1326)) )],[refute_0_56,refute_0_15]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959)))),X_1327),implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959))))
| is_a_theorem(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959))) ),
inference(subst,[],[refute_0_57:[bind(X_1326,$fot(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959))))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_1878,X_1879)),implies(X_1878,X_1879)),implies(X_1878,X_1879)),implies(implies(X_1878,implies(not(X_1879),X_1879)),implies(X_1878,X_1879))))
| is_a_theorem(implies(X_453,implies(implies(X_1878,implies(not(X_1879),X_1879)),implies(X_1878,X_1879)))) ),
inference(subst,[],[refute_0_51:[bind(X_452,$fot(implies(X_1878,X_1879))),bind(X_454,$fot(implies(implies(X_1878,implies(not(X_1879),X_1879)),implies(X_1878,X_1879))))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(implies(X_1836,implies(not(X_1837),X_1837)),implies(X_1835,implies(X_1836,X_1837))))
| is_a_theorem(implies(implies(implies(X_1835,implies(X_1836,X_1837)),Z),implies(implies(X_1836,implies(not(X_1837),X_1837)),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_1836,implies(not(X_1837),X_1837)))),bind(Y,$fot(implies(X_1835,implies(X_1836,X_1837))))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1763),X_1763),X_1763),implies(X_1761,X_1763)),implies(X_133,implies(X_1761,X_1763)))),
inference(subst,[],[refute_0_49:[bind(X_131,$fot(X_1763)),bind(X_451,$fot(implies(X_1761,X_1763)))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1763),X_1763),X_1763),implies(X_1761,X_1763)),implies(X_133,implies(X_1761,X_1763))))
| is_a_theorem(implies(implies(X_1761,implies(not(X_1763),X_1763)),implies(X_133,implies(X_1761,X_1763)))) ),
inference(subst,[],[refute_0_13:[bind(X_90,$fot(X_1761)),bind(X_91,$fot(implies(not(X_1763),X_1763))),bind(X_92,$fot(X_1763)),bind(X_93,$fot(implies(X_133,implies(X_1761,X_1763))))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(X_1761,implies(not(X_1763),X_1763)),implies(X_133,implies(X_1761,X_1763)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1763),X_1763),X_1763),implies(X_1761,X_1763)),implies(X_133,implies(X_1761,X_1763)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(X_1836,implies(not(X_1837),X_1837)),implies(X_1835,implies(X_1836,X_1837)))),
inference(subst,[],[refute_0_63:[bind(X_133,$fot(X_1835)),bind(X_1761,$fot(X_1836)),bind(X_1763,$fot(X_1837))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(X_1835,implies(X_1836,X_1837)),Z),implies(implies(X_1836,implies(not(X_1837),X_1837)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1836,implies(not(X_1837),X_1837)),implies(X_1835,implies(X_1836,X_1837)))) )],[refute_0_64,refute_0_60]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(not(implies(X_1878,X_1879)),implies(X_1878,X_1879)),implies(X_1878,X_1879)),implies(implies(X_1878,implies(not(X_1879),X_1879)),implies(X_1878,X_1879)))),
inference(subst,[],[refute_0_65:[bind(Z,$fot(implies(X_1878,X_1879))),bind(X_1835,$fot(not(implies(X_1878,X_1879)))),bind(X_1836,$fot(X_1878)),bind(X_1837,$fot(X_1879))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(X_453,implies(implies(X_1878,implies(not(X_1879),X_1879)),implies(X_1878,X_1879)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_1878,X_1879)),implies(X_1878,X_1879)),implies(X_1878,X_1879)),implies(implies(X_1878,implies(not(X_1879),X_1879)),implies(X_1878,X_1879)))) )],[refute_0_66,refute_0_59]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(not(not(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959)))),X_1327),implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959)))),
inference(subst,[],[refute_0_67:[bind(X_1878,$fot(X_1958)),bind(X_1879,$fot(X_1959)),bind(X_453,$fot(implies(not(not(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959)))),X_1327)))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959)))),X_1327),implies(implies(X_1958,implies(not(X_1959),X_1959)),implies(X_1958,X_1959)))) )],[refute_0_68,refute_0_58]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(X_4681,implies(not(X_1959),X_1959)),implies(X_4681,X_1959))),
inference(subst,[],[refute_0_69:[bind(X_1958,$fot(X_4681))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(implies(X_41,X_42),X_39))
| ~ is_a_theorem(implies(implies(implies(X_41,X_42),X_39),implies(implies(implies(not(X_41),X_40),X_42),X_39)))
| is_a_theorem(implies(implies(implies(not(X_41),X_40),X_42),X_39)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_41,X_42),X_39))),bind(Y,$fot(implies(implies(implies(not(X_41),X_40),X_42),X_39)))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(implies(X_41,X_42),X_39),implies(implies(implies(not(X_41),X_40),X_42),X_39))),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_39)),bind(X_28,$fot(X_40)),bind(X_29,$fot(X_41)),bind(X_30,$fot(X_42))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(X_41,X_42),X_39))
| is_a_theorem(implies(implies(implies(not(X_41),X_40),X_42),X_39)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_41,X_42),X_39),implies(implies(implies(not(X_41),X_40),X_42),X_39))) )],[refute_0_72,refute_0_71]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(X_4681,implies(not(X_1959),X_1959)),implies(X_4681,X_1959)))
| is_a_theorem(implies(implies(implies(not(X_4681),X_4680),implies(not(X_1959),X_1959)),implies(X_4681,X_1959))) ),
inference(subst,[],[refute_0_73:[bind(X_39,$fot(implies(X_4681,X_1959))),bind(X_40,$fot(X_4680)),bind(X_41,$fot(X_4681)),bind(X_42,$fot(implies(not(X_1959),X_1959)))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(implies(not(X_4681),X_4680),implies(not(X_1959),X_1959)),implies(X_4681,X_1959))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_4681,implies(not(X_1959),X_1959)),implies(X_4681,X_1959))) )],[refute_0_70,refute_0_74]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(not(X_4693),X_4691),implies(not(X_4691),X_4691)),implies(X_4693,X_4691))),
inference(subst,[],[refute_0_75:[bind(X_1959,$fot(X_4691)),bind(X_4680,$fot(X_4691)),bind(X_4681,$fot(X_4693))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(not(X_4691),not(X_4693)),implies(X_4693,X_4691))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_4693),X_4691),implies(not(X_4691),X_4691)),implies(X_4693,X_4691))) )],[refute_0_76,refute_0_14]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(not(X_4707),not(X_4708)),implies(X_4708,X_4707))),
inference(subst,[],[refute_0_77:[bind(X_4691,$fot(X_4707)),bind(X_4693,$fot(X_4708))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_4707,implies(X_4708,X_4707))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_4707),not(X_4708)),implies(X_4708,X_4707))) )],[refute_0_78,refute_0_8]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(a,implies(b,a))),
inference(subst,[],[refute_0_79:[bind(X_4707,$fot(a)),bind(X_4708,$fot(b))]]) ).
cnf(refute_0_81,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(b,a))) )],[refute_0_80,prove_cn_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 22:04:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.96/3.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.96/3.29
% 2.96/3.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/3.30
%------------------------------------------------------------------------------