%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL364-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:42:30 PM UTC 2026
% Result : Unsatisfiable 1.68s 1.90s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 52 ( 30 unt; 0 nHn; 16 RR)
% Number of literals : 80 ( 0 equ; 29 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 24 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_13,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),y),implies(z,implies(implies(y,x),x)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(X_32,X_33),implies(X_31,X_33)),X_34))
| ~ is_a_theorem(implies(implies(implies(implies(X_32,X_33),implies(X_31,X_33)),X_34),implies(implies(X_31,X_32),X_34)))
| is_a_theorem(implies(implies(X_31,X_32),X_34)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_32,X_33),implies(X_31,X_33)),X_34))),bind(Y,$fot(implies(implies(X_31,X_32),X_34)))]]) ).
cnf(refute_0_1,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_2,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(X_32,X_33),implies(X_31,X_33)),X_34),implies(implies(X_31,X_32),X_34))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33)),bind(X_25,$fot(X_34))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X_32,X_33),implies(X_31,X_33)),X_34))
| is_a_theorem(implies(implies(X_31,X_32),X_34)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_32,X_33),implies(X_31,X_33)),X_34),implies(implies(X_31,X_32),X_34))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X_32,X_1528),implies(not(X_1528),X_1528)),implies(X_1529,implies(implies(X_32,X_1528),X_1528))))
| is_a_theorem(implies(implies(not(X_1528),X_32),implies(X_1529,implies(implies(X_32,X_1528),X_1528)))) ),
inference(subst,[],[refute_0_6:[bind(X_31,$fot(not(X_1528))),bind(X_33,$fot(X_1528)),bind(X_34,$fot(implies(X_1529,implies(implies(X_32,X_1528),X_1528))))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(X_147,implies(not(implies(implies(not(X_145),X_145),X_145)),X_146)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),X_146),Z),implies(X_147,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_147)),bind(Y,$fot(implies(not(implies(implies(not(X_145),X_145),X_145)),X_146)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_10,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_11,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_11:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24)),
inference(subst,[],[refute_0_13:[bind(X_9,$fot(X_24))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(not(implies(implies(not(X),X),X)),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(not(implies(implies(not(X),X),X)),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(not(X_130),X_129),implies(not(implies(implies(not(X),X),X)),X_129))),
inference(subst,[],[refute_0_16:[bind(X_24,$fot(not(X_130))),bind(X_25,$fot(X_129))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(X_23,implies(not(X_23),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_20,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_2:[bind(X,$fot(X_23)),bind(Y,$fot(implies(not(X_23),Y))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(X_23,implies(not(X_23),Y))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))),
inference(subst,[],[refute_0_21:[bind(Y,$fot(X_28)),bind(X_23,$fot(X_29)),bind(X_25,$fot(X_30))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(not(X_130),X_129),implies(not(implies(implies(not(X),X),X)),X_129)))
| is_a_theorem(implies(X_130,implies(not(implies(implies(not(X),X),X)),X_129))) ),
inference(subst,[],[refute_0_23:[bind(X_28,$fot(X_129)),bind(X_29,$fot(X_130)),bind(X_30,$fot(implies(not(implies(implies(not(X),X),X)),X_129)))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(X_130,implies(not(implies(implies(not(X),X),X)),X_129))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_130),X_129),implies(not(implies(implies(not(X),X),X)),X_129))) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(X_147,implies(not(implies(implies(not(X_145),X_145),X_145)),X_146))),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_145)),bind(X_129,$fot(X_146)),bind(X_130,$fot(X_147))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),X_146),Z),implies(X_147,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_147,implies(not(implies(implies(not(X_145),X_145),X_145)),X_146))) )],[refute_0_26,refute_0_8]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),implies(implies(not(X_145),X_145),X_145)),X_856),implies(X_147,X_856))),
inference(subst,[],[refute_0_27:[bind(Z,$fot(X_856)),bind(X_146,$fot(implies(implies(not(X_145),X_145),X_145)))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_50),X_50),X_51),X_49),implies(implies(X_50,X_51),X_49)))
| ~ is_a_theorem(implies(implies(implies(not(X_50),X_50),X_51),X_49))
| is_a_theorem(implies(implies(X_50,X_51),X_49)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_50),X_50),X_51),X_49))),bind(Y,$fot(implies(implies(X_50,X_51),X_49)))]]) ).
cnf(refute_0_30,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_2:[bind(X,$fot(implies(X_26,X_27))),bind(Y,$fot(implies(implies(not(X_26),X_26),X_27)))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(not(X_24),X_24),X_24)),
inference(subst,[],[cn_2:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(not(X_24),X_24),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_24),X_24))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24),X_24),X_24)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))),
inference(subst,[],[refute_0_33:[bind(X_24,$fot(X_26)),bind(X_25,$fot(X_27))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(implies(implies(not(X_26),X_26),X_27),Z),implies(implies(X_26,X_27),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))) )],[refute_0_34,refute_0_30]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(implies(implies(not(X_50),X_50),X_51),X_49),implies(implies(X_50,X_51),X_49))),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_49)),bind(X_26,$fot(X_50)),bind(X_27,$fot(X_51))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_50),X_50),X_51),X_49))
| is_a_theorem(implies(implies(X_50,X_51),X_49)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_50),X_50),X_51),X_49),implies(implies(X_50,X_51),X_49))) )],[refute_0_36,refute_0_29]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),implies(implies(not(X_145),X_145),X_145)),X_856),implies(X_147,X_856)))
| is_a_theorem(implies(implies(implies(implies(not(X_145),X_145),X_145),X_856),implies(X_147,X_856))) ),
inference(subst,[],[refute_0_37:[bind(X_49,$fot(implies(X_147,X_856))),bind(X_50,$fot(implies(implies(not(X_145),X_145),X_145))),bind(X_51,$fot(X_856))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(implies(not(X_145),X_145),X_145),X_856),implies(X_147,X_856))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),implies(implies(not(X_145),X_145),X_145)),X_856),implies(X_147,X_856))) )],[refute_0_28,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1462),X_1462),X_1462),implies(X_1460,X_1462)),implies(X_147,implies(X_1460,X_1462)))),
inference(subst,[],[refute_0_39:[bind(X_145,$fot(X_1462)),bind(X_856,$fot(implies(X_1460,X_1462)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1462),X_1462),X_1462),implies(X_1460,X_1462)),implies(X_147,implies(X_1460,X_1462))))
| is_a_theorem(implies(implies(X_1460,implies(not(X_1462),X_1462)),implies(X_147,implies(X_1460,X_1462)))) ),
inference(subst,[],[refute_0_6:[bind(X_31,$fot(X_1460)),bind(X_32,$fot(implies(not(X_1462),X_1462))),bind(X_33,$fot(X_1462)),bind(X_34,$fot(implies(X_147,implies(X_1460,X_1462))))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(X_1460,implies(not(X_1462),X_1462)),implies(X_147,implies(X_1460,X_1462)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1462),X_1462),X_1462),implies(X_1460,X_1462)),implies(X_147,implies(X_1460,X_1462)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(implies(X_32,X_1528),implies(not(X_1528),X_1528)),implies(X_1529,implies(implies(X_32,X_1528),X_1528)))),
inference(subst,[],[refute_0_42:[bind(X_1460,$fot(implies(X_32,X_1528))),bind(X_1462,$fot(X_1528)),bind(X_147,$fot(X_1529))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(not(X_1528),X_32),implies(X_1529,implies(implies(X_32,X_1528),X_1528)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_32,X_1528),implies(not(X_1528),X_1528)),implies(X_1529,implies(implies(X_32,X_1528),X_1528)))) )],[refute_0_43,refute_0_7]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(not(x),y),implies(z,implies(implies(y,x),x)))),
inference(subst,[],[refute_0_44:[bind(X_1528,$fot(x)),bind(X_1529,$fot(z)),bind(X_32,$fot(y))]]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(x),y),implies(z,implies(implies(y,x),x)))) )],[refute_0_45,prove_cn_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL364-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 20:27:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.68/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.68/1.90
% 1.68/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.68/1.93
%------------------------------------------------------------------------------