%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL359-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:42:29 PM UTC 2026
% Result : Unsatisfiable 5.56s 5.82s
% Output : CNFRefutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 9 RR)
% Number of literals : 29 ( 0 equ; 12 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 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(prove_cn_08,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,x),implies(implies(y,u),implies(z,u))))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37))
| ~ is_a_theorem(implies(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37),implies(implies(X_34,X_35),X_37)))
| is_a_theorem(implies(implies(X_34,X_35),X_37)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37))),bind(Y,$fot(implies(implies(X_34,X_35),X_37)))]]) ).
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,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37),implies(implies(X_34,X_35),X_37))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_34)),bind(Y,$fot(X_35)),bind(Z,$fot(X_36)),bind(X_21,$fot(X_37))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37))
| is_a_theorem(implies(implies(X_34,X_35),X_37)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_35,X_36),implies(X_34,X_36)),X_37),implies(implies(X_34,X_35),X_37))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X_35,X_1878),implies(X_1877,X_1878)),implies(implies(X_1876,X_1877),implies(implies(X_35,X_1878),implies(X_1876,X_1878)))))
| is_a_theorem(implies(implies(X_1877,X_35),implies(implies(X_1876,X_1877),implies(implies(X_35,X_1878),implies(X_1876,X_1878))))) ),
inference(subst,[],[refute_0_6:[bind(X_34,$fot(X_1877)),bind(X_36,$fot(X_1878)),bind(X_37,$fot(implies(implies(X_1876,X_1877),implies(implies(X_35,X_1878),implies(X_1876,X_1878)))))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X_1318,implies(X,Z))),implies(implies(X,Y),implies(X_1318,implies(X,Z))))),
inference(subst,[],[refute_0_4:[bind(X_21,$fot(implies(X_1318,implies(X,Z))))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X_1318,implies(X,Z))),implies(implies(X,Y),implies(X_1318,implies(X,Z)))))
| is_a_theorem(implies(implies(X_1318,implies(Y,Z)),implies(implies(X,Y),implies(X_1318,implies(X,Z))))) ),
inference(subst,[],[refute_0_6:[bind(X_34,$fot(X_1318)),bind(X_35,$fot(implies(Y,Z))),bind(X_36,$fot(implies(X,Z))),bind(X_37,$fot(implies(implies(X,Y),implies(X_1318,implies(X,Z)))))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(X_1318,implies(Y,Z)),implies(implies(X,Y),implies(X_1318,implies(X,Z))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X_1318,implies(X,Z))),implies(implies(X,Y),implies(X_1318,implies(X,Z))))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(X_35,X_1878),implies(X_1877,X_1878)),implies(implies(X_1876,X_1877),implies(implies(X_35,X_1878),implies(X_1876,X_1878))))),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_1876)),bind(Y,$fot(X_1877)),bind(Z,$fot(X_1878)),bind(X_1318,$fot(implies(X_35,X_1878)))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(X_1877,X_35),implies(implies(X_1876,X_1877),implies(implies(X_35,X_1878),implies(X_1876,X_1878))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_35,X_1878),implies(X_1877,X_1878)),implies(implies(X_1876,X_1877),implies(implies(X_35,X_1878),implies(X_1876,X_1878))))) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(x,y),implies(implies(z,x),implies(implies(y,u),implies(z,u))))),
inference(subst,[],[refute_0_12:[bind(X_1876,$fot(z)),bind(X_1877,$fot(x)),bind(X_1878,$fot(u)),bind(X_35,$fot(y))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(x,y),implies(implies(z,x),implies(implies(y,u),implies(z,u))))) )],[refute_0_13,prove_cn_08]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL359-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 22:38:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.56/5.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.56/5.82
% 5.56/5.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.56/5.82
%------------------------------------------------------------------------------