%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL079-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:41:48 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 23 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 37 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 30 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
cnf(a_implies_b,hypothesis,
is_a_theorem(implies(a,b)) ).
cnf(b_implies_c,hypothesis,
is_a_theorem(implies(b,c)) ).
cnf(prove_transitivity,negated_conjecture,
~ is_a_theorem(implies(a,c)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(X_38,b))
| ~ is_a_theorem(implies(implies(X_38,b),implies(X_38,c)))
| is_a_theorem(implies(X_38,c)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_38,b))),bind(Y,$fot(implies(X_38,c)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_4,implies(Y,X_4))),
inference(subst,[],[cn_18:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X_4)
| ~ is_a_theorem(implies(X_4,implies(Y,X_4)))
| is_a_theorem(implies(Y,X_4)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_4)),bind(Y,$fot(implies(Y,X_4)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_4)
| is_a_theorem(implies(Y,X_4)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_4,implies(Y,X_4))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(b,c))
| is_a_theorem(implies(X_9,implies(b,c))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_9)),bind(X_4,$fot(implies(b,c)))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(X_9,implies(b,c))),
inference(resolve,[$cnf( is_a_theorem(implies(b,c)) )],[b_implies_c,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(X_34,implies(b,c))),
inference(subst,[],[refute_0_5:[bind(X_9,$fot(X_34))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X_6,implies(X_7,X_8)))
| ~ is_a_theorem(implies(implies(X_6,implies(X_7,X_8)),implies(implies(X_6,X_7),implies(X_6,X_8))))
| is_a_theorem(implies(implies(X_6,X_7),implies(X_6,X_8))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_6,implies(X_7,X_8)))),bind(Y,$fot(implies(implies(X_6,X_7),implies(X_6,X_8))))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(X_6,implies(X_7,X_8)),implies(implies(X_6,X_7),implies(X_6,X_8)))),
inference(subst,[],[cn_35:[bind(X,$fot(X_6)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X_6,implies(X_7,X_8)))
| is_a_theorem(implies(implies(X_6,X_7),implies(X_6,X_8))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_6,implies(X_7,X_8)),implies(implies(X_6,X_7),implies(X_6,X_8)))) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(X_34,implies(b,c)))
| is_a_theorem(implies(implies(X_34,b),implies(X_34,c))) ),
inference(subst,[],[refute_0_9:[bind(X_6,$fot(X_34)),bind(X_7,$fot(b)),bind(X_8,$fot(c))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(X_34,b),implies(X_34,c))),
inference(resolve,[$cnf( is_a_theorem(implies(X_34,implies(b,c))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(X_38,b),implies(X_38,c))),
inference(subst,[],[refute_0_11:[bind(X_34,$fot(X_38))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(X_38,b))
| is_a_theorem(implies(X_38,c)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_38,b),implies(X_38,c))) )],[refute_0_12,refute_0_0]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(a,b))
| is_a_theorem(implies(a,c)) ),
inference(subst,[],[refute_0_13:[bind(X_38,$fot(a))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(a,c)),
inference(resolve,[$cnf( is_a_theorem(implies(a,b)) )],[a_implies_b,refute_0_14]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,c)) )],[refute_0_15,prove_transitivity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL079-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n008.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 : Sun Sep 6 01:05:23 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------