%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL111-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:41:54 PM UTC 2026
% Result : Unsatisfiable 36.36s 36.69s
% Output : CNFRefutation 36.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 28 ( 16 unt; 0 nHn; 11 RR)
% Number of literals : 44 ( 0 equ; 17 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 : 73 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(mv_1,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(mv_2,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(mv_3,axiom,
is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) ).
cnf(prove_mv_25,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(X_59,X_60),X_61))
| ~ is_a_theorem(implies(implies(implies(X_59,X_60),X_61),implies(X_60,X_61)))
| is_a_theorem(implies(X_60,X_61)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_59,X_60),X_61))),bind(Y,$fot(implies(X_60,X_61)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_56,implies(Y,X_56))),
inference(subst,[],[mv_1:[bind(X,$fot(X_56))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$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)))) )],[mv_2,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_56,implies(Y,X_56)))
| is_a_theorem(implies(implies(implies(Y,X_56),X_58),implies(X_56,X_58))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_56)),bind(Y,$fot(implies(Y,X_56))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(Y,X_56),X_58),implies(X_56,X_58))),
inference(resolve,[$cnf( is_a_theorem(implies(X_56,implies(Y,X_56))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(X_59,X_60),X_61),implies(X_60,X_61))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_59)),bind(X_56,$fot(X_60)),bind(X_58,$fot(X_61))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(X_59,X_60),X_61))
| is_a_theorem(implies(X_60,X_61)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_59,X_60),X_61),implies(X_60,X_61))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28432,X_28434),implies(X_28433,X_28434)),implies(X_28433,X_28434)),implies(implies(X_28432,X_28433),implies(X_28432,X_28434))))
| is_a_theorem(implies(implies(X_28433,X_28434),implies(implies(X_28432,X_28433),implies(X_28432,X_28434)))) ),
inference(subst,[],[refute_0_7:[bind(X_59,$fot(implies(implies(X_28432,X_28434),implies(X_28433,X_28434)))),bind(X_60,$fot(implies(X_28433,X_28434))),bind(X_61,$fot(implies(implies(X_28432,X_28433),implies(X_28432,X_28434))))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_58),implies(implies(X,Y),X_58))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_58),implies(implies(X,Y),X_58))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_9]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(subst,[],[refute_0_10:[bind(X_58,$fot(implies(X,Z)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(X_149,X_148),X_148),X_150))
| ~ is_a_theorem(implies(implies(implies(implies(X_149,X_148),X_148),X_150),implies(implies(implies(X_148,X_149),X_149),X_150)))
| is_a_theorem(implies(implies(implies(X_148,X_149),X_149),X_150)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_149,X_148),X_148),X_150))),bind(Y,$fot(implies(implies(implies(X_148,X_149),X_149),X_150)))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(implies(implies(implies(Y,X),X),X_58),implies(implies(implies(X,Y),Y),X_58))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(X,Y),Y))),bind(Y,$fot(implies(implies(Y,X),X))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(implies(Y,X),X),X_58),implies(implies(implies(X,Y),Y),X_58))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_13]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(implies(X_149,X_148),X_148),X_150),implies(implies(implies(X_148,X_149),X_149),X_150))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_148)),bind(Y,$fot(X_149)),bind(X_58,$fot(X_150))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_149,X_148),X_148),X_150))
| is_a_theorem(implies(implies(implies(X_148,X_149),X_149),X_150)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_149,X_148),X_148),X_150),implies(implies(implies(X_148,X_149),X_149),X_150))) )],[refute_0_15,refute_0_12]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X,Z)),implies(implies(X,Y),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(X,Z),implies(Y,Z)),implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ),
inference(subst,[],[refute_0_16:[bind(X_148,$fot(implies(X,Z))),bind(X_149,$fot(implies(Y,Z))),bind(X_150,$fot(implies(implies(X,Y),implies(X,Z))))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(implies(X,Z),implies(Y,Z)),implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X,Z)),implies(implies(X,Y),implies(X,Z)))) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(implies(X_28432,X_28434),implies(X_28433,X_28434)),implies(X_28433,X_28434)),implies(implies(X_28432,X_28433),implies(X_28432,X_28434)))),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_28432)),bind(Y,$fot(X_28433)),bind(Z,$fot(X_28434))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(X_28433,X_28434),implies(implies(X_28432,X_28433),implies(X_28432,X_28434)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28432,X_28434),implies(X_28433,X_28434)),implies(X_28433,X_28434)),implies(implies(X_28432,X_28433),implies(X_28432,X_28434)))) )],[refute_0_19,refute_0_8]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b)))),
inference(subst,[],[refute_0_20:[bind(X_28432,$fot(c)),bind(X_28433,$fot(a)),bind(X_28434,$fot(b))]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b)))) )],[refute_0_21,prove_mv_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL111-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n027.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 : Fri Sep 4 19:02:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 36.36/36.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.36/36.69
% 36.36/36.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.36/36.69
%------------------------------------------------------------------------------