%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:42:13 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 12 RR)
% Number of literals : 40 ( 12 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_2,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
theorem(implies(X_3,or(not(X_11),X_3))),
inference(subst,[],[refute_0_2:[bind(X_4,$fot(not(X_11)))]]) ).
cnf(refute_0_4,plain,
implies(X_11,X_3) = or(not(X_11),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X_11,X_3) != or(not(X_11),X_3)
| or(not(X_11),X_3) = implies(X_11,X_3) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_11,X_3))),bind(Y0,$fot(or(not(X_11),X_3)))]]) ).
cnf(refute_0_9,plain,
or(not(X_11),X_3) = implies(X_11,X_3),
inference(resolve,[$cnf( $equal(implies(X_11,X_3),or(not(X_11),X_3)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X_11),X_3) != implies(X_11,X_3)
| ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) ),[0,1],$fot(implies(X_11,X_3))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_3),implies(X_11,X_3)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(X_3,implies(X_11,X_3))),
inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
theorem(implies(X_68,implies(X_11,X_68))),
inference(subst,[],[refute_0_12:[bind(X_3,$fot(X_68))]]) ).
cnf(refute_0_14,plain,
( ~ theorem(X_68)
| ~ theorem(implies(X_68,implies(X_11,X_68)))
| theorem(implies(X_11,X_68)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_11,X_68))),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(X_68)
| theorem(implies(X_11,X_68)) ),
inference(resolve,[$cnf( theorem(implies(X_68,implies(X_11,X_68))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ theorem(implies(X_3,implies(X_11,X_3)))
| theorem(implies(X_70,implies(X_3,implies(X_11,X_3)))) ),
inference(subst,[],[refute_0_15:[bind(X_11,$fot(X_70)),bind(X_68,$fot(implies(X_3,implies(X_11,X_3))))]]) ).
cnf(refute_0_17,plain,
theorem(implies(X_70,implies(X_3,implies(X_11,X_3)))),
inference(resolve,[$cnf( theorem(implies(X_3,implies(X_11,X_3))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
inference(subst,[],[refute_0_17:[bind(X_11,$fot(implies(p,q))),bind(X_3,$fot(q)),bind(X_70,$fot(not(p)))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( theorem(implies(not(p),implies(q,implies(implies(p,q),q)))) )],[refute_0_18,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n003.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 20:16:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.09/0.39
%------------------------------------------------------------------------------