%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL169-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n001.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 12:42:03 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 10 RR)
% Number of literals : 27 ( 12 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(implies(p,not(p)),not(p))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_1,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_0]) ).
cnf(refute_0_2,plain,
theorem(implies(or(not(X_5),not(X_5)),not(X_5))),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_5)))]]) ).
cnf(refute_0_3,plain,
implies(X_5,not(X_5)) = or(not(X_5),not(X_5)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_5)),bind(Y,$fot(not(X_5)))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( implies(X_5,not(X_5)) != or(not(X_5),not(X_5))
| or(not(X_5),not(X_5)) = implies(X_5,not(X_5)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X_5,not(X_5)))),bind(Y0,$fot(or(not(X_5),not(X_5))))]]) ).
cnf(refute_0_8,plain,
or(not(X_5),not(X_5)) = implies(X_5,not(X_5)),
inference(resolve,[$cnf( $equal(implies(X_5,not(X_5)),or(not(X_5),not(X_5))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( or(not(X_5),not(X_5)) != implies(X_5,not(X_5))
| ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) ),[0,0],$fot(implies(X_5,not(X_5)))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
| theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
inference(resolve,[$cnf( $equal(or(not(X_5),not(X_5)),implies(X_5,not(X_5))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
theorem(implies(implies(X_5,not(X_5)),not(X_5))),
inference(resolve,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(implies(p,not(p)),not(p))),
inference(subst,[],[refute_0_11:[bind(X_5,$fot(p))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(p,not(p)),not(p))) )],[refute_0_12,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL169-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 01:48:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------