%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL181+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:42:05 PM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 20 ~; 4 |; 8 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 3 ( 2 usr; 3 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel4,conjecture,
( ( ~ p
=> q )
<=> ( ~ q
=> p ) ) ).
fof(subgoal_0,plain,
( ( ( ~ p
=> q )
& ~ q )
=> p ),
inference(strip,[],[pel4]) ).
fof(subgoal_1,plain,
( ( ( ~ q
=> p )
& ~ p )
=> q ),
inference(strip,[],[pel4]) ).
fof(negate_0_0,plain,
~ ( ( ( ~ p
=> q )
& ~ q )
=> p ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ p
& ~ q
& ( p
| q ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( p
| q ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ p,
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_3,plain,
~ q,
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
$false,
inference(simplify,[],[normalize_0_1,normalize_0_2,normalize_0_3]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_4]) ).
fof(negate_1_0,plain,
~ ( ( ( ~ q
=> p )
& ~ p )
=> q ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ~ p
& ~ q
& ( p
| q ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( p
| q ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ p,
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_3,plain,
~ q,
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_4,plain,
$false,
inference(simplify,[],[normalize_1_1,normalize_1_2,normalize_1_3]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL181+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n004.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 23:21:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.09/0.37
%------------------------------------------------------------------------------