%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:43:11 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 67 ( 38 ~; 17 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).
fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p201(Y)
& p101(Y) ) )
| ~ ( p201(X)
& p101(X) ) ) ).
fof(subgoal_0,plain,
! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p201(Y)
& p101(Y) ) )
& p201(X) )
=> ~ p101(X) ),
inference(strip,[],[main]) ).
fof(negate_0_0,plain,
~ ! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p201(Y)
& p101(Y) ) )
& p201(X) )
=> ~ p101(X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : r1(X,X),
inference(canonicalize,[],[reflexivity]) ).
fof(normalize_0_1,plain,
! [X] : r1(X,X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X] :
( p101(X)
& p201(X)
& ! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(X,Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( p101(skolemFOFtoCNF_X)
& p201(skolemFOFtoCNF_X)
& ! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y] :
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
p101(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_7,plain,
p201(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
r1(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( ~ p101(Y)
| ~ p201(Y)
| ~ r1(skolemFOFtoCNF_X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ p101(skolemFOFtoCNF_X)
| ~ p201(skolemFOFtoCNF_X)
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_2:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_4,plain,
( ~ p101(skolemFOFtoCNF_X)
| ~ p201(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
p101(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
~ p201(skolemFOFtoCNF_X),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
p201(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( p201(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.08/0.35 % Computer : n029.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 21:20:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.08/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36
% 0.08/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.08/0.36
%------------------------------------------------------------------------------