%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL460+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 12:42:46 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 8 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).
fof(hilbert_and_1,axiom,
and_1 ).
fof(rosser_kn2,conjecture,
kn2 ).
fof(subgoal_0,plain,
kn2,
inference(strip,[],[rosser_kn2]) ).
fof(negate_0_0,plain,
~ kn2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ kn2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_2,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 )
& ( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( ~ and_1
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[and_1]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6))
| and_1 ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
and_1,
inference(canonicalize,[],[hilbert_and_1]) ).
cnf(refute_0_0,plain,
~ kn2,
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
and_1,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(and(X,Y),X)),
inference(resolve,[$cnf( and_1 )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1)),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_P_1)),bind(Y,$fot(skolemFOFtoCNF_Q))]]) ).
cnf(refute_0_6,plain,
kn2,
inference(resolve,[$cnf( is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1)) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
$false,
inference(resolve,[$cnf( kn2 )],[refute_0_6,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL460+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 10:27:12 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.11/0.38
%------------------------------------------------------------------------------