%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n002.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 12:42:48 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 65 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 18 |; 2 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 4 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_r2,axiom,
r2 ).
fof(hilbert_implies_1,conjecture,
implies_1 ).
fof(subgoal_0,plain,
implies_1,
inference(strip,[],[hilbert_implies_1]) ).
fof(negate_0_0,plain,
~ implies_1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ implies_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X))) ),
inference(canonicalize,[],[implies_1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ implies_1
| is_a_theorem(implies(X,implies(Y,X))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3)))
| implies_1 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3)))
| implies_1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ implies_1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_Q_4,or(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_4)))
| r2 )
& ( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_8,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3)))
| implies_1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ implies_1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3))),
inference(resolve,[$cnf( implies_1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r2,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(Q,or(not(X_7),Q))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_7,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
implies(X_7,Q) = or(not(X_7),Q),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_7)),bind(Y,$fot(Q))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X_7,Q) != or(not(X_7),Q)
| or(not(X_7),Q) = implies(X_7,Q) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_7,Q))),bind(Y0,$fot(or(not(X_7),Q)))]]) ).
cnf(refute_0_15,plain,
or(not(X_7),Q) = implies(X_7,Q),
inference(resolve,[$cnf( $equal(implies(X_7,Q),or(not(X_7),Q)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(not(X_7),Q) != implies(X_7,Q)
| ~ is_a_theorem(implies(Q,or(not(X_7),Q)))
| is_a_theorem(implies(Q,implies(X_7,Q))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(Q,or(not(X_7),Q))) ),[0,1],$fot(implies(X_7,Q))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(Q,or(not(X_7),Q)))
| is_a_theorem(implies(Q,implies(X_7,Q))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),Q),implies(X_7,Q)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(Q,implies(X_7,Q))),
inference(resolve,[$cnf( is_a_theorem(implies(Q,or(not(X_7),Q))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3))),
inference(subst,[],[refute_0_18:[bind(Q,$fot(skolemFOFtoCNF_X_3)),bind(X_7,$fot(skolemFOFtoCNF_Y_3))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3))) )],[refute_0_19,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n002.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 09:45:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------