TSTP Solution File: LCL451+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL451+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:52:24 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% 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 : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ) ).
fof(hilbert_implies_3,axiom,
implies_3 ).
fof(luka_cn1,conjecture,
cn1 ).
fof(subgoal_0,plain,
cn1,
inference(strip,[],[luka_cn1]) ).
fof(negate_0_0,plain,
~ cn1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ cn1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ cn1
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
inference(canonicalize,[],[cn1]) ).
fof(normalize_0_2,plain,
! [P,Q,R] :
( ( ~ cn1
| is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1))))
| cn1 ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1))))
| cn1 ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( ~ implies_3
<=> ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(canonicalize,[],[implies_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z))))
| implies_3 ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
implies_3,
inference(canonicalize,[],[hilbert_implies_3]) ).
cnf(refute_0_0,plain,
~ cn1,
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1))))
| cn1 ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
implies_3,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(resolve,[$cnf( implies_3 )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_P_3)),bind(Y,$fot(skolemFOFtoCNF_Q_2)),bind(Z,$fot(skolemFOFtoCNF_R_1))]]) ).
cnf(refute_0_6,plain,
cn1,
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1)))) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
$false,
inference(resolve,[$cnf( cn1 )],[refute_0_6,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL451+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 05:42:54 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------