TSTP Solution File: NUN069+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN069+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : Mon Jul 18 16:34:55 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 67 ( 19 ~; 10 |; 38 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 82 ( 7 sgn 34 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_5,axiom,
! [X20] : id(X20,X20) ).
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( id(Y3,Y2)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ) ).
fof(oneidone,conjecture,
? [Y1] :
( id(Y1,Y1)
& ? [Y2] :
( r1(Y2)
& r2(Y2,Y1) ) ) ).
fof(subgoal_0,plain,
? [Y1] :
( id(Y1,Y1)
& ? [Y2] :
( r1(Y2)
& r2(Y2,Y1) ) ),
inference(strip,[],[oneidone]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
( id(Y1,Y1)
& ? [Y2] :
( r1(Y2)
& r2(Y2,Y1) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(canonicalize,[],[axiom_4a]) ).
fof(normalize_0_1,plain,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X4] :
( id(skolemFOFtoCNF_Y9(X4),X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X4] :
? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X4] :
( r1(skolemFOFtoCNF_Y16(X4))
& r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X4] : r1(skolemFOFtoCNF_Y16(X4)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( id(Y3,Y2)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
inference(canonicalize,[],[axiom_2a]) ).
fof(normalize_0_7,plain,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( id(Y3,Y2)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X2,X9] :
( ? [Y3] :
( id(Y3,skolemFOFtoCNF_Y2(X2,X9))
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,skolemFOFtoCNF_Y2(X2,X9))
& r4(X2,X9,Y6) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X2,X9] :
? [Y3] :
( id(Y3,skolemFOFtoCNF_Y2(X2,X9))
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X2,X9] :
( id(skolemFOFtoCNF_Y3(X2,X9),skolemFOFtoCNF_Y2(X2,X9))
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X2,X9] :
? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X2,X9] :
( r2(X9,skolemFOFtoCNF_Y14(X2,X9))
& r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X2,X9] : r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [Y1] :
( ~ id(Y1,Y1)
| ! [Y2] :
( ~ r1(Y2)
| ~ r2(Y2,Y1) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
! [Y1] :
( ~ id(Y1,Y1)
| ! [Y2] :
( ~ r1(Y2)
| ~ r2(Y2,Y1) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [Y1,Y2] :
( ~ id(Y1,Y1)
| ~ r1(Y2)
| ~ r2(Y2,Y1) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X20] : id(X20,X20),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_18,plain,
! [X20] : id(X20,X20),
inference(specialize,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
r1(skolemFOFtoCNF_Y16(X4)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_2,plain,
r2(X_28,skolemFOFtoCNF_Y14(X2,X_28)),
inference(subst,[],[refute_0_1:[bind(X9,$fot(X_28))]]) ).
cnf(refute_0_3,plain,
( ~ id(Y1,Y1)
| ~ r1(Y2)
| ~ r2(Y2,Y1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_4,plain,
id(X20,X20),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_5,plain,
id(Y1,Y1),
inference(subst,[],[refute_0_4:[bind(X20,$fot(Y1))]]) ).
cnf(refute_0_6,plain,
( ~ r1(Y2)
| ~ r2(Y2,Y1) ),
inference(resolve,[$cnf( id(Y1,Y1) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( ~ r1(X_28)
| ~ r2(X_28,skolemFOFtoCNF_Y14(X2,X_28)) ),
inference(subst,[],[refute_0_6:[bind(Y1,$fot(skolemFOFtoCNF_Y14(X2,X_28))),bind(Y2,$fot(X_28))]]) ).
cnf(refute_0_8,plain,
~ r1(X_28),
inference(resolve,[$cnf( r2(X_28,skolemFOFtoCNF_Y14(X2,X_28)) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
~ r1(skolemFOFtoCNF_Y16(X4)),
inference(subst,[],[refute_0_8:[bind(X_28,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y16(X4)) )],[refute_0_0,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN069+1 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 10:44:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------