TSTP Solution File: NUN069+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% 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 : 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 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 90 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 88 ( 32 ~; 19 |; 37 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 70 ( 5 sgn 30 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) )
& Y3 = Y2 )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ) ).
fof(oneeqone,conjecture,
? [Y1] :
( Y1 = Y1
& ? [Y2] :
( r1(Y2)
& r2(Y2,Y1) ) ) ).
fof(subgoal_0,plain,
? [Y1] :
( Y1 = Y1
& ? [Y2] :
( r1(Y2)
& r2(Y2,Y1) ) ),
inference(strip,[],[oneeqone]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
( Y1 = Y1
& ? [Y2] :
( r1(Y2)
& r2(Y2,Y1) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_1,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X19] :
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( 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_6,plain,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X2,X9] :
( ? [Y3] :
( 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_6]) ).
fof(normalize_0_8,plain,
! [X2,X9] :
? [Y3] :
( Y3 = skolemFOFtoCNF_Y2(X2,X9)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X2,X9] :
( skolemFOFtoCNF_Y3(X2,X9) = skolemFOFtoCNF_Y2(X2,X9)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X2,X9] :
? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X2,X9] :
( r2(X9,skolemFOFtoCNF_Y14(X2,X9))
& r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X2,X9] : r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [Y1] :
( Y1 != Y1
| ! [Y2] :
( ~ r1(Y2)
| ~ r2(Y2,Y1) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_14,plain,
! [Y1] :
( Y1 != Y1
| ! [Y2] :
( ~ r1(Y2)
| ~ r2(Y2,Y1) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [Y1,Y2] :
( Y1 != Y1
| ~ r1(Y2)
| ~ r2(Y2,Y1) ),
inference(clausify,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
| r1(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_0:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_3,plain,
r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_5,plain,
r2(X_34,skolemFOFtoCNF_Y14(X2,X_34)),
inference(subst,[],[refute_0_4:[bind(X9,$fot(X_34))]]) ).
cnf(refute_0_6,plain,
( Y1 != Y1
| ~ r1(Y2)
| ~ r2(Y2,Y1) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
Y1 = Y1,
introduced(tautology,[refl,[$fot(Y1)]]) ).
cnf(refute_0_8,plain,
( ~ r1(Y2)
| ~ r2(Y2,Y1) ),
inference(resolve,[$cnf( $equal(Y1,Y1) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ r1(X_34)
| ~ r2(X_34,skolemFOFtoCNF_Y14(X2,X_34)) ),
inference(subst,[],[refute_0_8:[bind(Y1,$fot(skolemFOFtoCNF_Y14(X2,X_34))),bind(Y2,$fot(X_34))]]) ).
cnf(refute_0_10,plain,
~ r1(X_34),
inference(resolve,[$cnf( r2(X_34,skolemFOFtoCNF_Y14(X2,X_34)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
~ r1(skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_10:[bind(X_34,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_3,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 2 05:02:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------