TSTP Solution File: NUN087+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN087+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 16:34:57 EDT 2022
% Result : Theorem 0.75s 0.93s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 18 unt; 0 def)
% Number of atoms : 130 ( 40 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 129 ( 54 ~; 41 |; 34 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 79 ( 5 sgn 28 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ) ).
fof(zerotimeszeroeqzero,conjecture,
? [Y1] :
( ? [Y2] :
( r1(Y2)
& r4(Y2,Y2,Y1) )
& ? [Y3] :
( r1(Y3)
& Y1 = Y3 ) ) ).
fof(subgoal_0,plain,
? [Y1] :
( ? [Y2] :
( r1(Y2)
& r4(Y2,Y2,Y1) )
& ? [Y3] :
( r1(Y3)
& Y1 = Y3 ) ),
inference(strip,[],[zerotimeszeroeqzero]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
( ? [Y2] :
( r1(Y2)
& r4(Y2,Y2,Y1) )
& ? [Y3] :
( r1(Y3)
& Y1 = Y3 ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(canonicalize,[],[axiom_5a]) ).
fof(normalize_0_1,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X5] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) )
& ? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X5] :
? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X5] :
( r1(skolemFOFtoCNF_Y17(X5))
& r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X5] : r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X5] :
? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X5] :
( skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5)
& r1(skolemFOFtoCNF_Y18(X5)) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X5] : skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X5] : r1(skolemFOFtoCNF_Y17(X5)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_10,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_11,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X5] : r1(skolemFOFtoCNF_Y18(X5)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_16,plain,
! [Y1] :
( ! [Y2] :
( ~ r1(Y2)
| ~ r4(Y2,Y2,Y1) )
| ! [Y3] :
( Y1 != Y3
| ~ r1(Y3) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_17,plain,
! [Y1] :
( ! [Y2] :
( ~ r1(Y2)
| ~ r4(Y2,Y2,Y1) )
| ! [Y3] :
( Y1 != Y3
| ~ r1(Y3) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [Y1,Y2,Y3] :
( Y1 != Y3
| ~ r1(Y2)
| ~ r1(Y3)
| ~ r4(Y2,Y2,Y1) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X19] :
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y18(X5)
| ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5))
| r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) ),[2],$fot(skolemFOFtoCNF_Y18(X5))]]) ).
cnf(refute_0_3,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5))
| r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
r1(skolemFOFtoCNF_Y17(X5)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ r1(skolemFOFtoCNF_Y17(X5))
| skolemFOFtoCNF_Y17(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_6:[bind(X19,$fot(skolemFOFtoCNF_Y17(X5)))]]) ).
cnf(refute_0_8,plain,
skolemFOFtoCNF_Y17(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y17(X5)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_Y17(X5) != skolemFOFtoCNF_Y24
| ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_10,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y24) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
r1(skolemFOFtoCNF_Y18(X5)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ r1(skolemFOFtoCNF_Y18(X5))
| skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_6:[bind(X19,$fot(skolemFOFtoCNF_Y18(X5)))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y18(X5)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_Y18(X5) != skolemFOFtoCNF_Y24
| ~ r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),[2],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_15,plain,
( ~ r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y18(X5),skolemFOFtoCNF_Y24) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
r4(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_17:[bind(X5,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_19,plain,
( Y1 != Y3
| ~ r1(Y2)
| ~ r1(Y3)
| ~ r4(Y2,Y2,Y1) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_20,plain,
( Y3 != Y3
| ~ r1(Y2)
| ~ r1(Y3)
| ~ r4(Y2,Y2,Y3) ),
inference(subst,[],[refute_0_19:[bind(Y1,$fot(Y3))]]) ).
cnf(refute_0_21,plain,
Y3 = Y3,
introduced(tautology,[refl,[$fot(Y3)]]) ).
cnf(refute_0_22,plain,
( ~ r1(Y2)
| ~ r1(Y3)
| ~ r4(Y2,Y2,Y3) ),
inference(resolve,[$cnf( $equal(Y3,Y3) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( ~ r1(skolemFOFtoCNF_Y24)
| ~ r4(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_22:[bind(Y2,$fot(skolemFOFtoCNF_Y24)),bind(Y3,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_24,plain,
~ r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r4(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
| r1(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_25:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_28,plain,
r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_28,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 06:30:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.75/0.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.75/0.93
% 0.75/0.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.75/0.93
%------------------------------------------------------------------------------