TSTP Solution File: NUN067+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN067+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 16:34:54 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 30 unt; 0 def)
% Number of atoms : 169 ( 91 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 168 ( 79 ~; 58 |; 31 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 126 ( 28 sgn 45 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& X12 != Y21 )
| ( r2(X11,X12)
& X12 = Y21 ) ) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(nonzerosexist,conjecture,
? [Y1] :
! [Y2] :
( ~ r1(Y2)
| Y1 != Y2 ) ).
fof(subgoal_0,plain,
? [Y1] :
! [Y2] :
( ~ r1(Y2)
| Y1 != Y2 ),
inference(strip,[],[nonzerosexist]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
! [Y2] :
( ~ r1(Y2)
| Y1 != Y2 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(canonicalize,[],[axiom_7a]) ).
fof(normalize_0_1,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X7,Y10,Y20] :
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y1] :
? [Y2] :
( Y1 = Y2
& r1(Y2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
! [Y1] :
? [Y2] :
( Y1 = Y2
& r1(Y2) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
& r1(skolemFOFtoCNF_Y2_1(Y1)) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y1] : r1(skolemFOFtoCNF_Y2_1(Y1)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Y1] : Y1 = skolemFOFtoCNF_Y2_1(Y1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_9,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) )
& ( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X11,X12] :
( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(canonicalize,[],[axiom_4a]) ).
fof(normalize_0_15,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X4] :
( skolemFOFtoCNF_Y9(X4) = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X4] : skolemFOFtoCNF_Y9(X4) = X4,
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_19,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_21]) ).
cnf(refute_0_0,plain,
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( Y10 != Y10
| ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(subst,[],[refute_0_0:[bind(Y20,$fot(Y10))]]) ).
cnf(refute_0_2,plain,
Y10 = Y10,
introduced(tautology,[refl,[$fot(Y10)]]) ).
cnf(refute_0_3,plain,
( ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
r1(skolemFOFtoCNF_Y2_1(Y1)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
Y1 = skolemFOFtoCNF_Y2_1(Y1),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( Y1 != skolemFOFtoCNF_Y2_1(Y1)
| skolemFOFtoCNF_Y2_1(Y1) = Y1 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(Y1)),bind(Y,$fot(skolemFOFtoCNF_Y2_1(Y1)))]]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_Y2_1(Y1) = Y1,
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y2_1(Y1)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_Y2_1(Y1) != Y1
| ~ r1(skolemFOFtoCNF_Y2_1(Y1))
| r1(Y1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y2_1(Y1)) ),[0],$fot(Y1)]]) ).
cnf(refute_0_12,plain,
( ~ r1(skolemFOFtoCNF_Y2_1(Y1))
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1(Y1),Y1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
r1(Y1),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y2_1(Y1)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
r1(Y10),
inference(subst,[],[refute_0_13:[bind(Y1,$fot(Y10))]]) ).
cnf(refute_0_15,plain,
~ r2(X7,Y10),
inference(resolve,[$cnf( r1(Y10) )],[refute_0_14,refute_0_3]) ).
cnf(refute_0_16,plain,
( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_Y21(X11) != skolemFOFtoCNF_Y21(X11)
| r2(X11,skolemFOFtoCNF_Y21(X11)) ),
inference(subst,[],[refute_0_16:[bind(X12,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_Y21(X11) = skolemFOFtoCNF_Y21(X11),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y21(X11))]]) ).
cnf(refute_0_19,plain,
r2(X11,skolemFOFtoCNF_Y21(X11)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X11),skolemFOFtoCNF_Y21(X11)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_Y9(X4) = X4,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_21,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_22,plain,
r1(X19),
inference(subst,[],[refute_0_13:[bind(Y1,$fot(X19))]]) ).
cnf(refute_0_23,plain,
X19 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(X19) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_Y9(X4) = skolemFOFtoCNF_Y24,
inference(subst,[],[refute_0_23:[bind(X19,$fot(skolemFOFtoCNF_Y9(X4)))]]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_Y9(X4) != X4
| skolemFOFtoCNF_Y9(X4) != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y24 = X4 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y9(X4),X4) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_Y9(X4) != X4
| skolemFOFtoCNF_Y24 = X4 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y9(X4),skolemFOFtoCNF_Y24) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y24 = X4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y9(X4),X4) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Y24 != X4
| X4 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Y24)),bind(Y,$fot(X4))]]) ).
cnf(refute_0_29,plain,
X4 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,X4) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_Y2_1(Y1) = skolemFOFtoCNF_Y24,
inference(subst,[],[refute_0_29:[bind(X4,$fot(skolemFOFtoCNF_Y2_1(Y1)))]]) ).
cnf(refute_0_31,plain,
( Y1 != skolemFOFtoCNF_Y2_1(Y1)
| skolemFOFtoCNF_Y2_1(Y1) != skolemFOFtoCNF_Y24
| Y1 = skolemFOFtoCNF_Y24 ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y1,skolemFOFtoCNF_Y24) ),[0],$fot(skolemFOFtoCNF_Y2_1(Y1))]]) ).
cnf(refute_0_32,plain,
( Y1 != skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1(Y1),skolemFOFtoCNF_Y24) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
Y1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y2_1(Y1)) )],[refute_0_5,refute_0_32]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_Y21(X11) = skolemFOFtoCNF_Y24,
inference(subst,[],[refute_0_33:[bind(Y1,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_Y21(X11) != skolemFOFtoCNF_Y24
| ~ r2(X11,skolemFOFtoCNF_Y21(X11))
| r2(X11,skolemFOFtoCNF_Y24) ),
introduced(tautology,[equality,[$cnf( r2(X11,skolemFOFtoCNF_Y21(X11)) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_36,plain,
( ~ r2(X11,skolemFOFtoCNF_Y21(X11))
| r2(X11,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X11),skolemFOFtoCNF_Y24) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
r2(X11,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r2(X11,skolemFOFtoCNF_Y21(X11)) )],[refute_0_19,refute_0_36]) ).
cnf(refute_0_38,plain,
X_9 = skolemFOFtoCNF_Y24,
inference(subst,[],[refute_0_23:[bind(X19,$fot(X_9))]]) ).
cnf(refute_0_39,plain,
( X_9 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y24 = X_9 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_9)),bind(Y,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_40,plain,
skolemFOFtoCNF_Y24 = X_9,
inference(resolve,[$cnf( $equal(X_9,skolemFOFtoCNF_Y24) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( X19 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y24 != X_9
| X19 = X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(X19,X_9) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_42,plain,
( X19 != skolemFOFtoCNF_Y24
| X19 = X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,X_9) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
X19 = X_9,
inference(resolve,[$cnf( $equal(X19,skolemFOFtoCNF_Y24) )],[refute_0_23,refute_0_42]) ).
cnf(refute_0_44,plain,
skolemFOFtoCNF_Y24 = X_12,
inference(subst,[],[refute_0_43:[bind(X19,$fot(skolemFOFtoCNF_Y24)),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_Y24 != X_12
| ~ r2(X11,skolemFOFtoCNF_Y24)
| r2(X11,X_12) ),
introduced(tautology,[equality,[$cnf( r2(X11,skolemFOFtoCNF_Y24) ),[1],$fot(X_12)]]) ).
cnf(refute_0_46,plain,
( ~ r2(X11,skolemFOFtoCNF_Y24)
| r2(X11,X_12) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,X_12) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
r2(X11,X_12),
inference(resolve,[$cnf( r2(X11,skolemFOFtoCNF_Y24) )],[refute_0_37,refute_0_46]) ).
cnf(refute_0_48,plain,
r2(X7,Y10),
inference(subst,[],[refute_0_47:[bind(X11,$fot(X7)),bind(X_12,$fot(Y10))]]) ).
cnf(refute_0_49,plain,
$false,
inference(resolve,[$cnf( r2(X7,Y10) )],[refute_0_48,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN067+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.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 04:30:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------