TSTP Solution File: NUN088+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN088+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 16:34:58 EDT 2022
% Result : Theorem 0.22s 0.39s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 18 unt; 0 def)
% Number of atoms : 118 ( 49 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 67 ~; 42 |; 19 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 50 ( 3 sgn 27 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(zerouneqone,conjecture,
! [Y1] :
( ! [Y2] :
( ~ r1(Y2)
| Y2 != Y1 )
| ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y1) ) ) ).
fof(subgoal_0,plain,
! [Y1] :
( ~ ! [Y2] :
( ~ r1(Y2)
| Y2 != Y1 )
=> ! [Y3] :
( ~ ~ r1(Y3)
=> ~ r2(Y3,Y1) ) ),
inference(strip,[],[zerouneqone]) ).
fof(negate_0_0,plain,
~ ! [Y1] :
( ~ ! [Y2] :
( ~ r1(Y2)
| Y2 != Y1 )
=> ! [Y3] :
( ~ ~ r1(Y3)
=> ~ r2(Y3,Y1) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Y1] :
( ? [Y2] :
( Y2 = Y1
& r1(Y2) )
& ? [Y3] :
( r1(Y3)
& r2(Y3,Y1) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [Y2] :
( Y2 = skolemFOFtoCNF_Y1_1
& r1(Y2) )
& ? [Y3] :
( r1(Y3)
& r2(Y3,skolemFOFtoCNF_Y1_1) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [Y3] :
( r1(Y3)
& r2(Y3,skolemFOFtoCNF_Y1_1) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( r1(skolemFOFtoCNF_Y3_1)
& r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
r1(skolemFOFtoCNF_Y3_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_7,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [Y2] :
( Y2 = skolemFOFtoCNF_Y1_1
& r1(Y2) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
( skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1
& r1(skolemFOFtoCNF_Y2_1) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
r1(skolemFOFtoCNF_Y2_1),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1,
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_15,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(canonicalize,[],[axiom_7a]) ).
fof(normalize_0_16,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X7,Y10,Y20] :
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(clausify,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
r1(skolemFOFtoCNF_Y3_1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
( ~ r1(skolemFOFtoCNF_Y3_1)
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_2:[bind(X19,$fot(skolemFOFtoCNF_Y3_1))]]) ).
cnf(refute_0_4,plain,
skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y3_1) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
r1(skolemFOFtoCNF_Y2_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_Y2_1 != skolemFOFtoCNF_Y1_1
| ~ r1(skolemFOFtoCNF_Y2_1)
| r1(skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y2_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_8,plain,
( ~ r1(skolemFOFtoCNF_Y2_1)
| r1(skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y2_1) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ r1(skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_2:[bind(X19,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_11,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Y1_1)),bind(Y,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_16,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y24) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y24) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y24) )],[refute_0_4,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y1_1
| ~ r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
| r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_21,plain,
( ~ r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
| r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_0,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_24,plain,
( Y10 != Y10
| ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(subst,[],[refute_0_23:[bind(Y20,$fot(Y10))]]) ).
cnf(refute_0_25,plain,
Y10 = Y10,
introduced(tautology,[refl,[$fot(Y10)]]) ).
cnf(refute_0_26,plain,
( ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
( ~ r1(skolemFOFtoCNF_Y1_1)
| ~ r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_0_26:[bind(X7,$fot(skolemFOFtoCNF_Y1_1)),bind(Y10,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_28,plain,
~ r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) )],[refute_0_22,refute_0_27]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_9,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUN088+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 2 05:32:51 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.39
% 0.22/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.39
%------------------------------------------------------------------------------