TSTP Solution File: NUN089+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN089+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 72 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 46 ~; 25 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 43 ( 3 sgn 24 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(zerouneqtwo,conjecture,
! [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| ~ r2(Y2,Y1) )
| ! [Y4] :
( Y4 != Y1
| ~ r1(Y4) ) ) ).
fof(subgoal_0,plain,
! [Y1] :
( ~ ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| ~ r2(Y2,Y1) )
=> ! [Y4] :
( ~ ( Y4 != Y1 )
=> ~ r1(Y4) ) ),
inference(strip,[],[zerouneqtwo]) ).
fof(negate_0_0,plain,
~ ! [Y1] :
( ~ ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| ~ r2(Y2,Y1) )
=> ! [Y4] :
( ~ ( Y4 != Y1 )
=> ~ r1(Y4) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) ) )
& ? [Y4] :
( Y4 = Y1
& r1(Y4) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [Y2] :
( r2(Y2,skolemFOFtoCNF_Y1_1)
& ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) ) )
& ? [Y4] :
( Y4 = skolemFOFtoCNF_Y1_1
& r1(Y4) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [Y2] :
( r2(Y2,skolemFOFtoCNF_Y1_1)
& ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1)
& ? [Y3] :
( r1(Y3)
& r2(Y3,skolemFOFtoCNF_Y2_1) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(canonicalize,[],[axiom_7a]) ).
fof(normalize_0_6,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X7,Y10,Y20] :
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [Y4] :
( Y4 = skolemFOFtoCNF_Y1_1
& r1(Y4) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
( skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1
& r1(skolemFOFtoCNF_Y4_1) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
r1(skolemFOFtoCNF_Y4_1),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1,
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( Y10 != Y10
| ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(subst,[],[refute_0_1:[bind(Y20,$fot(Y10))]]) ).
cnf(refute_0_3,plain,
Y10 = Y10,
introduced(tautology,[refl,[$fot(Y10)]]) ).
cnf(refute_0_4,plain,
( ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ r1(skolemFOFtoCNF_Y1_1)
| ~ r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_0_4:[bind(X7,$fot(skolemFOFtoCNF_Y2_1)),bind(Y10,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_6,plain,
~ r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
r1(skolemFOFtoCNF_Y4_1),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y1_1
| ~ r1(skolemFOFtoCNF_Y4_1)
| r1(skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y4_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_10,plain,
( ~ r1(skolemFOFtoCNF_Y4_1)
| r1(skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_11,refute_0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN089+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 04:09:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------