TSTP Solution File: NUM303+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM303+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:25:50 EDT 2022
% Result : Theorem 6.06s 6.25s
% Output : CNFRefutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 22 unt; 0 def)
% Number of atoms : 89 ( 15 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 89 ( 45 ~; 34 |; 5 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 8 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn21,axiom,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))) ).
fof(rdn31,axiom,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less_multi_digit_high,axiom,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(Os,Ob)
=> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ) ).
fof(less_entry_point_pos_pos,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) ) ).
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( ~ less(Y,X)
& Y != X ) ) ).
fof(n31_not_n12,conjecture,
n31 != n21 ).
fof(subgoal_0,plain,
n31 != n21,
inference(strip,[],[n31_not_n12]) ).
fof(negate_0_0,plain,
~ ( n31 != n21 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(canonicalize,[],[rdn21]) ).
fof(normalize_0_1,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_2,plain,
! [Db,Ds,Ob,Os] :
( ~ rdn_positive_less(Os,Ob)
| rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
inference(canonicalize,[],[rdn_positive_less_multi_digit_high]) ).
fof(normalize_0_3,plain,
! [Db,Ds,Ob,Os] :
( ~ rdn_positive_less(Os,Ob)
| rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(canonicalize,[],[rdn31]) ).
fof(normalize_0_5,plain,
n31 = n21,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[less_entry_point_pos_pos]) ).
fof(normalize_0_7,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(canonicalize,[],[less_property]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( Y != X
| ~ less(X,Y) )
& ( ~ less(X,Y)
| ~ less(Y,X) )
& ( Y = X
| less(X,Y)
| less(Y,X) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( Y != X
| ~ less(X,Y) ),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
( ~ rdn_positive_less(Os,Ob)
| rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdn(rdnn(X_227),rdnn(n2)),rdn(rdnn(X_226),rdnn(n3))) ),
inference(subst,[],[refute_0_2:[bind(Db,$fot(X_226)),bind(Ds,$fot(X_227)),bind(Ob,$fot(rdnn(n3))),bind(Os,$fot(rdnn(n2)))]]) ).
cnf(refute_0_4,plain,
rdn_positive_less(rdn(rdnn(X_227),rdnn(n2)),rdn(rdnn(X_226),rdnn(n3))),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
rdn_positive_less(rdn(rdnn(X_227),rdnn(n2)),rdn(rdnn(n1),rdnn(n3))),
inference(subst,[],[refute_0_4:[bind(X_226,$fot(n1))]]) ).
cnf(refute_0_6,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_7,plain,
n31 = n21,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
( n31 != n21
| ~ rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3))))
| rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))) ),
introduced(tautology,[equality,[$cnf( rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))) ),[0],$fot(n21)]]) ).
cnf(refute_0_9,plain,
( ~ rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3))))
| rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))) ),
inference(resolve,[$cnf( $equal(n31,n21) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(resolve,[$cnf( rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,plain,
( ~ rdn_positive_less(X_9200,rdn(rdnn(n1),rdnn(n3)))
| ~ rdn_translate(X_9202,rdn_pos(X_9200))
| ~ rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3))))
| less(X_9202,n21) ),
inference(subst,[],[refute_0_11:[bind(RDN_X,$fot(X_9200)),bind(RDN_Y,$fot(rdn(rdnn(n1),rdnn(n3)))),bind(X,$fot(X_9202)),bind(Y,$fot(n21))]]) ).
cnf(refute_0_13,plain,
( ~ rdn_positive_less(X_9200,rdn(rdnn(n1),rdnn(n3)))
| ~ rdn_translate(X_9202,rdn_pos(X_9200))
| less(X_9202,n21) ),
inference(resolve,[$cnf( rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rdn_positive_less(rdn(rdnn(X_227),rdnn(n2)),rdn(rdnn(n1),rdnn(n3)))
| ~ rdn_translate(X_9582,rdn_pos(rdn(rdnn(X_227),rdnn(n2))))
| less(X_9582,n21) ),
inference(subst,[],[refute_0_13:[bind(X_9200,$fot(rdn(rdnn(X_227),rdnn(n2)))),bind(X_9202,$fot(X_9582))]]) ).
cnf(refute_0_15,plain,
( ~ rdn_translate(X_9582,rdn_pos(rdn(rdnn(X_227),rdnn(n2))))
| less(X_9582,n21) ),
inference(resolve,[$cnf( rdn_positive_less(rdn(rdnn(X_227),rdnn(n2)),rdn(rdnn(n1),rdnn(n3))) )],[refute_0_5,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2))))
| less(n21,n21) ),
inference(subst,[],[refute_0_15:[bind(X_227,$fot(n1)),bind(X_9582,$fot(n21))]]) ).
cnf(refute_0_17,plain,
less(n21,n21),
inference(resolve,[$cnf( rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
( Y != X
| ~ less(X,Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_19,plain,
( X != X
| ~ less(X,X) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X))]]) ).
cnf(refute_0_20,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_21,plain,
~ less(X,X),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
~ less(n21,n21),
inference(subst,[],[refute_0_21:[bind(X,$fot(n21))]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( less(n21,n21) )],[refute_0_17,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM303+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.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 Jul 7 01:08:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.06/6.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.06/6.25
% 6.06/6.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.06/6.25
%------------------------------------------------------------------------------