TSTP Solution File: NUM299+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM299+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:25:48 EDT 2022
% Result : Theorem 8.75s 8.92s
% Output : CNFRefutation 8.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 21 unt; 0 def)
% Number of atoms : 90 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 46 ~; 36 |; 6 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))) ).
fof(rdnn4,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less34,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)) ).
fof(rdn_positive_less_transitivity,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ) ).
fof(less_entry_point_neg_neg,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X) )
=> less(X,Y) ) ).
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( ~ less(Y,X)
& Y != X ) ) ).
fof(nn2_not_less_nn4,conjecture,
~ less(nn2,nn4) ).
fof(subgoal_0,plain,
~ less(nn2,nn4),
inference(strip,[],[nn2_not_less_nn4]) ).
fof(negate_0_0,plain,
~ ~ less(nn2,nn4),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(canonicalize,[],[less_property]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ less(Y,X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(canonicalize,[],[rdnn2]) ).
fof(normalize_0_5,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(canonicalize,[],[rdnn4]) ).
fof(normalize_0_6,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[less_entry_point_neg_neg]) ).
fof(normalize_0_7,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| less(X,Y) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_9,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(canonicalize,[],[rdn_positive_less34]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(canonicalize,[],[rdn_positive_less_transitivity]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
less(nn2,nn4),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ less(X,Y)
| ~ less(Y,X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ less(nn2,nn4)
| ~ less(nn4,nn2) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(nn4)),bind(Y,$fot(nn2))]]) ).
cnf(refute_0_2,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ rdn_positive_less(X_13514,rdnn(n4))
| ~ rdn_translate(X_13516,rdn_neg(X_13514))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| less(nn4,X_13516) ),
inference(subst,[],[refute_0_4:[bind(RDN_X,$fot(rdnn(n4))),bind(RDN_Y,$fot(X_13514)),bind(X,$fot(nn4)),bind(Y,$fot(X_13516))]]) ).
cnf(refute_0_6,plain,
( ~ rdn_positive_less(X_13514,rdnn(n4))
| ~ rdn_translate(X_13516,rdn_neg(X_13514))
| less(nn4,X_13516) ),
inference(resolve,[$cnf( rdn_translate(nn4,rdn_neg(rdnn(n4))) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n4))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| less(nn4,nn2) ),
inference(subst,[],[refute_0_6:[bind(X_13514,$fot(rdnn(n2))),bind(X_13516,$fot(nn2))]]) ).
cnf(refute_0_8,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n4))
| less(nn4,nn2) ),
inference(resolve,[$cnf( rdn_translate(nn2,rdn_neg(rdnn(n2))) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ rdn_positive_less(rdnn(X_2531),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(X_2531),rdnn(n4)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_2531)),bind(Y,$fot(n3)),bind(Z,$fot(n4))]]) ).
cnf(refute_0_13,plain,
( ~ rdn_positive_less(rdnn(X_2531),rdnn(n3))
| rdn_positive_less(rdnn(X_2531),rdnn(n4)) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n3),rdnn(n4)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(subst,[],[refute_0_13:[bind(X_2531,$fot(n2))]]) ).
cnf(refute_0_15,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
less(nn4,nn2),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n4)) )],[refute_0_15,refute_0_8]) ).
cnf(refute_0_17,plain,
~ less(nn2,nn4),
inference(resolve,[$cnf( less(nn4,nn2) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
less(nn2,nn4),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( less(nn2,nn4) )],[refute_0_18,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM299+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 : Tue Jul 5 18:21:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.75/8.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.75/8.92
% 8.75/8.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.75/8.92
%------------------------------------------------------------------------------