%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM295+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:25:47 EDT 2022
% Result : Theorem 0.60s 0.80s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 23 unt; 0 def)
% Number of atoms : 86 ( 17 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 86 ( 44 ~; 33 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 66 ( 13 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))) ).
fof(rdn_positive_less01,axiom,
rdn_positive_less(rdnn(n0),rdnn(n1)) ).
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(something_less_something,conjecture,
? [X,Y] : less(X,Y) ).
fof(subgoal_0,plain,
? [X,Y] : less(X,Y),
inference(strip,[],[something_less_something]) ).
fof(negate_0_0,plain,
~ ? [X,Y] : less(X,Y),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(canonicalize,[],[rdn1]) ).
fof(normalize_0_1,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_2,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_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(canonicalize,[],[less_property]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( Y != X
| ~ less(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( Y = X
| less(X,Y)
| less(Y,X) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [X,Y] : ~ less(X,Y),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
! [X,Y] : ~ less(X,Y),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
rdn_positive_less(rdnn(n0),rdnn(n1)),
inference(canonicalize,[],[rdn_positive_less01]) ).
cnf(refute_0_0,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,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_2]) ).
cnf(refute_0_2,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(Y,Y) ),
inference(subst,[],[refute_0_1:[bind(RDN_X,$fot(RDN_Y)),bind(X,$fot(Y))]]) ).
cnf(refute_0_3,plain,
( Y != X
| ~ less(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( X != X
| ~ less(X,X) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
~ less(X,X),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
~ less(Y,Y),
inference(subst,[],[refute_0_6:[bind(X,$fot(Y))]]) ).
cnf(refute_0_8,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(resolve,[$cnf( less(Y,Y) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ rdn_positive_less(rdnn(n1),rdnn(n1))
| ~ rdn_translate(n1,rdn_pos(rdnn(n1))) ),
inference(subst,[],[refute_0_8:[bind(RDN_Y,$fot(rdnn(n1))),bind(Y,$fot(n1))]]) ).
cnf(refute_0_10,plain,
~ rdn_positive_less(rdnn(n1),rdnn(n1)),
inference(resolve,[$cnf( rdn_translate(n1,rdn_pos(rdnn(n1))) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
( Y = X
| less(X,Y)
| less(Y,X) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,plain,
~ less(X,Y),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
( Y = X
| less(Y,X) ),
inference(resolve,[$cnf( less(X,Y) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
~ less(Y,X),
inference(subst,[],[refute_0_12:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_15,plain,
Y = X,
inference(resolve,[$cnf( less(Y,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
n1 = X_125,
inference(subst,[],[refute_0_15:[bind(X,$fot(X_125)),bind(Y,$fot(n1))]]) ).
cnf(refute_0_17,plain,
( n1 != X_125
| ~ rdn_positive_less(rdnn(X_125),rdnn(n1))
| rdn_positive_less(rdnn(n1),rdnn(n1)) ),
introduced(tautology,[equality,[$cnf( ~ rdn_positive_less(rdnn(n1),rdnn(n1)) ),[0,0],$fot(X_125)]]) ).
cnf(refute_0_18,plain,
( ~ rdn_positive_less(rdnn(X_125),rdnn(n1))
| rdn_positive_less(rdnn(n1),rdnn(n1)) ),
inference(resolve,[$cnf( $equal(n1,X_125) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
~ rdn_positive_less(rdnn(X_125),rdnn(n1)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n1),rdnn(n1)) )],[refute_0_18,refute_0_10]) ).
cnf(refute_0_20,plain,
rdn_positive_less(rdnn(n0),rdnn(n1)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_21,plain,
n0 = X_125,
inference(subst,[],[refute_0_15:[bind(X,$fot(X_125)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_22,plain,
( n0 != X_125
| ~ rdn_positive_less(rdnn(n0),rdnn(n1))
| rdn_positive_less(rdnn(X_125),rdnn(n1)) ),
introduced(tautology,[equality,[$cnf( rdn_positive_less(rdnn(n0),rdnn(n1)) ),[0,0],$fot(X_125)]]) ).
cnf(refute_0_23,plain,
( ~ rdn_positive_less(rdnn(n0),rdnn(n1))
| rdn_positive_less(rdnn(X_125),rdnn(n1)) ),
inference(resolve,[$cnf( $equal(n0,X_125) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
rdn_positive_less(rdnn(X_125),rdnn(n1)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n0),rdnn(n1)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( rdn_positive_less(rdnn(X_125),rdnn(n1)) )],[refute_0_24,refute_0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM295+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.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 Jul 7 06:03:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.80
% 0.60/0.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.80
%------------------------------------------------------------------------------