TSTP Solution File: NUM344+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM344+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:26:03 EDT 2022
% Result : Theorem 18.90s 19.12s
% Output : CNFRefutation 18.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 53 ~; 47 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 81 ( 12 sgn 49 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))) ).
fof(rdn1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))) ).
fof(rdnn1,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))) ).
fof(less_entry_point_neg_pos,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y)) )
=> less(X,Y) ) ).
fof(sum_entry_point_posx_negx,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ) ).
fof(sum_entry_point_neg_pos,axiom,
! [X,Y,Z,RDN_X,RDN_Y] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& sum(Y,X,Z) )
=> sum(X,Y,Z) ) ).
fof(exist_bigger_plus_one,conjecture,
? [X,Y] :
( sum(X,n1,Y)
& less(X,Y) ) ).
fof(subgoal_0,plain,
? [X,Y] :
( sum(X,n1,Y)
& less(X,Y) ),
inference(strip,[],[exist_bigger_plus_one]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
( sum(X,n1,Y)
& less(X,Y) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(canonicalize,[],[rdnn1]) ).
fof(normalize_0_3,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(canonicalize,[],[rdn1]) ).
fof(normalize_0_4,plain,
! [NEG_X,POS_X,RDN_X] :
( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| sum(POS_X,NEG_X,n0) ),
inference(canonicalize,[],[sum_entry_point_posx_negx]) ).
fof(normalize_0_5,plain,
! [NEG_X,POS_X,RDN_X] :
( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| sum(POS_X,NEG_X,n0) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ sum(Y,X,Z)
| sum(X,Y,Z)
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X))
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(canonicalize,[],[sum_entry_point_neg_pos]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ sum(Y,X,Z)
| sum(X,Y,Z)
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X))
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [RDN_X,RDN_Y,X,Y,Z] :
( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ sum(Y,X,Z)
| sum(X,Y,Z) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(canonicalize,[],[rdn0]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( less(X,Y)
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X))
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(canonicalize,[],[less_entry_point_neg_pos]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( less(X,Y)
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X))
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(clausify,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ less(nn1,n0)
| ~ sum(nn1,n1,n0) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(nn1)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_2,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| sum(POS_X,NEG_X,n0) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ rdn_translate(X_536,rdn_pos(rdnn(n1)))
| ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| sum(X_536,nn1,n0) ),
inference(subst,[],[refute_0_4:[bind(NEG_X,$fot(nn1)),bind(POS_X,$fot(X_536)),bind(RDN_X,$fot(rdnn(n1)))]]) ).
cnf(refute_0_6,plain,
( ~ rdn_translate(X_536,rdn_pos(rdnn(n1)))
| sum(X_536,nn1,n0) ),
inference(resolve,[$cnf( rdn_translate(nn1,rdn_neg(rdnn(n1))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ rdn_translate(n1,rdn_pos(rdnn(n1)))
| sum(n1,nn1,n0) ),
inference(subst,[],[refute_0_6:[bind(X_536,$fot(n1))]]) ).
cnf(refute_0_8,plain,
sum(n1,nn1,n0),
inference(resolve,[$cnf( rdn_translate(n1,rdn_pos(rdnn(n1))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ sum(Y,X,Z)
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( ~ rdn_translate(n1,rdn_pos(X_36665))
| ~ rdn_translate(nn1,rdn_neg(X_36664))
| ~ sum(n1,nn1,n0)
| sum(nn1,n1,n0) ),
inference(subst,[],[refute_0_9:[bind(RDN_X,$fot(X_36664)),bind(RDN_Y,$fot(X_36665)),bind(X,$fot(nn1)),bind(Y,$fot(n1)),bind(Z,$fot(n0))]]) ).
cnf(refute_0_11,plain,
( ~ rdn_translate(n1,rdn_pos(X_36665))
| ~ rdn_translate(nn1,rdn_neg(X_36664))
| sum(nn1,n1,n0) ),
inference(resolve,[$cnf( sum(n1,nn1,n0) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ rdn_translate(n1,rdn_pos(rdnn(n1)))
| ~ rdn_translate(nn1,rdn_neg(X_43138))
| sum(nn1,n1,n0) ),
inference(subst,[],[refute_0_11:[bind(X_36664,$fot(X_43138)),bind(X_36665,$fot(rdnn(n1)))]]) ).
cnf(refute_0_13,plain,
( ~ rdn_translate(nn1,rdn_neg(X_43138))
| sum(nn1,n1,n0) ),
inference(resolve,[$cnf( rdn_translate(n1,rdn_pos(rdnn(n1))) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| sum(nn1,n1,n0) ),
inference(subst,[],[refute_0_13:[bind(X_43138,$fot(rdnn(n1)))]]) ).
cnf(refute_0_15,plain,
sum(nn1,n1,n0),
inference(resolve,[$cnf( rdn_translate(nn1,rdn_neg(rdnn(n1))) )],[refute_0_2,refute_0_14]) ).
cnf(refute_0_16,plain,
~ less(nn1,n0),
inference(resolve,[$cnf( sum(nn1,n1,n0) )],[refute_0_15,refute_0_1]) ).
cnf(refute_0_17,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_18,plain,
( ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
( ~ rdn_translate(X_954,rdn_neg(X_952))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| less(X_954,n0) ),
inference(subst,[],[refute_0_18:[bind(RDN_X,$fot(X_952)),bind(RDN_Y,$fot(rdnn(n0))),bind(X,$fot(X_954)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(X_954,rdn_neg(X_952))
| less(X_954,n0) ),
inference(resolve,[$cnf( rdn_translate(n0,rdn_pos(rdnn(n0))) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rdn_translate(nn1,rdn_neg(rdnn(n1)))
| less(nn1,n0) ),
inference(subst,[],[refute_0_20:[bind(X_952,$fot(rdnn(n1))),bind(X_954,$fot(nn1))]]) ).
cnf(refute_0_22,plain,
less(nn1,n0),
inference(resolve,[$cnf( rdn_translate(nn1,rdn_neg(rdnn(n1))) )],[refute_0_2,refute_0_21]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( less(nn1,n0) )],[refute_0_22,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM344+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 11:32:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 18.90/19.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.90/19.12
% 18.90/19.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.90/19.13
%------------------------------------------------------------------------------