TSTP Solution File: NUM291+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM291+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 12:25:46 EDT 2022
% Result : Theorem 6.24s 6.45s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 67 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 71 ( 36 ~; 26 |; 5 &)
% ( 3 <=>; 1 =>; 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) ).
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(n3_not_less_n2,conjecture,
~ less(n3,n2) ).
fof(subgoal_0,plain,
~ less(n3,n2),
inference(strip,[],[n3_not_less_n2]) ).
fof(negate_0_0,plain,
~ ~ less(n3,n2),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[rdn3]) ).
fof(normalize_0_1,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[rdn2]) ).
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(canonicalize,[],[less_entry_point_pos_pos]) ).
fof(normalize_0_3,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_2]) ).
fof(normalize_0_4,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_5,plain,
less(n3,n2),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(canonicalize,[],[less_property]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ less(Y,X) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,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_3]) ).
cnf(refute_0_3,plain,
( ~ rdn_positive_less(rdnn(n2),X_9247)
| ~ rdn_translate(X_9249,rdn_pos(X_9247))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| less(n2,X_9249) ),
inference(subst,[],[refute_0_2:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(X_9247)),bind(X,$fot(n2)),bind(Y,$fot(X_9249))]]) ).
cnf(refute_0_4,plain,
( ~ rdn_positive_less(rdnn(n2),X_9247)
| ~ rdn_translate(X_9249,rdn_pos(X_9247))
| less(n2,X_9249) ),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| less(n2,n3) ),
inference(subst,[],[refute_0_4:[bind(X_9247,$fot(rdnn(n3))),bind(X_9249,$fot(n3))]]) ).
cnf(refute_0_6,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| less(n2,n3) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_8,plain,
less(n2,n3),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
less(n3,n2),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_10,plain,
( ~ less(X,Y)
| ~ less(Y,X) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ less(n2,n3)
| ~ less(n3,n2) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(n3)),bind(Y,$fot(n2))]]) ).
cnf(refute_0_12,plain,
~ less(n2,n3),
inference(resolve,[$cnf( less(n3,n2) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( less(n2,n3) )],[refute_0_8,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM291+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.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 12:53:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.24/6.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.24/6.45
% 6.24/6.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.24/6.45
%------------------------------------------------------------------------------