TSTP Solution File: NUM304+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM304+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 0.46s 0.68s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 76 ( 38 unt; 0 def)
% Number of atoms : 141 ( 50 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 135 ( 70 ~; 56 |; 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 : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 91 ( 27 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))) ).
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(something_not_n12,conjecture,
? [X] : X != n12 ).
fof(subgoal_0,plain,
? [X] : X != n12,
inference(strip,[],[something_not_n12]) ).
fof(negate_0_0,plain,
~ ? [X] : X != n12,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_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(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(canonicalize,[],[less_property]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( Y != X
| ~ less(X,Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : X = n12,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
! [X] : X = n12,
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_translate(n0,rdn_pos(rdnn(n0))),
inference(canonicalize,[],[rdn0]) ).
cnf(refute_0_0,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_1]) ).
cnf(refute_0_1,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(Y,Y) ),
inference(subst,[],[refute_0_0:[bind(RDN_X,$fot(RDN_Y)),bind(X,$fot(Y))]]) ).
cnf(refute_0_2,plain,
( Y != X
| ~ less(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( X != X
| ~ less(X,X) ),
inference(subst,[],[refute_0_2:[bind(Y,$fot(X))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
~ less(X,X),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
~ less(Y,Y),
inference(subst,[],[refute_0_5:[bind(X,$fot(Y))]]) ).
cnf(refute_0_7,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(resolve,[$cnf( less(Y,Y) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
X = n12,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
rdn_pos(RDN_Y) = n12,
inference(subst,[],[refute_0_8:[bind(X,$fot(rdn_pos(RDN_Y)))]]) ).
cnf(refute_0_10,plain,
( rdn_pos(RDN_Y) != n12
| ~ rdn_translate(Y,n12)
| rdn_translate(Y,rdn_pos(RDN_Y)) ),
introduced(tautology,[equality,[$cnf( ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),[1],$fot(n12)]]) ).
cnf(refute_0_11,plain,
( ~ rdn_translate(Y,n12)
| rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(resolve,[$cnf( $equal(rdn_pos(RDN_Y),n12) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,n12) ),
inference(resolve,[$cnf( rdn_translate(Y,rdn_pos(RDN_Y)) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_14,plain,
rdnn(n2) = n12,
inference(subst,[],[refute_0_8:[bind(X,$fot(rdnn(n2)))]]) ).
cnf(refute_0_15,plain,
( rdnn(n2) != n12
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(n12,rdnn(n3)) ),
introduced(tautology,[equality,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) ),[0],$fot(n12)]]) ).
cnf(refute_0_16,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(n12,rdnn(n3)) ),
inference(resolve,[$cnf( $equal(rdnn(n2),n12) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
rdnn(n3) = n12,
inference(subst,[],[refute_0_8:[bind(X,$fot(rdnn(n3)))]]) ).
cnf(refute_0_18,plain,
( rdnn(n3) != n12
| ~ rdn_positive_less(n12,rdnn(n3))
| rdn_positive_less(n12,n12) ),
introduced(tautology,[equality,[$cnf( rdn_positive_less(n12,rdnn(n3)) ),[1],$fot(n12)]]) ).
cnf(refute_0_19,plain,
( ~ rdn_positive_less(n12,rdnn(n3))
| rdn_positive_less(n12,n12) ),
inference(resolve,[$cnf( $equal(rdnn(n3),n12) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(n12,n12) ),
inference(resolve,[$cnf( rdn_positive_less(n12,rdnn(n3)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
rdn_positive_less(n12,n12),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
X_0 = n12,
inference(subst,[],[refute_0_8:[bind(X,$fot(X_0))]]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( X_0 != n12
| n12 = X_0 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(X_0)),bind(Y0,$fot(n12))]]) ).
cnf(refute_0_27,plain,
n12 = X_0,
inference(resolve,[$cnf( $equal(X_0,n12) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( n12 != X_0
| ~ rdn_positive_less(n12,n12)
| rdn_positive_less(n12,X_0) ),
introduced(tautology,[equality,[$cnf( rdn_positive_less(n12,n12) ),[1],$fot(X_0)]]) ).
cnf(refute_0_29,plain,
( ~ rdn_positive_less(n12,n12)
| rdn_positive_less(n12,X_0) ),
inference(resolve,[$cnf( $equal(n12,X_0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
rdn_positive_less(n12,X_0),
inference(resolve,[$cnf( rdn_positive_less(n12,n12) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
rdn_positive_less(n12,X_11),
inference(subst,[],[refute_0_30:[bind(X_0,$fot(X_11))]]) ).
cnf(refute_0_32,plain,
( X != n12
| n12 = X ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(X)),bind(Y0,$fot(n12))]]) ).
cnf(refute_0_33,plain,
n12 = X,
inference(resolve,[$cnf( $equal(X,n12) )],[refute_0_8,refute_0_32]) ).
cnf(refute_0_34,plain,
( n12 != X
| ~ rdn_positive_less(n12,X_11)
| rdn_positive_less(X,X_11) ),
introduced(tautology,[equality,[$cnf( rdn_positive_less(n12,X_11) ),[0],$fot(X)]]) ).
cnf(refute_0_35,plain,
( ~ rdn_positive_less(n12,X_11)
| rdn_positive_less(X,X_11) ),
inference(resolve,[$cnf( $equal(n12,X) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
rdn_positive_less(X,X_11),
inference(resolve,[$cnf( rdn_positive_less(n12,X_11) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
rdn_positive_less(RDN_Y,RDN_Y),
inference(subst,[],[refute_0_36:[bind(X,$fot(RDN_Y)),bind(X_11,$fot(RDN_Y))]]) ).
cnf(refute_0_38,plain,
~ rdn_translate(Y,n12),
inference(resolve,[$cnf( rdn_positive_less(RDN_Y,RDN_Y) )],[refute_0_37,refute_0_12]) ).
cnf(refute_0_39,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_40,plain,
rdn_pos(rdnn(n0)) = n12,
inference(subst,[],[refute_0_8:[bind(X,$fot(rdn_pos(rdnn(n0))))]]) ).
cnf(refute_0_41,plain,
( rdn_pos(rdnn(n0)) != n12
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| rdn_translate(n0,n12) ),
introduced(tautology,[equality,[$cnf( rdn_translate(n0,rdn_pos(rdnn(n0))) ),[1],$fot(n12)]]) ).
cnf(refute_0_42,plain,
( ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| rdn_translate(n0,n12) ),
inference(resolve,[$cnf( $equal(rdn_pos(rdnn(n0)),n12) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
rdn_translate(n0,n12),
inference(resolve,[$cnf( rdn_translate(n0,rdn_pos(rdnn(n0))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( n12 != X
| ~ rdn_translate(n0,n12)
| rdn_translate(n0,X) ),
introduced(tautology,[equality,[$cnf( rdn_translate(n0,n12) ),[1],$fot(X)]]) ).
cnf(refute_0_45,plain,
( ~ rdn_translate(n0,n12)
| rdn_translate(n0,X) ),
inference(resolve,[$cnf( $equal(n12,X) )],[refute_0_33,refute_0_44]) ).
cnf(refute_0_46,plain,
rdn_translate(n0,X),
inference(resolve,[$cnf( rdn_translate(n0,n12) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
rdn_translate(n0,X_5),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_48,plain,
( X != n12
| n12 != X_0
| X = X_0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,X_0) ),[0],$fot(n12)]]) ).
cnf(refute_0_49,plain,
( X != n12
| X = X_0 ),
inference(resolve,[$cnf( $equal(n12,X_0) )],[refute_0_27,refute_0_48]) ).
cnf(refute_0_50,plain,
X = X_0,
inference(resolve,[$cnf( $equal(X,n12) )],[refute_0_8,refute_0_49]) ).
cnf(refute_0_51,plain,
X = n0,
inference(subst,[],[refute_0_50:[bind(X_0,$fot(n0))]]) ).
cnf(refute_0_52,plain,
( X != n0
| n0 = X ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(X)),bind(Y0,$fot(n0))]]) ).
cnf(refute_0_53,plain,
n0 = X,
inference(resolve,[$cnf( $equal(X,n0) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( n0 != X
| ~ rdn_translate(n0,X_5)
| rdn_translate(X,X_5) ),
introduced(tautology,[equality,[$cnf( rdn_translate(n0,X_5) ),[0],$fot(X)]]) ).
cnf(refute_0_55,plain,
( ~ rdn_translate(n0,X_5)
| rdn_translate(X,X_5) ),
inference(resolve,[$cnf( $equal(n0,X) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
rdn_translate(X,X_5),
inference(resolve,[$cnf( rdn_translate(n0,X_5) )],[refute_0_47,refute_0_55]) ).
cnf(refute_0_57,plain,
rdn_translate(Y,n12),
inference(subst,[],[refute_0_56:[bind(X,$fot(Y)),bind(X_5,$fot(n12))]]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( rdn_translate(Y,n12) )],[refute_0_57,refute_0_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM304+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 07:20:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.46/0.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.68
% 0.46/0.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.46/0.69
%------------------------------------------------------------------------------