TSTP Solution File: NUM409+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:26:27 EDT 2022
% Result : Theorem 253.16s 253.34s
% Output : CNFRefutation 253.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 28 unt; 0 def)
% Number of atoms : 210 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 230 ( 98 ~; 86 |; 35 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 51 ( 4 sgn 34 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_ordinal1,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ) ).
fof(d8_ordinal1,axiom,
! [A,B] :
( ( relation(B)
& function(B)
& transfinite_sequence(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ) ).
fof(fc2_ordinal1,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A) ).
fof(t45_ordinal1,conjecture,
! [A] : transfinite_sequence_of(empty_set,A) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A] : transfinite_sequence_of(empty_set,A),
inference(strip,[],[t45_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] : transfinite_sequence_of(empty_set,A),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ transfinite_sequence_of(empty_set,A),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ transfinite_sequence_of(empty_set,skolemFOFtoCNF_A_14),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ~ transfinite_sequence(B)
| ( ~ subset(relation_rng(B),A)
<=> ~ transfinite_sequence_of(B,A) ) ),
inference(canonicalize,[],[d8_ordinal1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ~ transfinite_sequence(B)
| ( ~ subset(relation_rng(B),A)
<=> ~ transfinite_sequence_of(B,A) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ( ~ function(B)
| ~ relation(B)
| ~ subset(relation_rng(B),A)
| ~ transfinite_sequence(B)
| transfinite_sequence_of(B,A) )
& ( ~ function(B)
| ~ relation(B)
| ~ transfinite_sequence(B)
| ~ transfinite_sequence_of(B,A)
| subset(relation_rng(B),A) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ~ subset(relation_rng(B),A)
| ~ transfinite_sequence(B)
| transfinite_sequence_of(B,A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
inference(canonicalize,[],[fc12_relat_1]) ).
fof(normalize_0_7,plain,
empty(empty_set),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
inference(canonicalize,[],[fc8_relat_1]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] :
( ( ~ empty(A)
| empty(relation_rng(A)) )
& ( ~ empty(A)
| relation(relation_rng(A)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ empty(A)
| empty(relation_rng(A)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_13,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
( empty(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& ordinal(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
inference(canonicalize,[],[fc2_ordinal1]) ).
fof(normalize_0_15,plain,
relation(empty_set),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_16,plain,
relation_empty_yielding(empty_set),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_17,plain,
( epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& ordinal(empty_set) ),
inference(simplify,[],[normalize_0_14,normalize_0_7,normalize_0_15,normalize_0_16]) ).
fof(normalize_0_18,plain,
function(empty_set),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] : subset(empty_set,A),
inference(canonicalize,[],[t2_xboole_1]) ).
fof(normalize_0_20,plain,
! [A] : subset(empty_set,A),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| ( ~ ordinal(relation_dom(A))
<=> ~ transfinite_sequence(A) ) ),
inference(canonicalize,[],[d7_ordinal1]) ).
fof(normalize_0_22,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| ( ~ ordinal(relation_dom(A))
<=> ~ transfinite_sequence(A) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A] :
( ( ~ function(A)
| ~ ordinal(relation_dom(A))
| ~ relation(A)
| transfinite_sequence(A) )
& ( ~ function(A)
| ~ relation(A)
| ~ transfinite_sequence(A)
| ordinal(relation_dom(A)) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A] :
( ~ function(A)
| ~ ordinal(relation_dom(A))
| ~ relation(A)
| transfinite_sequence(A) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
inference(canonicalize,[],[fc7_relat_1]) ).
fof(normalize_0_26,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A] :
( ( ~ empty(A)
| empty(relation_dom(A)) )
& ( ~ empty(A)
| relation(relation_dom(A)) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A] :
( ~ empty(A)
| empty(relation_dom(A)) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
ordinal(empty_set),
inference(conjunct,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
~ transfinite_sequence_of(empty_set,skolemFOFtoCNF_A_14),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ function(B)
| ~ relation(B)
| ~ subset(relation_rng(B),A)
| ~ transfinite_sequence(B)
| transfinite_sequence_of(B,A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(relation_rng(empty_set),X_348)
| ~ transfinite_sequence(empty_set)
| transfinite_sequence_of(empty_set,X_348) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_348)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_3,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ empty(A)
| empty(relation_rng(A)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ empty(empty_set)
| empty(relation_rng(empty_set)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_6,plain,
empty(relation_rng(empty_set)),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_8,plain,
( ~ empty(relation_rng(empty_set))
| relation_rng(empty_set) = empty_set ),
inference(subst,[],[refute_0_7:[bind(A,$fot(relation_rng(empty_set)))]]) ).
cnf(refute_0_9,plain,
relation_rng(empty_set) = empty_set,
inference(resolve,[$cnf( empty(relation_rng(empty_set)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( relation_rng(empty_set) != empty_set
| ~ subset(empty_set,X_348)
| subset(relation_rng(empty_set),X_348) ),
introduced(tautology,[equality,[$cnf( ~ subset(relation_rng(empty_set),X_348) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_11,plain,
( ~ subset(empty_set,X_348)
| subset(relation_rng(empty_set),X_348) ),
inference(resolve,[$cnf( $equal(relation_rng(empty_set),empty_set) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(empty_set,X_348)
| ~ transfinite_sequence(empty_set)
| transfinite_sequence_of(empty_set,X_348) ),
inference(resolve,[$cnf( subset(relation_rng(empty_set),X_348) )],[refute_0_11,refute_0_2]) ).
cnf(refute_0_13,plain,
function(empty_set),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_14,plain,
( ~ relation(empty_set)
| ~ subset(empty_set,X_348)
| ~ transfinite_sequence(empty_set)
| transfinite_sequence_of(empty_set,X_348) ),
inference(resolve,[$cnf( function(empty_set) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
relation(empty_set),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_16,plain,
( ~ subset(empty_set,X_348)
| ~ transfinite_sequence(empty_set)
| transfinite_sequence_of(empty_set,X_348) ),
inference(resolve,[$cnf( relation(empty_set) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
subset(empty_set,A),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_18,plain,
subset(empty_set,X_348),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_348))]]) ).
cnf(refute_0_19,plain,
( ~ transfinite_sequence(empty_set)
| transfinite_sequence_of(empty_set,X_348) ),
inference(resolve,[$cnf( subset(empty_set,X_348) )],[refute_0_18,refute_0_16]) ).
cnf(refute_0_20,plain,
( ~ function(A)
| ~ ordinal(relation_dom(A))
| ~ relation(A)
| transfinite_sequence(A) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_21,plain,
( ~ function(empty_set)
| ~ ordinal(relation_dom(empty_set))
| ~ relation(empty_set)
| transfinite_sequence(empty_set) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_22,plain,
( ~ empty(A)
| empty(relation_dom(A)) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_23,plain,
( ~ empty(empty_set)
| empty(relation_dom(empty_set)) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_24,plain,
empty(relation_dom(empty_set)),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_3,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ empty(relation_dom(empty_set))
| relation_dom(empty_set) = empty_set ),
inference(subst,[],[refute_0_7:[bind(A,$fot(relation_dom(empty_set)))]]) ).
cnf(refute_0_26,plain,
relation_dom(empty_set) = empty_set,
inference(resolve,[$cnf( empty(relation_dom(empty_set)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( relation_dom(empty_set) != empty_set
| ~ ordinal(empty_set)
| ordinal(relation_dom(empty_set)) ),
introduced(tautology,[equality,[$cnf( ~ ordinal(relation_dom(empty_set)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_28,plain,
( ~ ordinal(empty_set)
| ordinal(relation_dom(empty_set)) ),
inference(resolve,[$cnf( $equal(relation_dom(empty_set),empty_set) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ function(empty_set)
| ~ ordinal(empty_set)
| ~ relation(empty_set)
| transfinite_sequence(empty_set) ),
inference(resolve,[$cnf( ordinal(relation_dom(empty_set)) )],[refute_0_28,refute_0_21]) ).
cnf(refute_0_30,plain,
( ~ ordinal(empty_set)
| ~ relation(empty_set)
| transfinite_sequence(empty_set) ),
inference(resolve,[$cnf( function(empty_set) )],[refute_0_13,refute_0_29]) ).
cnf(refute_0_31,plain,
ordinal(empty_set),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_32,plain,
( ~ relation(empty_set)
| transfinite_sequence(empty_set) ),
inference(resolve,[$cnf( ordinal(empty_set) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
transfinite_sequence(empty_set),
inference(resolve,[$cnf( relation(empty_set) )],[refute_0_15,refute_0_32]) ).
cnf(refute_0_34,plain,
transfinite_sequence_of(empty_set,X_348),
inference(resolve,[$cnf( transfinite_sequence(empty_set) )],[refute_0_33,refute_0_19]) ).
cnf(refute_0_35,plain,
transfinite_sequence_of(empty_set,skolemFOFtoCNF_A_14),
inference(subst,[],[refute_0_34:[bind(X_348,$fot(skolemFOFtoCNF_A_14))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( transfinite_sequence_of(empty_set,skolemFOFtoCNF_A_14) )],[refute_0_35,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 23:24:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 253.16/253.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 253.16/253.34
% 253.16/253.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 253.16/253.34
%------------------------------------------------------------------------------