%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM411+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:26:28 EDT 2022
% Result : Theorem 0.91s 1.09s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 13 unt; 0 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 189 ( 85 ~; 74 |; 18 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 64 ( 3 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_ordinal1,axiom,
! [A,B] :
( ( relation(B)
& function(B)
& transfinite_sequence(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ) ).
fof(dt_m1_ordinal1,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( relation(B)
& function(B)
& transfinite_sequence(B) ) ) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ) ).
fof(t47_ordinal1,conjecture,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(strip,[],[t47_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_1,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ~ transfinite_sequence(B)
| ( ~ subset(relation_rng(B),A)
<=> ~ transfinite_sequence_of(B,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ~ subset(relation_rng(B),A)
| ~ transfinite_sequence(B)
| transfinite_sequence_of(B,A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( subset(A,B)
& ? [C] :
( ~ transfinite_sequence_of(C,B)
& transfinite_sequence_of(C,A) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_2)
& ? [C] :
( ~ transfinite_sequence_of(C,skolemFOFtoCNF_B_2)
& transfinite_sequence_of(C,skolemFOFtoCNF_A_14) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[t1_xboole_1]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [C] :
( ~ transfinite_sequence_of(C,skolemFOFtoCNF_B_2)
& transfinite_sequence_of(C,skolemFOFtoCNF_A_14) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
( ~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2)
& transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ~ transfinite_sequence(B)
| ~ transfinite_sequence_of(B,A)
| subset(relation_rng(B),A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| ( function(B)
& relation(B)
& transfinite_sequence(B) ) ),
inference(canonicalize,[],[dt_m1_ordinal1]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| ( function(B)
& relation(B)
& transfinite_sequence(B) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ( ~ transfinite_sequence_of(B,A)
| function(B) )
& ( ~ transfinite_sequence_of(B,A)
| relation(B) )
& ( ~ transfinite_sequence_of(B,A)
| transfinite_sequence(B) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| function(B) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| relation(B) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_18,plain,
! [A,B] :
( ~ transfinite_sequence_of(B,A)
| transfinite_sequence(B) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_19,plain,
~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ function(B)
| ~ relation(B)
| ~ subset(relation_rng(B),A)
| ~ transfinite_sequence(B)
| transfinite_sequence_of(B,A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_C)
| ~ subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_B_2)
| ~ transfinite_sequence(skolemFOFtoCNF_C)
| transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ subset(X_47,skolemFOFtoCNF_A_14)
| ~ subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_2)
| subset(X_47,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_47)),bind(B,$fot(skolemFOFtoCNF_A_14)),bind(C,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_5,plain,
( ~ subset(X_47,skolemFOFtoCNF_A_14)
| subset(X_47,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_2) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14)
| subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_5:[bind(X_47,$fot(relation_rng(skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_7,plain,
transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ function(B)
| ~ relation(B)
| ~ transfinite_sequence(B)
| ~ transfinite_sequence_of(B,A)
| subset(relation_rng(B),A) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_C)
| ~ transfinite_sequence(skolemFOFtoCNF_C)
| ~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14)
| subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_10,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_C)
| ~ transfinite_sequence(skolemFOFtoCNF_C)
| subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ transfinite_sequence_of(B,A)
| function(B) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_12,plain,
( ~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14)
| function(skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_13,plain,
function(skolemFOFtoCNF_C),
inference(resolve,[$cnf( transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ relation(skolemFOFtoCNF_C)
| ~ transfinite_sequence(skolemFOFtoCNF_C)
| subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
( ~ transfinite_sequence_of(B,A)
| relation(B) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( ~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14)
| relation(skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_17,plain,
relation(skolemFOFtoCNF_C),
inference(resolve,[$cnf( transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ transfinite_sequence(skolemFOFtoCNF_C)
| subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_17,refute_0_14]) ).
cnf(refute_0_19,plain,
( ~ transfinite_sequence_of(B,A)
| transfinite_sequence(B) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_20,plain,
( ~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14)
| transfinite_sequence(skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_21,plain,
transfinite_sequence(skolemFOFtoCNF_C),
inference(resolve,[$cnf( transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_A_14) )],[refute_0_7,refute_0_20]) ).
cnf(refute_0_22,plain,
subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14),
inference(resolve,[$cnf( transfinite_sequence(skolemFOFtoCNF_C) )],[refute_0_21,refute_0_18]) ).
cnf(refute_0_23,plain,
subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_A_14) )],[refute_0_22,refute_0_6]) ).
cnf(refute_0_24,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_C)
| ~ transfinite_sequence(skolemFOFtoCNF_C)
| transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( subset(relation_rng(skolemFOFtoCNF_C),skolemFOFtoCNF_B_2) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
( ~ relation(skolemFOFtoCNF_C)
| ~ transfinite_sequence(skolemFOFtoCNF_C)
| transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ transfinite_sequence(skolemFOFtoCNF_C)
| transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_17,refute_0_25]) ).
cnf(refute_0_27,plain,
transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( transfinite_sequence(skolemFOFtoCNF_C) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
~ transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( transfinite_sequence_of(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) )],[refute_0_27,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM411+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.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 : Tue Jul 5 05:26:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.91/1.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.91/1.09
% 0.91/1.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.91/1.09
%------------------------------------------------------------------------------