TSTP Solution File: NUM393+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 12:26:23 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 152 ( 64 ~; 61 |; 13 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ) ).
fof(d9_xboole_0,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(A,B)
| subset(B,A) ) ) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ) ).
fof(t25_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
inference(strip,[],[t25_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ inclusion_comparable(A,B)
<=> ( ~ subset(A,B)
& ~ subset(B,A) ) ),
inference(canonicalize,[],[d9_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ inclusion_comparable(A,B)
<=> ( ~ subset(A,B)
& ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( ~ subset(A,B)
| inclusion_comparable(A,B) )
& ( ~ subset(B,A)
| inclusion_comparable(A,B) )
& ( ~ inclusion_comparable(A,B)
| subset(A,B)
| subset(B,A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| inclusion_comparable(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ~ ordinal_subset(A,B)
<=> ~ subset(A,B) ) ),
inference(canonicalize,[],[redefinition_r1_ordinal1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ~ ordinal_subset(A,B)
<=> ~ subset(A,B) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) )
& ( ~ ordinal(A)
| ~ ordinal(B)
| ~ subset(A,B)
| ordinal_subset(A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(B,A)
| inclusion_comparable(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
? [A] :
( ordinal(A)
& ? [B] :
( ~ inclusion_comparable(A,B)
& ordinal(B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( ordinal(skolemFOFtoCNF_A_11)
& ? [B] :
( ~ inclusion_comparable(skolemFOFtoCNF_A_11,B)
& ordinal(B) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [B] :
( ~ inclusion_comparable(skolemFOFtoCNF_A_11,B)
& ordinal(B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( ~ inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
& ordinal(skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
ordinal(skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
ordinal(skolemFOFtoCNF_A_11),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(canonicalize,[],[connectedness_r1_ordinal1]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
~ inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| inclusion_comparable(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_2,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_B_1)
| ~ ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_4,plain,
( ~ subset(B,A)
| inclusion_comparable(A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11)
| inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_6,plain,
ordinal(skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
ordinal(skolemFOFtoCNF_A_11),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ ordinal(X_68)
| ~ ordinal(skolemFOFtoCNF_A_11)
| ordinal_subset(X_68,skolemFOFtoCNF_A_11)
| ordinal_subset(skolemFOFtoCNF_A_11,X_68) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(X_68))]]) ).
cnf(refute_0_10,plain,
( ~ ordinal(X_68)
| ordinal_subset(X_68,skolemFOFtoCNF_A_11)
| ordinal_subset(skolemFOFtoCNF_A_11,X_68) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ ordinal(skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_10:[bind(X_68,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_12,plain,
( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_B_1)
| ~ ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_14,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ordinal(skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_7,refute_0_14]) ).
cnf(refute_0_16,plain,
( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
( inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_11) )],[refute_0_16,refute_0_5]) ).
cnf(refute_0_18,plain,
~ inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_19,refute_0_3]) ).
cnf(refute_0_21,plain,
( ~ ordinal(skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_7,refute_0_20]) ).
cnf(refute_0_22,plain,
subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_6,refute_0_21]) ).
cnf(refute_0_23,plain,
inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( inclusion_comparable(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_1) )],[refute_0_23,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.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 : Wed Jul 6 00:25:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.40
%------------------------------------------------------------------------------