TSTP Solution File: NUM414+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:26:29 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 16 unt; 0 def)
% Number of atoms : 169 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 198 ( 87 ~; 71 |; 26 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 49 ( 0 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ) ).
fof(t50_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(A,B)
& A != B
& ~ proper_subset(B,A) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ordinal(A)
=> ! [B] :
( ( ordinal(B)
& ~ proper_subset(A,B)
& A != B )
=> proper_subset(B,A) ) ),
inference(strip,[],[t50_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ( ordinal(B)
& ~ proper_subset(A,B)
& A != B )
=> proper_subset(B,A) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ proper_subset(A,B)
<=> ( ~ subset(A,B)
| A = B ) ),
inference(canonicalize,[],[d8_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ proper_subset(A,B)
<=> ( ~ subset(A,B)
| A = B ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( A != B
| ~ proper_subset(A,B) )
& ( ~ proper_subset(A,B)
| subset(A,B) )
& ( ~ subset(A,B)
| A = B
| proper_subset(A,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| A = B
| proper_subset(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] :
( ordinal(A)
& ? [B] :
( A != B
& ~ proper_subset(A,B)
& ~ proper_subset(B,A)
& ordinal(B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ordinal(skolemFOFtoCNF_A_14)
& ? [B] :
( skolemFOFtoCNF_A_14 != B
& ~ proper_subset(B,skolemFOFtoCNF_A_14)
& ~ proper_subset(skolemFOFtoCNF_A_14,B)
& ordinal(B) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [B] :
( skolemFOFtoCNF_A_14 != B
& ~ proper_subset(B,skolemFOFtoCNF_A_14)
& ~ proper_subset(skolemFOFtoCNF_A_14,B)
& ordinal(B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( skolemFOFtoCNF_A_14 != skolemFOFtoCNF_B_1
& ~ proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
& ~ proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14)
& ordinal(skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
ordinal(skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
ordinal(skolemFOFtoCNF_A_14),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(canonicalize,[],[connectedness_r1_ordinal1]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
skolemFOFtoCNF_A_14 != skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_17,plain,
~ proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_18,plain,
~ proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| A = B
| proper_subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_A_14 = skolemFOFtoCNF_B_1
| proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$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_14)
| ~ ordinal(skolemFOFtoCNF_B_1)
| ~ ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_4,plain,
( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14)
| skolemFOFtoCNF_B_1 = skolemFOFtoCNF_A_14
| proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_14))]]) ).
cnf(refute_0_5,plain,
ordinal(skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
ordinal(skolemFOFtoCNF_A_14),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_8,plain,
( ~ ordinal(X_52)
| ~ ordinal(skolemFOFtoCNF_A_14)
| ordinal_subset(X_52,skolemFOFtoCNF_A_14)
| ordinal_subset(skolemFOFtoCNF_A_14,X_52) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_14)),bind(B,$fot(X_52))]]) ).
cnf(refute_0_9,plain,
( ~ ordinal(X_52)
| ordinal_subset(X_52,skolemFOFtoCNF_A_14)
| ordinal_subset(skolemFOFtoCNF_A_14,X_52) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_14) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ ordinal(skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(subst,[],[refute_0_9:[bind(X_52,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_11,plain,
( ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_5,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ ordinal(skolemFOFtoCNF_A_14)
| ~ ordinal(skolemFOFtoCNF_B_1)
| ~ ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_14))]]) ).
cnf(refute_0_13,plain,
( ~ ordinal(skolemFOFtoCNF_A_14)
| ~ ordinal(skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ordinal(skolemFOFtoCNF_B_1)
| ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_14) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
( ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_5,refute_0_14]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_B_1 = skolemFOFtoCNF_A_14
| ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) )],[refute_0_15,refute_0_4]) ).
cnf(refute_0_17,plain,
skolemFOFtoCNF_A_14 != skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_B_1 != skolemFOFtoCNF_A_14
| skolemFOFtoCNF_A_14 = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_20:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(skolemFOFtoCNF_A_14))]]) ).
cnf(refute_0_22,plain,
skolemFOFtoCNF_B_1 != skolemFOFtoCNF_A_14,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
( ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1)
| proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) )],[refute_0_16,refute_0_22]) ).
cnf(refute_0_24,plain,
~ proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_25,plain,
ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( proper_subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_14) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ ordinal(skolemFOFtoCNF_A_14)
| ~ ordinal(skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) )],[refute_0_25,refute_0_3]) ).
cnf(refute_0_27,plain,
( ~ ordinal(skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_14) )],[refute_0_6,refute_0_26]) ).
cnf(refute_0_28,plain,
subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_1) )],[refute_0_5,refute_0_27]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_A_14 = skolemFOFtoCNF_B_1
| proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) )],[refute_0_28,refute_0_1]) ).
cnf(refute_0_30,plain,
proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) )],[refute_0_29,refute_0_17]) ).
cnf(refute_0_31,plain,
~ proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( proper_subset(skolemFOFtoCNF_A_14,skolemFOFtoCNF_B_1) )],[refute_0_30,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM414+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 : n013.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 18:38:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------