TSTP Solution File: SET873+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 : Tue Jul 19 03:38:02 EDT 2022
% Result : Theorem 0.18s 0.34s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 21 unt; 0 def)
% Number of atoms : 100 ( 57 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 91 ( 42 ~; 34 |; 5 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 1 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(l21_zfmisc_1,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t13_zfmisc_1,conjecture,
! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ) ).
fof(subgoal_0,plain,
! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(strip,[],[t13_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ subset(set_union2(singleton(A),B),B)
| in(A,B) ),
inference(canonicalize,[],[l21_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ subset(set_union2(singleton(A),B),B)
| in(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_7,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A,B] :
( A != B
& set_union2(singleton(A),singleton(B)) = singleton(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
& set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_12,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_2,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_3,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ in(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_B = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_5,plain,
( ~ subset(set_union2(singleton(A),B),B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
( ~ subset(set_union2(singleton(X_12),X_13),X_13)
| in(X_12,X_13) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_12)),bind(B,$fot(X_13))]]) ).
cnf(refute_0_7,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
set_union2(X_13,singleton(X_12)) = set_union2(singleton(X_12),X_13),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_13)),bind(B,$fot(singleton(X_12)))]]) ).
cnf(refute_0_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( set_union2(X_13,singleton(X_12)) != set_union2(singleton(X_12),X_13)
| set_union2(singleton(X_12),X_13) = set_union2(X_13,singleton(X_12)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(set_union2(X_13,singleton(X_12)))),bind(Y,$fot(set_union2(singleton(X_12),X_13)))]]) ).
cnf(refute_0_13,plain,
set_union2(singleton(X_12),X_13) = set_union2(X_13,singleton(X_12)),
inference(resolve,[$cnf( $equal(set_union2(X_13,singleton(X_12)),set_union2(singleton(X_12),X_13)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( set_union2(singleton(X_12),X_13) != set_union2(X_13,singleton(X_12))
| ~ subset(set_union2(X_13,singleton(X_12)),X_13)
| subset(set_union2(singleton(X_12),X_13),X_13) ),
introduced(tautology,[equality,[$cnf( ~ subset(set_union2(singleton(X_12),X_13),X_13) ),[0],$fot(set_union2(X_13,singleton(X_12)))]]) ).
cnf(refute_0_15,plain,
( ~ subset(set_union2(X_13,singleton(X_12)),X_13)
| subset(set_union2(singleton(X_12),X_13),X_13) ),
inference(resolve,[$cnf( $equal(set_union2(singleton(X_12),X_13),set_union2(X_13,singleton(X_12))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ subset(set_union2(X_13,singleton(X_12)),X_13)
| in(X_12,X_13) ),
inference(resolve,[$cnf( subset(set_union2(singleton(X_12),X_13),X_13) )],[refute_0_15,refute_0_6]) ).
cnf(refute_0_17,plain,
( ~ subset(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2))
| in(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_16:[bind(X_12,$fot(skolemFOFtoCNF_B)),bind(X_13,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_18,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2)
| ~ subset(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2))
| subset(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( ~ subset(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_20,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2))
| subset(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2))
| in(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( subset(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_20,refute_0_17]) ).
cnf(refute_0_22,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_23,plain,
subset(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_22:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_24,plain,
in(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_23,refute_0_21]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_24,refute_0_4]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_25,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.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 : Sat Jul 9 20:07:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.34
% 0.18/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.35
%------------------------------------------------------------------------------