TSTP Solution File: SET977+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 03:38:44 EDT 2022
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 21 unt; 0 def)
% Number of atoms : 166 ( 81 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 181 ( 92 ~; 56 |; 17 &)
% ( 11 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 118 ( 6 sgn 66 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(t128_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( A = C
& in(B,D) ) ) ).
fof(t129_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& B = D ) ) ).
fof(t130_zfmisc_1,conjecture,
! [A,B] :
( A != empty_set
=> ( cartesian_product2(singleton(B),A) != empty_set
& cartesian_product2(A,singleton(B)) != empty_set ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( A != empty_set
=> cartesian_product2(singleton(B),A) != empty_set ),
inference(strip,[],[t130_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( ( A != empty_set
& cartesian_product2(singleton(B),A) != empty_set )
=> cartesian_product2(A,singleton(B)) != empty_set ),
inference(strip,[],[t130_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( A != empty_set
=> cartesian_product2(singleton(B),A) != empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_1,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( A != C
| ~ in(B,D) ) ),
inference(canonicalize,[],[t128_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( A != C
| ~ in(B,D) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
| A = C )
& ( ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
| in(B,D) )
& ( A != C
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( A != C
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A] :
( A != empty_set
& ? [B] : cartesian_product2(singleton(B),A) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( skolemFOFtoCNF_A_2 != empty_set
& ? [B] : cartesian_product2(singleton(B),skolemFOFtoCNF_A_2) = empty_set ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [B] : cartesian_product2(singleton(B),skolemFOFtoCNF_A_2) = empty_set,
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) = empty_set,
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_13,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( X_32 = empty_set
| in(skolemFOFtoCNF_B(X_32),X_32) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_32))]]) ).
cnf(refute_0_2,plain,
( A != C
| ~ in(B,D)
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( C != C
| ~ in(B,D)
| in(ordered_pair(C,B),cartesian_product2(singleton(C),D)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(C))]]) ).
cnf(refute_0_4,plain,
C = C,
introduced(tautology,[refl,[$fot(C)]]) ).
cnf(refute_0_5,plain,
( ~ in(B,D)
| in(ordered_pair(C,B),cartesian_product2(singleton(C),D)) ),
inference(resolve,[$cnf( $equal(C,C) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ in(skolemFOFtoCNF_B(X_32),X_32)
| in(ordered_pair(X_31,skolemFOFtoCNF_B(X_32)),cartesian_product2(singleton(X_31),X_32)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(skolemFOFtoCNF_B(X_32))),bind(C,$fot(X_31)),bind(D,$fot(X_32))]]) ).
cnf(refute_0_7,plain,
( X_32 = empty_set
| in(ordered_pair(X_31,skolemFOFtoCNF_B(X_32)),cartesian_product2(singleton(X_31),X_32)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(X_32),X_32) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_A_2 = empty_set
| in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_7:[bind(X_31,$fot(skolemFOFtoCNF_B_1)),bind(X_32,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_9,plain,
cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) = empty_set,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) != empty_set
| ~ in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2))
| in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),empty_set) ),
introduced(tautology,[equality,[$cnf( in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_11,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2))
| in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),empty_set) ),
inference(resolve,[$cnf( $equal(cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),empty_set) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_A_2 = empty_set
| in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),empty_set) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),cartesian_product2(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_17,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_18,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
~ in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),empty_set),
inference(subst,[],[refute_0_18:[bind(B,$fot(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B(skolemFOFtoCNF_A_2)),empty_set) )],[refute_0_14,refute_0_19]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ( A != empty_set
& cartesian_product2(singleton(B),A) != empty_set )
=> cartesian_product2(A,singleton(B)) != empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_1_1,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( B != D
| ~ in(A,C) ) ),
inference(canonicalize,[],[t129_zfmisc_1]) ).
fof(normalize_1_5,plain,
! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( B != D
| ~ in(A,C) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| B = D )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| in(A,C) )
& ( B != D
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C,D] :
( B != D
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [A,B] :
( A != empty_set
& cartesian_product2(singleton(B),A) != empty_set
& cartesian_product2(A,singleton(B)) = empty_set ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_9,plain,
( cartesian_product2(singleton(skolemFOFtoCNF_B_2),skolemFOFtoCNF_A_3) != empty_set
& skolemFOFtoCNF_A_3 != empty_set
& cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) = empty_set ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) = empty_set,
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
skolemFOFtoCNF_A_3 != empty_set,
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_12,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( X_77 = empty_set
| in(skolemFOFtoCNF_B(X_77),X_77) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(X_77))]]) ).
cnf(refute_1_2,plain,
( B != D
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( D != D
| ~ in(A,C)
| in(ordered_pair(A,D),cartesian_product2(C,singleton(D))) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(D))]]) ).
cnf(refute_1_4,plain,
D = D,
introduced(tautology,[refl,[$fot(D)]]) ).
cnf(refute_1_5,plain,
( ~ in(A,C)
| in(ordered_pair(A,D),cartesian_product2(C,singleton(D))) ),
inference(resolve,[$cnf( $equal(D,D) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
( ~ in(skolemFOFtoCNF_B(X_77),X_77)
| in(ordered_pair(skolemFOFtoCNF_B(X_77),X_78),cartesian_product2(X_77,singleton(X_78))) ),
inference(subst,[],[refute_1_5:[bind(A,$fot(skolemFOFtoCNF_B(X_77))),bind(C,$fot(X_77)),bind(D,$fot(X_78))]]) ).
cnf(refute_1_7,plain,
( X_77 = empty_set
| in(ordered_pair(skolemFOFtoCNF_B(X_77),X_78),cartesian_product2(X_77,singleton(X_78))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(X_77),X_77) )],[refute_1_1,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_A_3 = empty_set
| in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2))) ),
inference(subst,[],[refute_1_7:[bind(X_77,$fot(skolemFOFtoCNF_A_3)),bind(X_78,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_9,plain,
cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) = empty_set,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_10,plain,
( cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)) != empty_set
| ~ in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)))
| in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),empty_set) ),
introduced(tautology,[equality,[$cnf( in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2))) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_11,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)))
| in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),empty_set) ),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2)),empty_set) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
( skolemFOFtoCNF_A_3 = empty_set
| in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),empty_set) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),cartesian_product2(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_2))) )],[refute_1_8,refute_1_11]) ).
cnf(refute_1_13,plain,
skolemFOFtoCNF_A_3 != empty_set,
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_14,plain,
in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,empty_set) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_16,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_1_15:[bind(A,$fot(empty_set))]]) ).
cnf(refute_1_17,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_1_18,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_1_17,refute_1_16]) ).
cnf(refute_1_19,plain,
~ in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),empty_set),
inference(subst,[],[refute_1_18:[bind(B,$fot(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2)))]]) ).
cnf(refute_1_20,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_2),empty_set) )],[refute_1_14,refute_1_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 22:40:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.57
% 0.19/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.57
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