TSTP Solution File: SET985+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:38:47 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 16 unt; 0 def)
% Number of atoms : 148 ( 66 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 141 ( 50 ~; 67 |; 14 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 3 sgn 49 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(t113_zfmisc_1,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( A = empty_set
| B = empty_set ) ) ).
fof(t138_zfmisc_1,axiom,
! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( cartesian_product2(A,B) = empty_set
| ( subset(A,C)
& subset(B,D) ) ) ) ).
fof(t139_zfmisc_1,conjecture,
! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
| subset(cartesian_product2(B,A),cartesian_product2(D,C)) )
=> subset(B,D) ) ) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A) ).
fof(subgoal_0,plain,
! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
| subset(cartesian_product2(B,A),cartesian_product2(D,C)) )
=> subset(B,D) ) ),
inference(strip,[],[t139_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
| subset(cartesian_product2(B,A),cartesian_product2(D,C)) )
=> subset(B,D) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ empty(A)
& ? [B,C,D] :
( ~ subset(B,D)
& ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
| subset(cartesian_product2(B,A),cartesian_product2(D,C)) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ empty(skolemFOFtoCNF_A_2)
& ? [B,C,D] :
( ~ subset(B,D)
& ( subset(cartesian_product2(B,skolemFOFtoCNF_A_2),cartesian_product2(D,C))
| subset(cartesian_product2(skolemFOFtoCNF_A_2,B),cartesian_product2(C,D)) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ empty(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [B,C,D] :
( ~ subset(B,D)
& ( subset(cartesian_product2(B,skolemFOFtoCNF_A_2),cartesian_product2(D,C))
| subset(cartesian_product2(skolemFOFtoCNF_A_2,B),cartesian_product2(C,D)) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D)
& ( subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( cartesian_product2(A,B) != empty_set
<=> ( A != empty_set
& B != empty_set ) ),
inference(canonicalize,[],[t113_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B] :
( cartesian_product2(A,B) != empty_set
<=> ( A != empty_set
& B != empty_set ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ( A != empty_set
| cartesian_product2(A,B) = empty_set )
& ( B != empty_set
| cartesian_product2(A,B) = empty_set )
& ( cartesian_product2(A,B) != empty_set
| A = empty_set
| B = empty_set ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( cartesian_product2(A,B) != empty_set
| A = empty_set
| B = empty_set ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| ( subset(A,C)
& subset(B,D) ) ),
inference(canonicalize,[],[t138_zfmisc_1]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| ( subset(A,C)
& subset(B,D) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C,D] :
( ( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(A,C) )
& ( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(B,D) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(A,C) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C,D] :
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(B,D) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_16,plain,
! [A] : subset(empty_set,A),
inference(canonicalize,[],[t2_xboole_1]) ).
fof(normalize_0_17,plain,
! [A] : subset(empty_set,A),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
cnf(refute_0_0,plain,
~ empty(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( cartesian_product2(A,B) != empty_set
| A = empty_set
| B = empty_set ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != empty_set
| skolemFOFtoCNF_A_2 = empty_set
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_4,plain,
( cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) != empty_set
| skolemFOFtoCNF_A_2 = empty_set
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_5,plain,
( subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(A,C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C))
| cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_D)),bind(D,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_8,plain,
( cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set
| subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),cartesian_product2(skolemFOFtoCNF_D,skolemFOFtoCNF_C)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set
| subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
( ~ subset(cartesian_product2(A,B),cartesian_product2(C,D))
| cartesian_product2(A,B) = empty_set
| subset(B,D) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
| cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_12,plain,
( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set
| cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set
| cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
( cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) != empty_set
| empty_set != empty_set
| cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),empty_set) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_15,plain,
( empty_set != empty_set
| cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set
| cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = empty_set ),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),empty_set) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( empty_set != empty_set
| cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set
| skolemFOFtoCNF_A_2 = empty_set
| skolemFOFtoCNF_B = empty_set ),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),empty_set) )],[refute_0_15,refute_0_4]) ).
cnf(refute_0_17,plain,
( empty_set != empty_set
| skolemFOFtoCNF_A_2 = empty_set
| skolemFOFtoCNF_B = empty_set ),
inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),empty_set) )],[refute_0_16,refute_0_3]) ).
cnf(refute_0_18,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_A_2 = empty_set
| skolemFOFtoCNF_B = empty_set ),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_B != empty_set
| ~ subset(empty_set,skolemFOFtoCNF_D)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_21,plain,
( ~ subset(empty_set,skolemFOFtoCNF_D)
| skolemFOFtoCNF_A_2 = empty_set
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ subset(empty_set,skolemFOFtoCNF_D)
| skolemFOFtoCNF_A_2 = empty_set ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
subset(empty_set,A),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_24,plain,
subset(empty_set,skolemFOFtoCNF_D),
inference(subst,[],[refute_0_23:[bind(A,$fot(skolemFOFtoCNF_D))]]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_A_2 = empty_set,
inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_D) )],[refute_0_24,refute_0_22]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_A_2 != empty_set
| ~ empty(empty_set)
| empty(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ empty(skolemFOFtoCNF_A_2) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_27,plain,
( ~ empty(empty_set)
| empty(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
~ empty(empty_set),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_2) )],[refute_0_27,refute_0_0]) ).
cnf(refute_0_29,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_29,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.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 : Mon Jul 11 06:08:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------