TSTP Solution File: SET664+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 03:36:27 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 17 unt; 0 def)
% Number of atoms : 237 ( 47 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 278 ( 117 ~; 104 |; 29 &)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 113 ( 7 sgn 71 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> B = empty_set ) ) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( domain_of(B) = empty_set
| range_of(B) = empty_set )
=> B = empty_set ) ) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ) ).
fof(p28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ) ).
fof(p33,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_27,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ilf_type(D,relation_type(C,empty_set))
=> D = empty_set ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& ilf_type(D,relation_type(C,empty_set)) )
=> D = empty_set ) ) ),
inference(strip,[],[prove_relset_1_27]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& ilf_type(D,relation_type(C,empty_set)) )
=> D = empty_set ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| B = empty_set
| ( domain_of(B) != empty_set
& range_of(B) != empty_set ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_1,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| B = empty_set
| ( domain_of(B) != empty_set
& range_of(B) != empty_set ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B] :
( ( domain_of(B) != empty_set
| ~ ilf_type(B,binary_relation_type)
| B = empty_set )
& ( range_of(B) != empty_set
| ~ ilf_type(B,binary_relation_type)
| B = empty_set ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B] :
( range_of(B) != empty_set
| ~ ilf_type(B,binary_relation_type)
| B = empty_set ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p13]) ).
fof(normalize_0_5,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p33]) ).
fof(normalize_0_9,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p28]) ).
fof(normalize_0_11,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( D != empty_set
& ilf_type(D,relation_type(C,B))
& ilf_type(D,relation_type(C,empty_set)) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_14,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( D != empty_set
& ilf_type(D,relation_type(C,B))
& ilf_type(D,relation_type(C,empty_set)) ) ),
inference(simplify,[],[normalize_0_13,normalize_0_9]) ).
fof(normalize_0_15,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( D != empty_set
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,empty_set))
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) ) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
? [D] :
( D != empty_set
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,empty_set))
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
( skolemFOFtoCNF_D_5 != empty_set
& ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set))
& ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) ),
inference(skolemize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set)),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p6]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B,C,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ subset(B,empty_set)
| B = empty_set ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ subset(B,empty_set)
| B = empty_set ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
inference(canonicalize,[],[p3]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| subset(domain_of(D),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| subset(range_of(D),C) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| subset(range_of(D),C) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
skolemFOFtoCNF_D_5 != empty_set,
inference(conjunct,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
( range_of(B) != empty_set
| ~ ilf_type(B,binary_relation_type)
| B = empty_set ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( range_of(skolemFOFtoCNF_D_5) != empty_set
| ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
| skolemFOFtoCNF_D_5 = empty_set ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ relation_like(skolemFOFtoCNF_D_5)
| ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(C))]]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,empty_set)))
| relation_like(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(empty_set)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_11,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set))
| ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,empty_set))) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(empty_set)),bind(E,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_16,plain,
ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,empty_set))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
relation_like(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,empty_set))) )],[refute_0_16,refute_0_10]) ).
cnf(refute_0_18,plain,
ilf_type(skolemFOFtoCNF_D_5,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_5) )],[refute_0_17,refute_0_5]) ).
cnf(refute_0_19,plain,
( range_of(skolemFOFtoCNF_D_5) != empty_set
| skolemFOFtoCNF_D_5 = empty_set ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) )],[refute_0_18,refute_0_1]) ).
cnf(refute_0_20,plain,
( ~ ilf_type(B,set_type)
| ~ subset(B,empty_set)
| B = empty_set ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_21,plain,
( ~ subset(B,empty_set)
| B = empty_set ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ subset(range_of(skolemFOFtoCNF_D_5),empty_set)
| range_of(skolemFOFtoCNF_D_5) = empty_set ),
inference(subst,[],[refute_0_21:[bind(B,$fot(range_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_23,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| subset(range_of(D),C) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_24,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| subset(range_of(D),C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ ilf_type(D,relation_type(B,C))
| subset(range_of(D),C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set))
| subset(range_of(skolemFOFtoCNF_D_5),empty_set) ),
inference(subst,[],[refute_0_25:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(empty_set)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_27,plain,
subset(range_of(skolemFOFtoCNF_D_5),empty_set),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,empty_set)) )],[refute_0_11,refute_0_26]) ).
cnf(refute_0_28,plain,
range_of(skolemFOFtoCNF_D_5) = empty_set,
inference(resolve,[$cnf( subset(range_of(skolemFOFtoCNF_D_5),empty_set) )],[refute_0_27,refute_0_22]) ).
cnf(refute_0_29,plain,
( empty_set != empty_set
| range_of(skolemFOFtoCNF_D_5) != empty_set
| range_of(skolemFOFtoCNF_D_5) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(range_of(skolemFOFtoCNF_D_5),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_30,plain,
( empty_set != empty_set
| range_of(skolemFOFtoCNF_D_5) = empty_set ),
inference(resolve,[$cnf( $equal(range_of(skolemFOFtoCNF_D_5),empty_set) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( empty_set != empty_set
| skolemFOFtoCNF_D_5 = empty_set ),
inference(resolve,[$cnf( $equal(range_of(skolemFOFtoCNF_D_5),empty_set) )],[refute_0_30,refute_0_19]) ).
cnf(refute_0_32,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_33,plain,
skolemFOFtoCNF_D_5 = empty_set,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_D_5 != empty_set,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_5,empty_set) )],[refute_0_33,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.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 : Sun Jul 10 10:57:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------