TSTP Solution File: SET942+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET942+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 03:38:31 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 7 unt; 0 def)
% Number of atoms : 156 ( 19 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 168 ( 68 ~; 73 |; 14 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 44 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ) ).
fof(t95_zfmisc_1,conjecture,
! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ),
inference(strip,[],[t95_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_tarski]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( ( B != union(A)
| ~ in(C,B)
| in(C,skolemFOFtoCNF_D_1(A,C)) )
& ( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) )
& ( B = union(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| in(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B)) )
& ( B = union(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| in(skolemFOFtoCNF_D(A,B),A) )
& ( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) )
& ( ~ in(D,A)
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ in(skolemFOFtoCNF_C_1(A,B),D)
| B = union(A) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( B != union(A)
| ~ in(C,B)
| in(C,skolemFOFtoCNF_D_1(A,C)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
? [A,B] :
( ~ subset(union(A),union(B))
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B))
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
~ subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)),union(skolemFOFtoCNF_B))
| subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(union(skolemFOFtoCNF_A_2))),bind(B,$fot(union(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( in(skolemFOFtoCNF_C(union(X_10),B),union(X_10))
| subset(union(X_10),B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(union(X_10)))]]) ).
cnf(refute_0_4,plain,
( B != union(A)
| ~ in(C,B)
| in(C,skolemFOFtoCNF_D_1(A,C)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( union(A) != union(A)
| ~ in(C,union(A))
| in(C,skolemFOFtoCNF_D_1(A,C)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(union(A)))]]) ).
cnf(refute_0_6,plain,
union(A) = union(A),
introduced(tautology,[refl,[$fot(union(A))]]) ).
cnf(refute_0_7,plain,
( ~ in(C,union(A))
| in(C,skolemFOFtoCNF_D_1(A,C)) ),
inference(resolve,[$cnf( $equal(union(A),union(A)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ in(skolemFOFtoCNF_C(union(X_10),B),union(X_10))
| in(skolemFOFtoCNF_C(union(X_10),B),skolemFOFtoCNF_D_1(X_10,skolemFOFtoCNF_C(union(X_10),B))) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_10)),bind(C,$fot(skolemFOFtoCNF_C(union(X_10),B)))]]) ).
cnf(refute_0_9,plain,
( in(skolemFOFtoCNF_C(union(X_10),B),skolemFOFtoCNF_D_1(X_10,skolemFOFtoCNF_C(union(X_10),B)))
| subset(union(X_10),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(union(X_10),B),union(X_10)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88)))
| subset(union(skolemFOFtoCNF_A_2),X_88) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_88)),bind(X_10,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_C(union(X_12),B),union(X_12))
| subset(union(X_12),B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(union(X_12)))]]) ).
cnf(refute_0_12,plain,
( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
( union(A) != union(A)
| ~ in(C,union(A))
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(union(A)))]]) ).
cnf(refute_0_14,plain,
( ~ in(C,union(A))
| in(skolemFOFtoCNF_D_1(A,C),A) ),
inference(resolve,[$cnf( $equal(union(A),union(A)) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ in(skolemFOFtoCNF_C(union(X_12),B),union(X_12))
| in(skolemFOFtoCNF_D_1(X_12,skolemFOFtoCNF_C(union(X_12),B)),X_12) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_12)),bind(C,$fot(skolemFOFtoCNF_C(union(X_12),B)))]]) ).
cnf(refute_0_16,plain,
( in(skolemFOFtoCNF_D_1(X_12,skolemFOFtoCNF_C(union(X_12),B)),X_12)
| subset(union(X_12),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(union(X_12),B),union(X_12)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_A_2)
| subset(union(skolemFOFtoCNF_A_2),B) ),
inference(subst,[],[refute_0_16:[bind(X_12,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_18,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
( ~ in(X_22,skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| in(X_22,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_22))]]) ).
cnf(refute_0_21,plain,
( ~ in(X_22,skolemFOFtoCNF_A_2)
| in(X_22,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_21:[bind(X_22,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B))))]]) ).
cnf(refute_0_23,plain,
( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_B)
| subset(union(skolemFOFtoCNF_A_2),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_A_2) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_25,plain,
( union(A) != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,union(A)) ),
inference(subst,[],[refute_0_24:[bind(B,$fot(union(A)))]]) ).
cnf(refute_0_26,plain,
( ~ in(C,D)
| ~ in(D,A)
| in(C,union(A)) ),
inference(resolve,[$cnf( $equal(union(A),union(A)) )],[refute_0_6,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ in(X_36,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_B)
| in(X_36,union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_36)),bind(D,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B))))]]) ).
cnf(refute_0_28,plain,
( ~ in(X_36,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)))
| in(X_36,union(skolemFOFtoCNF_B))
| subset(union(skolemFOFtoCNF_A_2),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),B)),skolemFOFtoCNF_B) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88)))
| in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88),union(skolemFOFtoCNF_B))
| subset(union(skolemFOFtoCNF_A_2),X_88) ),
inference(subst,[],[refute_0_28:[bind(B,$fot(X_88)),bind(X_36,$fot(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88)))]]) ).
cnf(refute_0_30,plain,
( in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88),union(skolemFOFtoCNF_B))
| subset(union(skolemFOFtoCNF_A_2),X_88) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),X_88))) )],[refute_0_10,refute_0_29]) ).
cnf(refute_0_31,plain,
( in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)),union(skolemFOFtoCNF_B))
| subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_30:[bind(X_88,$fot(union(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_32,plain,
subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)),union(skolemFOFtoCNF_B)) )],[refute_0_31,refute_0_1]) ).
cnf(refute_0_33,plain,
~ subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( subset(union(skolemFOFtoCNF_A_2),union(skolemFOFtoCNF_B)) )],[refute_0_32,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET942+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 20:14:37 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.40
% 0.21/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.41
%------------------------------------------------------------------------------