TSTP Solution File: SET063+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET063+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 03:32:03 EDT 2022
% Result : Theorem 1.16s 1.36s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 19 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 101 ( 48 ~; 33 |; 10 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 11 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set) ).
fof(thI17,conjecture,
! [A] : equal_set(intersection(A,empty_set),empty_set) ).
fof(subgoal_0,plain,
! [A] : equal_set(intersection(A,empty_set),empty_set),
inference(strip,[],[thI17]) ).
fof(negate_0_0,plain,
~ ! [A] : equal_set(intersection(A,empty_set),empty_set),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ equal_set(intersection(A,empty_set),empty_set),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ equal_set(intersection(skolemFOFtoCNF_A,empty_set),empty_set),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : ~ member(X,empty_set),
inference(canonicalize,[],[empty_set]) ).
fof(normalize_0_3,plain,
! [X] : ~ member(X,empty_set),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,X] :
( ( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) )
& ( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) )
& ( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[equal_set]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| subset(A,B) )
& ( ~ equal_set(A,B)
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,X] :
( ~ member(X,intersection(A,B))
<=> ( ~ member(X,A)
| ~ member(X,B) ) ),
inference(canonicalize,[],[intersection]) ).
fof(normalize_0_13,plain,
! [A,B,X] :
( ~ member(X,intersection(A,B))
<=> ( ~ member(X,A)
| ~ member(X,B) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,X] :
( ( ~ member(X,intersection(A,B))
| member(X,A) )
& ( ~ member(X,intersection(A,B))
| member(X,B) )
& ( ~ member(X,A)
| ~ member(X,B)
| member(X,intersection(A,B)) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,X] :
( ~ member(X,intersection(A,B))
| member(X,B) ),
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
~ equal_set(intersection(skolemFOFtoCNF_A,empty_set),empty_set),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ member(X,empty_set),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ member(skolemFOFtoCNF_X(empty_set,X_21),empty_set),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X(empty_set,X_21)))]]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( member(skolemFOFtoCNF_X(empty_set,X_21),empty_set)
| subset(empty_set,X_21) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(empty_set)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_5,plain,
subset(empty_set,X_21),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(empty_set,X_21),empty_set) )],[refute_0_4,refute_0_2]) ).
cnf(refute_0_6,plain,
subset(empty_set,X_579),
inference(subst,[],[refute_0_5:[bind(X_21,$fot(X_579))]]) ).
cnf(refute_0_7,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ subset(X_579,empty_set)
| ~ subset(empty_set,X_579)
| equal_set(X_579,empty_set) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_579)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_9,plain,
( ~ subset(X_579,empty_set)
| equal_set(X_579,empty_set) ),
inference(resolve,[$cnf( subset(empty_set,X_579) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ subset(intersection(X_3806,empty_set),empty_set)
| equal_set(intersection(X_3806,empty_set),empty_set) ),
inference(subst,[],[refute_0_9:[bind(X_579,$fot(intersection(X_3806,empty_set)))]]) ).
cnf(refute_0_11,plain,
~ member(skolemFOFtoCNF_X(intersection(X_3803,empty_set),X_3802),empty_set),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X(intersection(X_3803,empty_set),X_3802)))]]) ).
cnf(refute_0_12,plain,
( member(skolemFOFtoCNF_X(intersection(X_109,X_110),B),intersection(X_109,X_110))
| subset(intersection(X_109,X_110),B) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(intersection(X_109,X_110)))]]) ).
cnf(refute_0_13,plain,
( ~ member(X,intersection(A,B))
| member(X,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( ~ member(skolemFOFtoCNF_X(intersection(X_109,X_110),B),intersection(X_109,X_110))
| member(skolemFOFtoCNF_X(intersection(X_109,X_110),B),X_110) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_109)),bind(B,$fot(X_110)),bind(X,$fot(skolemFOFtoCNF_X(intersection(X_109,X_110),B)))]]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_X(intersection(X_109,X_110),B),X_110)
| subset(intersection(X_109,X_110),B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(intersection(X_109,X_110),B),intersection(X_109,X_110)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( member(skolemFOFtoCNF_X(intersection(X_3803,empty_set),X_3802),empty_set)
| subset(intersection(X_3803,empty_set),X_3802) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(X_3802)),bind(X_109,$fot(X_3803)),bind(X_110,$fot(empty_set))]]) ).
cnf(refute_0_17,plain,
subset(intersection(X_3803,empty_set),X_3802),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(intersection(X_3803,empty_set),X_3802),empty_set) )],[refute_0_16,refute_0_11]) ).
cnf(refute_0_18,plain,
subset(intersection(X_3806,empty_set),empty_set),
inference(subst,[],[refute_0_17:[bind(X_3802,$fot(empty_set)),bind(X_3803,$fot(X_3806))]]) ).
cnf(refute_0_19,plain,
equal_set(intersection(X_3806,empty_set),empty_set),
inference(resolve,[$cnf( subset(intersection(X_3806,empty_set),empty_set) )],[refute_0_18,refute_0_10]) ).
cnf(refute_0_20,plain,
equal_set(intersection(skolemFOFtoCNF_A,empty_set),empty_set),
inference(subst,[],[refute_0_19:[bind(X_3806,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( equal_set(intersection(skolemFOFtoCNF_A,empty_set),empty_set) )],[refute_0_20,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET063+4 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 09:26:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.16/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.16/1.36
% 1.16/1.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.16/1.37
%------------------------------------------------------------------------------