TSTP Solution File: SET631+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET631+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:36:11 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 98 ( 46 ~; 34 |; 8 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 1 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ) ).
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ) ).
fof(prove_th113,conjecture,
! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
inference(strip,[],[prove_th113]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(canonicalize,[],[symmetry_of_intersect]) ).
fof(normalize_0_1,plain,
! [B,C] :
( ~ intersect(B,C)
| intersect(C,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B,C] :
( ~ intersect(B,C)
& ? [D] : intersect(B,difference(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& ? [D] : intersect(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C,D)) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [D] : intersect(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C,D)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
intersect(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) )
& ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) )
& ( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,difference(B,C)) )
& ( ~ member(D,difference(B,C))
| member(D,B) )
& ( ~ member(D,B)
| member(D,C)
| member(D,difference(B,C)) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_16,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ intersect(B,C)
| intersect(C,B) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ intersect(skolemFOFtoCNF_C,skolemFOFtoCNF_B)
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
intersect(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ intersect(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| intersect(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)))]]) ).
cnf(refute_0_4,plain,
intersect(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ intersect(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_7,plain,
member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(resolve,[$cnf( intersect(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ member(D,difference(B,C))
| member(D,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_1)),bind(D,$fot(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_10,plain,
member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ intersect(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_11:[bind(B,$fot(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_13,plain,
member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_B),
inference(resolve,[$cnf( intersect(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_15,plain,
( ~ member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),X_14)
| ~ member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| intersect(X_14,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_14)),bind(C,$fot(skolemFOFtoCNF_B)),bind(D,$fot(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),X_14)
| intersect(X_14,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| intersect(skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_16:[bind(X_14,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_18,plain,
intersect(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B),skolemFOFtoCNF_C) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_18,refute_0_1]) ).
cnf(refute_0_20,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_19,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET631+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 00:08:47 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------