TSTP Solution File: SET185+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 03:33:25 EDT 2022
% Result : Theorem 0.40s 0.61s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 17 unt; 0 def)
% Number of atoms : 173 ( 57 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 169 ( 66 ~; 74 |; 13 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 3 sgn 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(commutativity_of_union,axiom,
! [B,C] : union(B,C) = union(C,B) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ) ).
fof(prove_subset_union,conjecture,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ) ).
fof(subgoal_0,plain,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
inference(strip,[],[prove_subset_union]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_0_1,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C,D] :
( ( B != C
| ~ member(D,B)
| member(D,C) )
& ( B != C
| ~ member(D,C)
| member(D,B) )
& ( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C )
& ( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ( ~ member(D,B)
| member(D,union(B,C)) )
& ( ~ member(D,C)
| member(D,union(B,C)) )
& ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_0_10,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [B,C] :
( union(B,C) != C
& subset(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
( union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != skolemFOFtoCNF_C
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_15,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_19,plain,
union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_108,X_107),X_108),X_108)
| ~ member(skolemFOFtoCNF_D_1(union(X_108,X_107),X_108),union(X_108,X_107))
| union(X_108,X_107) = X_108 ),
inference(subst,[],[refute_0_0:[bind(B,$fot(union(X_108,X_107))),bind(C,$fot(X_108))]]) ).
cnf(refute_0_2,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ member(skolemFOFtoCNF_D_1(X_56,X_57),X_57)
| member(skolemFOFtoCNF_D_1(X_56,X_57),union(X_57,C)) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_57)),bind(D,$fot(skolemFOFtoCNF_D_1(X_56,X_57)))]]) ).
cnf(refute_0_4,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( X_56 = X_57
| member(skolemFOFtoCNF_D_1(X_56,X_57),X_56)
| member(skolemFOFtoCNF_D_1(X_56,X_57),X_57) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(X_56)),bind(C,$fot(X_57))]]) ).
cnf(refute_0_6,plain,
( X_56 = X_57
| member(skolemFOFtoCNF_D_1(X_56,X_57),X_56)
| member(skolemFOFtoCNF_D_1(X_56,X_57),union(X_57,C)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_56,X_57),X_57) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( union(X_108,X_107) = X_108
| member(skolemFOFtoCNF_D_1(union(X_108,X_107),X_108),union(X_108,X_107)) ),
inference(subst,[],[refute_0_6:[bind(C,$fot(X_107)),bind(X_56,$fot(union(X_108,X_107))),bind(X_57,$fot(X_108))]]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_108,X_107),X_108),X_108)
| union(X_108,X_107) = X_108 ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_108,X_107),X_108),union(X_108,X_107)) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_110,X_109),X_110),X_110)
| union(X_110,X_109) = X_110 ),
inference(subst,[],[refute_0_8:[bind(X_107,$fot(X_109)),bind(X_108,$fot(X_110))]]) ).
cnf(refute_0_10,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
union(X_109,X_110) = union(X_110,X_109),
inference(subst,[],[refute_0_10:[bind(B,$fot(X_109)),bind(C,$fot(X_110))]]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( union(X_109,X_110) != union(X_110,X_109)
| union(X_110,X_109) = union(X_109,X_110) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(union(X_109,X_110))),bind(Y,$fot(union(X_110,X_109)))]]) ).
cnf(refute_0_16,plain,
union(X_110,X_109) = union(X_109,X_110),
inference(resolve,[$cnf( $equal(union(X_109,X_110),union(X_110,X_109)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( union(X_110,X_109) != union(X_109,X_110)
| ~ member(skolemFOFtoCNF_D_1(union(X_109,X_110),X_110),X_110)
| member(skolemFOFtoCNF_D_1(union(X_110,X_109),X_110),X_110) ),
introduced(tautology,[equality,[$cnf( ~ member(skolemFOFtoCNF_D_1(union(X_110,X_109),X_110),X_110) ),[0,0],$fot(union(X_109,X_110))]]) ).
cnf(refute_0_18,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_109,X_110),X_110),X_110)
| member(skolemFOFtoCNF_D_1(union(X_110,X_109),X_110),X_110) ),
inference(resolve,[$cnf( $equal(union(X_110,X_109),union(X_109,X_110)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_109,X_110),X_110),X_110)
| union(X_110,X_109) = X_110 ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_110,X_109),X_110),X_110) )],[refute_0_18,refute_0_9]) ).
cnf(refute_0_20,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C),skolemFOFtoCNF_C)
| union(skolemFOFtoCNF_C,skolemFOFtoCNF_B) = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_19:[bind(X_109,$fot(skolemFOFtoCNF_B)),bind(X_110,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_21,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_23,plain,
( ~ member(X_47,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_47,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_22:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(X_47))]]) ).
cnf(refute_0_24,plain,
( ~ member(X_47,skolemFOFtoCNF_B)
| member(X_47,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_24:[bind(X_47,$fot(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269)))]]) ).
cnf(refute_0_26,plain,
( union(X_62,X_63) = C
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),C)
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),union(X_62,X_63)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(union(X_62,X_63)))]]) ).
cnf(refute_0_27,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_28,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),union(X_62,X_63))
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),X_62)
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),X_63) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_62)),bind(C,$fot(X_63)),bind(D,$fot(skolemFOFtoCNF_D_1(union(X_62,X_63),C)))]]) ).
cnf(refute_0_29,plain,
( union(X_62,X_63) = C
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),C)
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),X_62)
| member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),X_63) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_62,X_63),C),union(X_62,X_63)) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( union(skolemFOFtoCNF_B,X_269) = X_269
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),X_269)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_29:[bind(C,$fot(X_269)),bind(X_62,$fot(skolemFOFtoCNF_B)),bind(X_63,$fot(X_269))]]) ).
cnf(refute_0_31,plain,
( union(skolemFOFtoCNF_B,X_269) = X_269
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),X_269)
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,X_269),X_269),skolemFOFtoCNF_B) )],[refute_0_30,refute_0_25]) ).
cnf(refute_0_32,plain,
( union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = skolemFOFtoCNF_C
| member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_31:[bind(X_269,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_33,plain,
union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_34,plain,
member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
union(skolemFOFtoCNF_C,skolemFOFtoCNF_B) = skolemFOFtoCNF_C,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C),skolemFOFtoCNF_C) )],[refute_0_34,refute_0_20]) ).
cnf(refute_0_36,plain,
( union(B,C) != union(C,B)
| union(C,B) = union(B,C) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(union(B,C))),bind(Y,$fot(union(C,B)))]]) ).
cnf(refute_0_37,plain,
union(C,B) = union(B,C),
inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_0_10,refute_0_36]) ).
cnf(refute_0_38,plain,
union(skolemFOFtoCNF_C,skolemFOFtoCNF_B) = union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(subst,[],[refute_0_37:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_39,plain,
( union(skolemFOFtoCNF_C,skolemFOFtoCNF_B) != skolemFOFtoCNF_C
| union(skolemFOFtoCNF_C,skolemFOFtoCNF_B) != union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = skolemFOFtoCNF_C ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),[0],$fot(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_40,plain,
( union(skolemFOFtoCNF_C,skolemFOFtoCNF_B) != skolemFOFtoCNF_C
| union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = skolemFOFtoCNF_C ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C,skolemFOFtoCNF_B),union(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
union(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = skolemFOFtoCNF_C,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_C,skolemFOFtoCNF_B),skolemFOFtoCNF_C) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C) )],[refute_0_41,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 10:37:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.61
% 0.40/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.40/0.62
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