TSTP Solution File: SET175+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:33:20 EDT 2022
% Result : Theorem 0.69s 0.87s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 20 unt; 0 def)
% Number of atoms : 153 ( 58 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 151 ( 61 ~; 68 |; 10 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 135 ( 7 sgn 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ) ).
fof(prove_absorbtion_for_union,conjecture,
! [B,C] : union(B,intersection(B,C)) = B ).
fof(subgoal_0,plain,
! [B,C] : union(B,intersection(B,C)) = B,
inference(strip,[],[prove_absorbtion_for_union]) ).
fof(negate_0_0,plain,
~ ! [B,C] : union(B,intersection(B,C)) = B,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] : union(B,intersection(B,C)) != B,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != skolemFOFtoCNF_B,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_0_3,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| member(D,B) )
& ( ~ member(D,intersection(B,C))
| member(D,C) )
& ( ~ member(D,B)
| ~ member(D,C)
| member(D,intersection(B,C)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_16,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_17,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_158,X_157),X_158),X_158)
| ~ member(skolemFOFtoCNF_D_1(union(X_158,X_157),X_158),union(X_158,X_157))
| union(X_158,X_157) = X_158 ),
inference(subst,[],[refute_0_1:[bind(B,$fot(union(X_158,X_157))),bind(C,$fot(X_158))]]) ).
cnf(refute_0_3,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_D_1(X_101,X_102),X_102)
| member(skolemFOFtoCNF_D_1(X_101,X_102),union(X_102,C)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_102)),bind(D,$fot(skolemFOFtoCNF_D_1(X_101,X_102)))]]) ).
cnf(refute_0_5,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( X_101 = X_102
| member(skolemFOFtoCNF_D_1(X_101,X_102),X_101)
| member(skolemFOFtoCNF_D_1(X_101,X_102),X_102) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_101)),bind(C,$fot(X_102))]]) ).
cnf(refute_0_7,plain,
( X_101 = X_102
| member(skolemFOFtoCNF_D_1(X_101,X_102),X_101)
| member(skolemFOFtoCNF_D_1(X_101,X_102),union(X_102,C)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_101,X_102),X_102) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
( union(X_158,X_157) = X_158
| member(skolemFOFtoCNF_D_1(union(X_158,X_157),X_158),union(X_158,X_157)) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(X_157)),bind(X_101,$fot(union(X_158,X_157))),bind(X_102,$fot(X_158))]]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_158,X_157),X_158),X_158)
| union(X_158,X_157) = X_158 ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_158,X_157),X_158),union(X_158,X_157)) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_464,intersection(X_463,X_464)),X_464),X_464)
| union(X_464,intersection(X_463,X_464)) = X_464 ),
inference(subst,[],[refute_0_9:[bind(X_157,$fot(intersection(X_463,X_464))),bind(X_158,$fot(X_464))]]) ).
cnf(refute_0_11,plain,
( ~ member(D,intersection(B,C))
| member(D,C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),intersection(B,C))
| member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),C) ),
inference(subst,[],[refute_0_11:[bind(D,$fot(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246)))]]) ).
cnf(refute_0_13,plain,
( union(X_107,X_108) = C
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),C)
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),union(X_107,X_108)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(union(X_107,X_108)))]]) ).
cnf(refute_0_14,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_15,plain,
( ~ member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),union(X_107,X_108))
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),X_107)
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),X_108) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_107)),bind(C,$fot(X_108)),bind(D,$fot(skolemFOFtoCNF_D_1(union(X_107,X_108),C)))]]) ).
cnf(refute_0_16,plain,
( union(X_107,X_108) = C
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),C)
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),X_107)
| member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),X_108) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_107,X_108),C),union(X_107,X_108)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( union(X_246,intersection(B,C)) = X_246
| member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),X_246)
| member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),intersection(B,C)) ),
inference(subst,[],[refute_0_16:[bind(C,$fot(X_246)),bind(X_107,$fot(X_246)),bind(X_108,$fot(intersection(B,C)))]]) ).
cnf(refute_0_18,plain,
( union(X_246,intersection(B,C)) = X_246
| member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),C)
| member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),X_246) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_246,intersection(B,C)),X_246),intersection(B,C)) )],[refute_0_17,refute_0_12]) ).
cnf(refute_0_19,plain,
( union(X_464,intersection(X_463,X_464)) = X_464
| member(skolemFOFtoCNF_D_1(union(X_464,intersection(X_463,X_464)),X_464),X_464) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(X_463)),bind(C,$fot(X_464)),bind(X_246,$fot(X_464))]]) ).
cnf(refute_0_20,plain,
union(X_464,intersection(X_463,X_464)) = X_464,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(union(X_464,intersection(X_463,X_464)),X_464),X_464) )],[refute_0_19,refute_0_10]) ).
cnf(refute_0_21,plain,
union(X_466,intersection(X_465,X_466)) = X_466,
inference(subst,[],[refute_0_20:[bind(X_463,$fot(X_465)),bind(X_464,$fot(X_466))]]) ).
cnf(refute_0_22,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_23,plain,
intersection(X_466,X_465) = intersection(X_465,X_466),
inference(subst,[],[refute_0_22:[bind(B,$fot(X_466)),bind(C,$fot(X_465))]]) ).
cnf(refute_0_24,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_26,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( intersection(X_466,X_465) != intersection(X_465,X_466)
| intersection(X_465,X_466) = intersection(X_466,X_465) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(intersection(X_466,X_465))),bind(Y,$fot(intersection(X_465,X_466)))]]) ).
cnf(refute_0_28,plain,
intersection(X_465,X_466) = intersection(X_466,X_465),
inference(resolve,[$cnf( $equal(intersection(X_466,X_465),intersection(X_465,X_466)) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( intersection(X_465,X_466) != intersection(X_466,X_465)
| union(X_466,intersection(X_465,X_466)) != X_466
| union(X_466,intersection(X_466,X_465)) = X_466 ),
introduced(tautology,[equality,[$cnf( $equal(union(X_466,intersection(X_465,X_466)),X_466) ),[0,1],$fot(intersection(X_466,X_465))]]) ).
cnf(refute_0_30,plain,
( union(X_466,intersection(X_465,X_466)) != X_466
| union(X_466,intersection(X_466,X_465)) = X_466 ),
inference(resolve,[$cnf( $equal(intersection(X_465,X_466),intersection(X_466,X_465)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
union(X_466,intersection(X_466,X_465)) = X_466,
inference(resolve,[$cnf( $equal(union(X_466,intersection(X_465,X_466)),X_466) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = skolemFOFtoCNF_B,
inference(subst,[],[refute_0_31:[bind(X_465,$fot(skolemFOFtoCNF_C)),bind(X_466,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != skolemFOFtoCNF_B
| union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),skolemFOFtoCNF_B) ),[0,0],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),skolemFOFtoCNF_B) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),skolemFOFtoCNF_B) )],[refute_0_34,refute_0_0]) ).
cnf(refute_0_36,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_36,refute_0_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 11:09:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.69/0.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.87
% 0.69/0.87 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.69/0.87
%------------------------------------------------------------------------------