TSTP Solution File: SET162+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:33:12 EDT 2022
% Result : Theorem 0.36s 0.57s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 28 unt; 0 def)
% Number of atoms : 145 ( 68 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 136 ( 58 ~; 62 |; 7 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 4 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
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_union_empty_set,conjecture,
! [B] : union(B,empty_set) = B ).
fof(subgoal_0,plain,
! [B] : union(B,empty_set) = B,
inference(strip,[],[prove_union_empty_set]) ).
fof(negate_0_0,plain,
~ ! [B] : union(B,empty_set) = B,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] : union(B,empty_set) != B,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
union(skolemFOFtoCNF_B,empty_set) != skolemFOFtoCNF_B,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] : union(B,C) = union(C,B),
inference(canonicalize,[],[commutativity_of_union]) ).
fof(normalize_0_3,plain,
! [B,C] : union(B,C) = union(C,B),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_0_5,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(canonicalize,[],[union_defn]) ).
fof(normalize_0_9,plain,
! [B,C,D] :
( ~ member(D,union(B,C))
<=> ( ~ member(D,B)
& ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_14,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[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_10]) ).
cnf(refute_0_0,plain,
union(skolemFOFtoCNF_B,empty_set) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
union(B,C) = union(C,B),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( union(B,C) != union(C,B)
| union(C,B) = union(B,C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(union(B,C))),bind(Y,$fot(union(C,B)))]]) ).
cnf(refute_0_6,plain,
union(C,B) = union(B,C),
inference(resolve,[$cnf( $equal(union(B,C),union(C,B)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
union(skolemFOFtoCNF_B,empty_set) = union(empty_set,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_6:[bind(B,$fot(empty_set)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
( union(empty_set,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| union(skolemFOFtoCNF_B,empty_set) != union(empty_set,skolemFOFtoCNF_B)
| union(skolemFOFtoCNF_B,empty_set) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B,empty_set),union(empty_set,skolemFOFtoCNF_B)) ),[1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_9,plain,
( union(empty_set,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| union(skolemFOFtoCNF_B,empty_set) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,empty_set),union(empty_set,skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
union(empty_set,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,empty_set),skolemFOFtoCNF_B) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
union(empty_set,C) = union(C,empty_set),
inference(subst,[],[refute_0_1:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_13,plain,
( ~ member(skolemFOFtoCNF_D_1(X_141,union(X_141,X_140)),X_141)
| ~ member(skolemFOFtoCNF_D_1(X_141,union(X_141,X_140)),union(X_141,X_140))
| X_141 = union(X_141,X_140) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(X_141)),bind(C,$fot(union(X_141,X_140)))]]) ).
cnf(refute_0_14,plain,
( ~ member(D,B)
| member(D,union(B,C)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
( ~ member(skolemFOFtoCNF_D_1(X_58,X_59),X_58)
| member(skolemFOFtoCNF_D_1(X_58,X_59),union(X_58,C)) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(X_58)),bind(D,$fot(skolemFOFtoCNF_D_1(X_58,X_59)))]]) ).
cnf(refute_0_16,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_17,plain,
( X_58 = X_59
| member(skolemFOFtoCNF_D_1(X_58,X_59),X_58)
| member(skolemFOFtoCNF_D_1(X_58,X_59),X_59) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(X_58)),bind(C,$fot(X_59))]]) ).
cnf(refute_0_18,plain,
( X_58 = X_59
| member(skolemFOFtoCNF_D_1(X_58,X_59),X_59)
| member(skolemFOFtoCNF_D_1(X_58,X_59),union(X_58,C)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_58,X_59),X_58) )],[refute_0_17,refute_0_15]) ).
cnf(refute_0_19,plain,
( X_141 = union(X_141,X_140)
| member(skolemFOFtoCNF_D_1(X_141,union(X_141,X_140)),union(X_141,X_140)) ),
inference(subst,[],[refute_0_18:[bind(C,$fot(X_140)),bind(X_58,$fot(X_141)),bind(X_59,$fot(union(X_141,X_140)))]]) ).
cnf(refute_0_20,plain,
( ~ member(skolemFOFtoCNF_D_1(X_141,union(X_141,X_140)),X_141)
| X_141 = union(X_141,X_140) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_141,union(X_141,X_140)),union(X_141,X_140)) )],[refute_0_19,refute_0_13]) ).
cnf(refute_0_21,plain,
( ~ member(skolemFOFtoCNF_D_1(X_395,union(X_395,empty_set)),X_395)
| X_395 = union(X_395,empty_set) ),
inference(subst,[],[refute_0_20:[bind(X_140,$fot(empty_set)),bind(X_141,$fot(X_395))]]) ).
cnf(refute_0_22,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
~ member(skolemFOFtoCNF_D_1(X_393,union(X_393,empty_set)),empty_set),
inference(subst,[],[refute_0_22:[bind(B,$fot(skolemFOFtoCNF_D_1(X_393,union(X_393,empty_set))))]]) ).
cnf(refute_0_24,plain,
( B = union(X_102,X_103)
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),B)
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),union(X_102,X_103)) ),
inference(subst,[],[refute_0_16:[bind(C,$fot(union(X_102,X_103)))]]) ).
cnf(refute_0_25,plain,
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_26,plain,
( ~ member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),union(X_102,X_103))
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),X_102)
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),X_103) ),
inference(subst,[],[refute_0_25:[bind(B,$fot(X_102)),bind(C,$fot(X_103)),bind(D,$fot(skolemFOFtoCNF_D_1(B,union(X_102,X_103))))]]) ).
cnf(refute_0_27,plain,
( B = union(X_102,X_103)
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),B)
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),X_102)
| member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),X_103) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(B,union(X_102,X_103)),union(X_102,X_103)) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( X_393 = union(X_393,empty_set)
| member(skolemFOFtoCNF_D_1(X_393,union(X_393,empty_set)),X_393)
| member(skolemFOFtoCNF_D_1(X_393,union(X_393,empty_set)),empty_set) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_393)),bind(X_102,$fot(X_393)),bind(X_103,$fot(empty_set))]]) ).
cnf(refute_0_29,plain,
( X_393 = union(X_393,empty_set)
| member(skolemFOFtoCNF_D_1(X_393,union(X_393,empty_set)),X_393) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_393,union(X_393,empty_set)),empty_set) )],[refute_0_28,refute_0_23]) ).
cnf(refute_0_30,plain,
( X_395 = union(X_395,empty_set)
| member(skolemFOFtoCNF_D_1(X_395,union(X_395,empty_set)),X_395) ),
inference(subst,[],[refute_0_29:[bind(X_393,$fot(X_395))]]) ).
cnf(refute_0_31,plain,
X_395 = union(X_395,empty_set),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_395,union(X_395,empty_set)),X_395) )],[refute_0_30,refute_0_21]) ).
cnf(refute_0_32,plain,
C = union(C,empty_set),
inference(subst,[],[refute_0_31:[bind(X_395,$fot(C))]]) ).
cnf(refute_0_33,plain,
( C != union(C,empty_set)
| union(C,empty_set) = C ),
inference(subst,[],[refute_0_4:[bind(X,$fot(C)),bind(Y,$fot(union(C,empty_set)))]]) ).
cnf(refute_0_34,plain,
union(C,empty_set) = C,
inference(resolve,[$cnf( $equal(C,union(C,empty_set)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( union(C,empty_set) != C
| union(empty_set,C) != union(C,empty_set)
| union(empty_set,C) = C ),
introduced(tautology,[equality,[$cnf( $equal(union(empty_set,C),union(C,empty_set)) ),[1],$fot(C)]]) ).
cnf(refute_0_36,plain,
( union(empty_set,C) != union(C,empty_set)
| union(empty_set,C) = C ),
inference(resolve,[$cnf( $equal(union(C,empty_set),C) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
union(empty_set,C) = C,
inference(resolve,[$cnf( $equal(union(empty_set,C),union(C,empty_set)) )],[refute_0_11,refute_0_36]) ).
cnf(refute_0_38,plain,
union(empty_set,skolemFOFtoCNF_B) = skolemFOFtoCNF_B,
inference(subst,[],[refute_0_37:[bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| union(empty_set,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| union(empty_set,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),[0,1],$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_B
| union(empty_set,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
skolemFOFtoCNF_B != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(union(empty_set,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_40,refute_0_10]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_B,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B)]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_42,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jul 11 02:29:32 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.36/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.57
% 0.36/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.36/0.58
%------------------------------------------------------------------------------