TSTP Solution File: SET637+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 03:36:15 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 89 ( 27 unt; 0 def)
% Number of atoms : 187 ( 42 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 190 ( 92 ~; 57 |; 13 &)
% ( 24 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 128 ( 4 sgn 91 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(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(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ) ).
fof(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ) ).
fof(prove_th119,conjecture,
! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ) ).
fof(subgoal_0,plain,
! [B,C] :
( intersect(B,C)
=> not_equal(intersection(B,C),empty_set) ),
inference(strip,[],[prove_th119]) ).
fof(subgoal_1,plain,
! [B,C] :
( not_equal(intersection(B,C),empty_set)
=> intersect(B,C) ),
inference(strip,[],[prove_th119]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( intersect(B,C)
=> not_equal(intersection(B,C),empty_set) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] :
( ~ not_equal(intersection(B,C),empty_set)
& intersect(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ not_equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set)
& intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_0_4,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(simplify,[],[normalize_0_3,normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) )
& ( ~ member(D,intersection(B,C))
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ not_equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(canonicalize,[],[not_equal_defn]) ).
fof(normalize_0_12,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C] :
( ( B != C
| ~ not_equal(B,C) )
& ( B = C
| not_equal(B,C) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C] :
( B = C
| not_equal(B,C) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_16,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_3,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
~ not_equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( B = C
| not_equal(B,C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set
| not_equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_7,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
inference(resolve,[$cnf( not_equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_12,plain,
~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set),
inference(subst,[],[refute_0_11:[bind(B,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_10,refute_0_12]) ).
fof(negate_1_0,plain,
~ ! [B,C] :
( not_equal(intersection(B,C),empty_set)
=> intersect(B,C) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B,C] :
( ~ intersect(B,C)
& not_equal(intersection(B,C),empty_set) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
& not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_1_4,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersection_defn]) ).
fof(normalize_1_5,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
<=> ( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(simplify,[],[normalize_1_3,normalize_1_5]) ).
fof(normalize_1_7,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] : ~ member(D,intersection(B,C)) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),intersection(B,C)) )
& ( ~ member(D,intersection(B,C))
| intersect(B,C) ) ),
inference(clausify,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| intersect(B,C) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_1_11,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_1_13,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,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_1_13]) ).
fof(normalize_1_15,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_17,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(canonicalize,[],[not_equal_defn]) ).
fof(normalize_1_18,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [B,C] :
( ( B != C
| ~ not_equal(B,C) )
& ( B = C
| not_equal(B,C) ) ),
inference(clausify,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [B,C] :
( B != C
| ~ not_equal(B,C) ),
inference(conjunct,[],[normalize_1_19]) ).
cnf(refute_1_0,plain,
not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ member(D,intersection(B,C))
| intersect(B,C) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
( ~ member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),intersection(B,C))
| intersect(B,C) ),
inference(subst,[],[refute_1_1:[bind(D,$fot(skolemFOFtoCNF_D_1(empty_set,intersection(B,C))))]]) ).
cnf(refute_1_3,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_4,plain,
~ member(skolemFOFtoCNF_D_1(empty_set,X_139),empty_set),
inference(subst,[],[refute_1_3:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,X_139)))]]) ).
cnf(refute_1_5,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_6,plain,
( empty_set = X_139
| member(skolemFOFtoCNF_D_1(empty_set,X_139),X_139)
| member(skolemFOFtoCNF_D_1(empty_set,X_139),empty_set) ),
inference(subst,[],[refute_1_5:[bind(B,$fot(empty_set)),bind(C,$fot(X_139))]]) ).
cnf(refute_1_7,plain,
( empty_set = X_139
| member(skolemFOFtoCNF_D_1(empty_set,X_139),X_139) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,X_139),empty_set) )],[refute_1_6,refute_1_4]) ).
cnf(refute_1_8,plain,
( empty_set = intersection(B,C)
| member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),intersection(B,C)) ),
inference(subst,[],[refute_1_7:[bind(X_139,$fot(intersection(B,C)))]]) ).
cnf(refute_1_9,plain,
( empty_set = intersection(B,C)
| intersect(B,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,intersection(B,C)),intersection(B,C)) )],[refute_1_8,refute_1_2]) ).
cnf(refute_1_10,plain,
( empty_set = intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_9:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
( empty_set != intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set ),
inference(subst,[],[refute_1_13:[bind(X,$fot(empty_set)),bind(Y,$fot(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_15,plain,
( intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( $equal(empty_set,intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_10,refute_1_14]) ).
cnf(refute_1_16,plain,
( intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set
| ~ not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set)
| not_equal(empty_set,empty_set) ),
introduced(tautology,[equality,[$cnf( not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_17,plain,
( ~ not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| not_equal(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
| not_equal(empty_set,empty_set) ),
inference(resolve,[$cnf( not_equal(intersection(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_0,refute_1_17]) ).
cnf(refute_1_19,plain,
~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_20,plain,
not_equal(empty_set,empty_set),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
( B != C
| ~ not_equal(B,C) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_22,plain,
( C != C
| ~ not_equal(C,C) ),
inference(subst,[],[refute_1_21:[bind(B,$fot(C))]]) ).
cnf(refute_1_23,plain,
C = C,
introduced(tautology,[refl,[$fot(C)]]) ).
cnf(refute_1_24,plain,
~ not_equal(C,C),
inference(resolve,[$cnf( $equal(C,C) )],[refute_1_23,refute_1_22]) ).
cnf(refute_1_25,plain,
~ not_equal(empty_set,empty_set),
inference(subst,[],[refute_1_24:[bind(C,$fot(empty_set))]]) ).
cnf(refute_1_26,plain,
$false,
inference(resolve,[$cnf( not_equal(empty_set,empty_set) )],[refute_1_20,refute_1_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 23:50:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.45
%------------------------------------------------------------------------------