TSTP Solution File: SET591+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 03:35:42 EDT 2022
% Result : Theorem 0.11s 0.35s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 19 unt; 0 def)
% Number of atoms : 154 ( 28 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 161 ( 77 ~; 55 |; 13 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 10 sgn 58 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ).
fof(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ) ).
fof(prove_th50,conjecture,
! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ) ).
fof(subgoal_0,plain,
! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ),
inference(strip,[],[prove_th50]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_1,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [B,C] :
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(canonicalize,[],[equal_defn]) ).
fof(normalize_0_7,plain,
! [B,C] :
( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ( B != C
| subset(B,C) )
& ( B != C
| subset(C,B) )
& ( ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(canonicalize,[],[empty_defn]) ).
fof(normalize_0_11,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( ( ~ empty(B)
| ~ member(C,B) )
& ( empty(B)
| member(skolemFOFtoCNF_C(B),B) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C] :
( ~ empty(B)
| ~ member(C,B) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(canonicalize,[],[difference_defn]) ).
fof(normalize_0_16,plain,
! [B,C,D] :
( ~ member(D,difference(B,C))
<=> ( ~ member(D,B)
| member(D,C) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [B,C,D] :
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
? [B] :
( B != empty_set
& ? [C] : subset(B,difference(C,B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_20,plain,
( skolemFOFtoCNF_B != empty_set
& ? [C] : subset(skolemFOFtoCNF_B,difference(C,skolemFOFtoCNF_B)) ),
inference(skolemize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
? [C] : subset(skolemFOFtoCNF_B,difference(C,skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)),
inference(skolemize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_24,plain,
skolemFOFtoCNF_B != empty_set,
inference(conjunct,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ member(skolemFOFtoCNF_D(empty_set,X_8),empty_set),
inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_D(empty_set,X_8)))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_D(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_D(empty_set,X_8),empty_set)
| subset(empty_set,X_8) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(empty_set)),bind(C,$fot(X_8))]]) ).
cnf(refute_0_4,plain,
subset(empty_set,X_8),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(empty_set,X_8),empty_set) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
subset(empty_set,X_47),
inference(subst,[],[refute_0_4:[bind(X_8,$fot(X_47))]]) ).
cnf(refute_0_6,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ subset(X_47,empty_set)
| ~ subset(empty_set,X_47)
| empty_set = X_47 ),
inference(subst,[],[refute_0_6:[bind(B,$fot(empty_set)),bind(C,$fot(X_47))]]) ).
cnf(refute_0_8,plain,
( ~ subset(X_47,empty_set)
| empty_set = X_47 ),
inference(resolve,[$cnf( subset(empty_set,X_47) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ subset(skolemFOFtoCNF_B,empty_set)
| empty_set = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_8:[bind(X_47,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_10,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ empty(X_7)
| ~ member(skolemFOFtoCNF_D(X_7,X_8),X_7) ),
inference(subst,[],[refute_0_10:[bind(B,$fot(X_7)),bind(C,$fot(skolemFOFtoCNF_D(X_7,X_8)))]]) ).
cnf(refute_0_12,plain,
( member(skolemFOFtoCNF_D(X_7,X_8),X_7)
| subset(X_7,X_8) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_7)),bind(C,$fot(X_8))]]) ).
cnf(refute_0_13,plain,
( ~ empty(X_7)
| subset(X_7,X_8) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_7,X_8),X_7) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ empty(skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_B,X_8) ),
inference(subst,[],[refute_0_13:[bind(X_7,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_15,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
( empty(skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_17,plain,
( ~ member(D,C)
| ~ member(D,difference(B,C)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_18,plain,
( ~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B))
| ~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B)),bind(D,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_19,plain,
subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_20,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_21,plain,
( ~ member(X_61,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B))
| member(X_61,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_20:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B))),bind(D,$fot(X_61))]]) ).
cnf(refute_0_22,plain,
( ~ member(X_61,skolemFOFtoCNF_B)
| member(X_61,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_22:[bind(X_61,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_24,plain,
( empty(skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_16,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| empty(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),difference(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B)) )],[refute_0_24,refute_0_18]) ).
cnf(refute_0_26,plain,
empty(skolemFOFtoCNF_B),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
subset(skolemFOFtoCNF_B,X_8),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B) )],[refute_0_26,refute_0_14]) ).
cnf(refute_0_28,plain,
subset(skolemFOFtoCNF_B,empty_set),
inference(subst,[],[refute_0_27:[bind(X_8,$fot(empty_set))]]) ).
cnf(refute_0_29,plain,
empty_set = skolemFOFtoCNF_B,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,empty_set) )],[refute_0_28,refute_0_9]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_B != empty_set,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_31,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_32,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_33,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( empty_set != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_33:[bind(X,$fot(empty_set)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_35,plain,
empty_set != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_34,refute_0_30]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,skolemFOFtoCNF_B) )],[refute_0_29,refute_0_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 12:45:38 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35
% 0.11/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.11/0.36
%------------------------------------------------------------------------------