TSTP Solution File: SET628+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET628+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 03:36:09 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 28 unt; 0 def)
% Number of atoms : 200 ( 35 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 204 ( 97 ~; 68 |; 15 &)
% ( 20 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 4 sgn 74 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(empty_defn,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ) ).
fof(prove_th110,conjecture,
! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ) ).
fof(subgoal_0,plain,
! [B] :
( intersect(B,B)
=> not_equal(B,empty_set) ),
inference(strip,[],[prove_th110]) ).
fof(subgoal_1,plain,
! [B] :
( not_equal(B,empty_set)
=> intersect(B,B) ),
inference(strip,[],[prove_th110]) ).
fof(negate_0_0,plain,
~ ! [B] :
( intersect(B,B)
=> not_equal(B,empty_set) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ~ not_equal(B,empty_set)
& intersect(B,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ not_equal(skolemFOFtoCNF_B,empty_set)
& intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ not_equal(skolemFOFtoCNF_B,empty_set),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(canonicalize,[],[not_equal_defn]) ).
fof(normalize_0_5,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ( B != C
| ~ not_equal(B,C) )
& ( B = C
| not_equal(B,C) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( B = C
| not_equal(B,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) )
& ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) )
& ( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_0_13,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ not_equal(skolemFOFtoCNF_B,empty_set),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( B = C
| not_equal(B,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( skolemFOFtoCNF_B = empty_set
| not_equal(skolemFOFtoCNF_B,empty_set) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_4,plain,
skolemFOFtoCNF_B = empty_set,
inference(resolve,[$cnf( not_equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_B != empty_set
| ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B)
| intersect(empty_set,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_6,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B)
| intersect(empty_set,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_B != empty_set
| ~ intersect(empty_set,skolemFOFtoCNF_B)
| intersect(empty_set,empty_set) ),
introduced(tautology,[equality,[$cnf( intersect(empty_set,skolemFOFtoCNF_B) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_8,plain,
( ~ intersect(empty_set,skolemFOFtoCNF_B)
| intersect(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B)
| intersect(empty_set,empty_set) ),
inference(resolve,[$cnf( intersect(empty_set,skolemFOFtoCNF_B) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
intersect(empty_set,empty_set),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ intersect(empty_set,empty_set)
| member(skolemFOFtoCNF_D(empty_set,empty_set),empty_set) ),
inference(subst,[],[refute_0_11:[bind(B,$fot(empty_set)),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_13,plain,
member(skolemFOFtoCNF_D(empty_set,empty_set),empty_set),
inference(resolve,[$cnf( intersect(empty_set,empty_set) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
~ member(skolemFOFtoCNF_D(empty_set,empty_set),empty_set),
inference(subst,[],[refute_0_14:[bind(B,$fot(skolemFOFtoCNF_D(empty_set,empty_set)))]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(empty_set,empty_set),empty_set) )],[refute_0_13,refute_0_15]) ).
fof(negate_1_0,plain,
~ ! [B] :
( not_equal(B,empty_set)
=> intersect(B,B) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B] :
( ~ intersect(B,B)
& not_equal(B,empty_set) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
& not_equal(skolemFOFtoCNF_B_1,empty_set) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
not_equal(skolemFOFtoCNF_B_1,empty_set),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_4,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(canonicalize,[],[empty_defn]) ).
fof(normalize_1_5,plain,
! [B] :
( ~ empty(B)
<=> ? [C] : member(C,B) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [B,C] :
( ( ~ empty(B)
| ~ member(C,B) )
& ( empty(B)
| member(skolemFOFtoCNF_C(B),B) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [B] :
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_1_9,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) )
& ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) )
& ( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C] :
( ~ empty(B)
| ~ member(C,B) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_13,plain,
! [B] : ~ member(B,empty_set),
inference(canonicalize,[],[empty_set_defn]) ).
fof(normalize_1_14,plain,
! [B] : ~ member(B,empty_set),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(canonicalize,[],[equal_member_defn]) ).
fof(normalize_1_16,plain,
! [B,C] :
( B != C
<=> ? [D] :
( ~ member(D,B)
<=> member(D,C) ) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,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_16]) ).
fof(normalize_1_18,plain,
! [B,C] :
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(canonicalize,[],[not_equal_defn]) ).
fof(normalize_1_20,plain,
! [B,C] :
( B != C
<=> not_equal(B,C) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [B,C] :
( ( B != C
| ~ not_equal(B,C) )
& ( B = C
| not_equal(B,C) ) ),
inference(clausify,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [B,C] :
( B != C
| ~ not_equal(B,C) ),
inference(conjunct,[],[normalize_1_21]) ).
cnf(refute_1_0,plain,
not_equal(skolemFOFtoCNF_B_1,empty_set),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( empty(X_23)
| member(skolemFOFtoCNF_C(X_23),X_23) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(X_23))]]) ).
cnf(refute_1_4,plain,
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_5,plain,
( ~ member(skolemFOFtoCNF_C(X_23),X_23)
| intersect(X_23,X_23) ),
inference(subst,[],[refute_1_4:[bind(B,$fot(X_23)),bind(C,$fot(X_23)),bind(D,$fot(skolemFOFtoCNF_C(X_23)))]]) ).
cnf(refute_1_6,plain,
( empty(X_23)
| intersect(X_23,X_23) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(X_23),X_23) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( empty(skolemFOFtoCNF_B_1)
| intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_6:[bind(X_23,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_8,plain,
empty(skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_1_7,refute_1_1]) ).
cnf(refute_1_9,plain,
( ~ empty(B)
| ~ member(C,B) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_10,plain,
( ~ empty(X_38)
| ~ member(skolemFOFtoCNF_D_1(X_38,empty_set),X_38) ),
inference(subst,[],[refute_1_9:[bind(B,$fot(X_38)),bind(C,$fot(skolemFOFtoCNF_D_1(X_38,empty_set)))]]) ).
cnf(refute_1_11,plain,
~ member(B,empty_set),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_12,plain,
~ member(skolemFOFtoCNF_D_1(X_36,empty_set),empty_set),
inference(subst,[],[refute_1_11:[bind(B,$fot(skolemFOFtoCNF_D_1(X_36,empty_set)))]]) ).
cnf(refute_1_13,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_14,plain,
( X_36 = empty_set
| member(skolemFOFtoCNF_D_1(X_36,empty_set),X_36)
| member(skolemFOFtoCNF_D_1(X_36,empty_set),empty_set) ),
inference(subst,[],[refute_1_13:[bind(B,$fot(X_36)),bind(C,$fot(empty_set))]]) ).
cnf(refute_1_15,plain,
( X_36 = empty_set
| member(skolemFOFtoCNF_D_1(X_36,empty_set),X_36) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_36,empty_set),empty_set) )],[refute_1_14,refute_1_12]) ).
cnf(refute_1_16,plain,
( X_38 = empty_set
| member(skolemFOFtoCNF_D_1(X_38,empty_set),X_38) ),
inference(subst,[],[refute_1_15:[bind(X_36,$fot(X_38))]]) ).
cnf(refute_1_17,plain,
( ~ empty(X_38)
| X_38 = empty_set ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_38,empty_set),X_38) )],[refute_1_16,refute_1_10]) ).
cnf(refute_1_18,plain,
( ~ empty(skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = empty_set ),
inference(subst,[],[refute_1_17:[bind(X_38,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_19,plain,
skolemFOFtoCNF_B_1 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B_1) )],[refute_1_8,refute_1_18]) ).
cnf(refute_1_20,plain,
( skolemFOFtoCNF_B_1 != empty_set
| ~ not_equal(skolemFOFtoCNF_B_1,empty_set)
| not_equal(empty_set,empty_set) ),
introduced(tautology,[equality,[$cnf( not_equal(skolemFOFtoCNF_B_1,empty_set) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_21,plain,
( ~ not_equal(skolemFOFtoCNF_B_1,empty_set)
| not_equal(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,empty_set) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
not_equal(empty_set,empty_set),
inference(resolve,[$cnf( not_equal(skolemFOFtoCNF_B_1,empty_set) )],[refute_1_0,refute_1_21]) ).
cnf(refute_1_23,plain,
( B != C
| ~ not_equal(B,C) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_24,plain,
( C != C
| ~ not_equal(C,C) ),
inference(subst,[],[refute_1_23:[bind(B,$fot(C))]]) ).
cnf(refute_1_25,plain,
C = C,
introduced(tautology,[refl,[$fot(C)]]) ).
cnf(refute_1_26,plain,
~ not_equal(C,C),
inference(resolve,[$cnf( $equal(C,C) )],[refute_1_25,refute_1_24]) ).
cnf(refute_1_27,plain,
~ not_equal(empty_set,empty_set),
inference(subst,[],[refute_1_26:[bind(C,$fot(empty_set))]]) ).
cnf(refute_1_28,plain,
$false,
inference(resolve,[$cnf( not_equal(empty_set,empty_set) )],[refute_1_22,refute_1_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 02:34:43 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------