%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 12:38:31 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 50 ( 9 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 48 ( 24 ~; 12 |; 5 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 5 sgn 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t2_xboole_1,conjecture,
! [A] : subset(empty_set,A) ).
fof(subgoal_0,plain,
! [A] : subset(empty_set,A),
inference(strip,[],[t2_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A] : subset(empty_set,A),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ subset(empty_set,A),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(empty_set,skolemFOFtoCNF_A_2),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_3,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
~ subset(empty_set,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_3,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_4,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
~ in(skolemFOFtoCNF_C(empty_set,X_27),empty_set),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_C(empty_set,X_27)))]]) ).
cnf(refute_0_6,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( in(skolemFOFtoCNF_C(empty_set,X_27),empty_set)
| subset(empty_set,X_27) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(empty_set)),bind(B,$fot(X_27))]]) ).
cnf(refute_0_8,plain,
subset(empty_set,X_27),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(empty_set,X_27),empty_set) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
subset(empty_set,skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_8:[bind(X_27,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_A_2) )],[refute_0_9,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 11:57:02 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------