%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:38:50 EDT 2022
% Result : Theorem 15.65s 15.83s
% Output : CNFRefutation 15.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% Number of atoms : 99 ( 26 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 101 ( 40 ~; 37 |; 15 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(l28_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(strip,[],[l28_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( ~ disjoint(singleton(A),B)
& ~ in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
& ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,A)
| ~ in(C,B) ) )
& ! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) ) ),
inference(canonicalize,[],[t3_xboole_0]) ).
fof(normalize_0_4,plain,
! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),A) )
& ( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_9,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( disjoint(singleton(A),X_715)
| in(skolemFOFtoCNF_C_4(singleton(A),X_715),X_715) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(singleton(A))),bind(B,$fot(X_715))]]) ).
cnf(refute_0_3,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_4,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_3:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_5,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_6,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ in(skolemFOFtoCNF_C_4(singleton(A),X_708),singleton(A))
| skolemFOFtoCNF_C_4(singleton(A),X_708) = A ),
inference(subst,[],[refute_0_6:[bind(C,$fot(skolemFOFtoCNF_C_4(singleton(A),X_708)))]]) ).
cnf(refute_0_8,plain,
( disjoint(A,B)
| in(skolemFOFtoCNF_C_4(A,B),A) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( disjoint(singleton(A),X_708)
| in(skolemFOFtoCNF_C_4(singleton(A),X_708),singleton(A)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(singleton(A))),bind(B,$fot(X_708))]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_C_4(singleton(A),X_708) = A
| disjoint(singleton(A),X_708) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_4(singleton(A),X_708),singleton(A)) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_C_4(singleton(A),X_715) = A
| disjoint(singleton(A),X_715) ),
inference(subst,[],[refute_0_10:[bind(X_708,$fot(X_715))]]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_C_4(singleton(A),X_715) != A
| ~ in(skolemFOFtoCNF_C_4(singleton(A),X_715),X_715)
| in(A,X_715) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_C_4(singleton(A),X_715),X_715) ),[0],$fot(A)]]) ).
cnf(refute_0_13,plain,
( ~ in(skolemFOFtoCNF_C_4(singleton(A),X_715),X_715)
| disjoint(singleton(A),X_715)
| in(A,X_715) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_4(singleton(A),X_715),A) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( disjoint(singleton(A),X_715)
| in(A,X_715) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_4(singleton(A),X_715),X_715) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(X_715,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_16,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_16,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 03:26:07 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 15.65/15.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.65/15.83
% 15.65/15.83 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.65/15.83
%------------------------------------------------------------------------------