%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET875+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:38:02 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 84 ( 47 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 85 ( 41 ~; 29 |; 7 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 44 ( 0 sgn 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(l25_zfmisc_1,axiom,
! [A,B] :
~ ( disjoint(singleton(A),B)
& in(A,B) ) ).
fof(t16_zfmisc_1,conjecture,
! [A,B] :
~ ( disjoint(singleton(A),singleton(B))
& A = B ) ).
fof(subgoal_0,plain,
! [A,B] :
( disjoint(singleton(A),singleton(B))
=> A != B ),
inference(strip,[],[t16_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( disjoint(singleton(A),singleton(B))
=> A != B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( A = B
& disjoint(singleton(A),singleton(B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B
& disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(canonicalize,[],[l25_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_7,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
( singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_B)
| skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
| singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) ),[1,0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
| singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
| ~ disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))
| disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_12,plain,
( ~ disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))
| disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_15,plain,
( ~ disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2))
| ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_16,plain,
~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_18,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_19,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_20,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_22,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_23,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET875+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 01:00:42 EDT 2022
% 0.13/0.34 % 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
% 0.13/0.35
%------------------------------------------------------------------------------