TSTP Solution File: SET923+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 03:38:22 EDT 2022
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 55 ( 37 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 31 ~; 10 |; 11 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t66_zfmisc_1,conjecture,
! [A,B] :
~ ( set_difference(A,singleton(B)) = empty_set
& A != empty_set
& A != singleton(B) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) = empty_set
& A != empty_set )
=> A = singleton(B) ),
inference(strip,[],[t66_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ( set_difference(A,singleton(B)) = empty_set
& A != empty_set )
=> A = singleton(B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( ~ subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( A != empty_set
& A != singleton(B)
& set_difference(A,singleton(B)) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ subset(A,singleton(B))
<=> ( A != empty_set
& A != singleton(B) ) ),
inference(canonicalize,[],[l4_zfmisc_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ subset(A,singleton(B))
<=> ( A != empty_set
& A != singleton(B) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [A,B] :
( ~ subset(A,singleton(B))
& set_difference(A,singleton(B)) = empty_set ),
inference(simplify,[],[normalize_0_4,normalize_0_6]) ).
fof(normalize_0_8,plain,
( ~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
& set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set,
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( set_difference(A,B) != empty_set
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) != empty_set
| subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( empty_set != empty_set
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) != empty_set
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_4,plain,
( empty_set != empty_set
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),empty_set) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( empty_set != empty_set
| subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),empty_set) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_7,plain,
subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n011.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 Jul 11 09:13:42 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------