TSTP Solution File: SET924+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET924+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:38:23 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 77 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 40 ~; 19 |; 6 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t67_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ) ).
fof(l34_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ) ).
fof(subgoal_0,plain,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
=> ~ in(A,B) ),
inference(strip,[],[t67_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( ~ in(A,B)
=> set_difference(singleton(A),B) = singleton(A) ),
inference(strip,[],[t67_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
=> ~ in(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
<=> in(A,B) ),
inference(canonicalize,[],[l34_zfmisc_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
<=> in(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) )
& ( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( set_difference(singleton(A),B) = singleton(A)
& in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2)
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_4,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_7,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_8,refute_0_7]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ~ in(A,B)
=> set_difference(singleton(A),B) = singleton(A) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( set_difference(singleton(A),B) != singleton(A)
& ~ in(A,B) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_A_3)
& ~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
<=> in(A,B) ),
inference(canonicalize,[],[l34_zfmisc_1]) ).
fof(normalize_1_4,plain,
! [A,B] :
( set_difference(singleton(A),B) != singleton(A)
<=> in(A,B) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) )
& ( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_A_3)
| in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_3,plain,
( set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_A_3)
| singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
| set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_A_3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_A_3)) ),[0],$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_4,plain,
( singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
| set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_A_3)
| in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
| in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_4,refute_1_0]) ).
cnf(refute_1_6,plain,
singleton(skolemFOFtoCNF_A_3) = singleton(skolemFOFtoCNF_A_3),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_7,plain,
in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_9,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) )],[refute_1_7,refute_1_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET924+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n013.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 : Sun Jul 10 15:30:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------