TSTP Solution File: SEU162+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU162+3 : 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 12:38:56 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 16 unt; 0 def)
% Number of atoms : 125 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 118 ( 60 ~; 39 |; 7 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l25_zfmisc_1,axiom,
! [A,B] :
~ ( disjoint(singleton(A),B)
& in(A,B) ) ).
fof(l28_zfmisc_1,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ) ).
fof(t65_zfmisc_1,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ) ).
fof(subgoal_0,plain,
! [A,B] :
( set_difference(A,singleton(B)) = A
=> ~ in(B,A) ),
inference(strip,[],[t65_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( ~ in(B,A)
=> set_difference(A,singleton(B)) = A ),
inference(strip,[],[t65_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
=> ~ in(B,A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(canonicalize,[],[l25_zfmisc_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(canonicalize,[],[symmetry_r1_xboole_0]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[t83_xboole_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_difference(A,B) = A ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A,B] :
( set_difference(A,singleton(B)) = A
& in(B,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2
& in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2,
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ disjoint(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_2,plain,
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ disjoint(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
| disjoint(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_4,plain,
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) != skolemFOFtoCNF_A_2
| disjoint(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_6,plain,
set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_A_2) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_A_2) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| disjoint(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),skolemFOFtoCNF_A_2) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_A_2,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_11,plain,
disjoint(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
disjoint(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_11,refute_0_3]) ).
cnf(refute_0_13,plain,
~ in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_14,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ~ in(B,A)
=> set_difference(A,singleton(B)) = A ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( set_difference(A,singleton(B)) != A
& ~ in(B,A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_3
& ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_3,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(canonicalize,[],[symmetry_r1_xboole_0]) ).
fof(normalize_1_4,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(canonicalize,[],[l28_zfmisc_1]) ).
fof(normalize_1_6,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[t83_xboole_1]) ).
fof(normalize_1_8,plain,
! [A,B] :
( set_difference(A,B) != A
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_difference(A,B) = A ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_3,
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ disjoint(singleton(X_20),X_21)
| disjoint(X_21,singleton(X_20)) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(singleton(X_20))),bind(B,$fot(X_21))]]) ).
cnf(refute_1_3,plain,
( disjoint(singleton(A),B)
| in(A,B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
( disjoint(singleton(X_20),X_21)
| in(X_20,X_21) ),
inference(subst,[],[refute_1_3:[bind(A,$fot(X_20)),bind(B,$fot(X_21))]]) ).
cnf(refute_1_5,plain,
( disjoint(X_21,singleton(X_20))
| in(X_20,X_21) ),
inference(resolve,[$cnf( disjoint(singleton(X_20),X_21) )],[refute_1_4,refute_1_2]) ).
cnf(refute_1_6,plain,
( disjoint(X_26,singleton(X_20))
| in(X_20,X_26) ),
inference(subst,[],[refute_1_5:[bind(X_21,$fot(X_26))]]) ).
cnf(refute_1_7,plain,
( ~ disjoint(A,B)
| set_difference(A,B) = A ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_8,plain,
( ~ disjoint(X_26,singleton(X_20))
| set_difference(X_26,singleton(X_20)) = X_26 ),
inference(subst,[],[refute_1_7:[bind(A,$fot(X_26)),bind(B,$fot(singleton(X_20)))]]) ).
cnf(refute_1_9,plain,
( set_difference(X_26,singleton(X_20)) = X_26
| in(X_20,X_26) ),
inference(resolve,[$cnf( disjoint(X_26,singleton(X_20)) )],[refute_1_6,refute_1_8]) ).
cnf(refute_1_10,plain,
( set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_3
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_9:[bind(X_20,$fot(skolemFOFtoCNF_B_1)),bind(X_26,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_11,plain,
( set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_3
| skolemFOFtoCNF_A_3 != skolemFOFtoCNF_A_3
| set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_3) ),[0],$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_12,plain,
( skolemFOFtoCNF_A_3 != skolemFOFtoCNF_A_3
| set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_3
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_A_3 != skolemFOFtoCNF_A_3
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_3) )],[refute_1_12,refute_1_0]) ).
cnf(refute_1_14,plain,
skolemFOFtoCNF_A_3 = skolemFOFtoCNF_A_3,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_15,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3) )],[refute_1_14,refute_1_13]) ).
cnf(refute_1_16,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_17,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_3) )],[refute_1_15,refute_1_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n013.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 : Sun Jun 19 15:00:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------