TSTP Solution File: SEU120+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:38:29 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 21 unt; 0 def)
% Number of atoms : 121 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 132 ( 72 ~; 29 |; 17 &)
% ( 10 <=>; 4 =>; 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 4 sgn 50 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ) ).
fof(t4_xboole_0,conjecture,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ~ disjoint(A,B)
=> ~ ! [C] : ~ in(C,set_intersection2(A,B)) ),
inference(strip,[],[t4_xboole_0]) ).
fof(subgoal_1,plain,
! [A,B] :
( ( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ? [C] : in(C,set_intersection2(A,B)) )
=> ~ disjoint(A,B) ),
inference(strip,[],[t4_xboole_0]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ~ disjoint(A,B)
=> ~ ! [C] : ~ in(C,set_intersection2(A,B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
& ! [C] : ~ in(C,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [C] : ~ in(C,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [C] : ~ in(C,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_9,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_2,plain,
~ in(C,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_0_2:[bind(C,$fot(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_0_4,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_6,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( empty_set != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_8,plain,
( empty_set != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( empty_set != empty_set
| disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_11,plain,
disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_11,refute_0_12]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ? [C] : in(C,set_intersection2(A,B)) )
=> ~ disjoint(A,B) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( disjoint(A,B)
& ( disjoint(A,B)
| ? [C] : in(C,set_intersection2(A,B)) )
& ? [C] : in(C,set_intersection2(A,B)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
& ( disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| ? [C] : in(C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) )
& ? [C] : in(C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [C] : in(C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_5,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_1_6,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ) ),
inference(clausify,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_1_10,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_3,plain,
( ~ disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) = empty_set ),
inference(subst,[],[refute_1_2:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_4,plain,
set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) = empty_set,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_1,refute_1_3]) ).
cnf(refute_1_5,plain,
( set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) != empty_set
| ~ in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2))
| in(skolemFOFtoCNF_C,empty_set) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_6,plain,
( ~ in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2))
| in(skolemFOFtoCNF_C,empty_set) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),empty_set) )],[refute_1_4,refute_1_5]) ).
cnf(refute_1_7,plain,
in(skolemFOFtoCNF_C,empty_set),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) )],[refute_1_0,refute_1_6]) ).
cnf(refute_1_8,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_9,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(empty_set))]]) ).
cnf(refute_1_10,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_1_11,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_1_10,refute_1_9]) ).
cnf(refute_1_12,plain,
~ in(skolemFOFtoCNF_C,empty_set),
inference(subst,[],[refute_1_11:[bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_1_13,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,empty_set) )],[refute_1_7,refute_1_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.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 Jun 19 23:22:14 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
% 0.13/0.36
%------------------------------------------------------------------------------