TSTP Solution File: SET908+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 03:38:16 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 26 unt; 0 def)
% Number of atoms : 136 ( 72 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 145 ( 66 ~; 55 |; 9 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 7 sgn 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ) ).
fof(t49_zfmisc_1,conjecture,
! [A,B] : set_union2(singleton(A),B) != empty_set ).
fof(subgoal_0,plain,
! [A,B] : set_union2(singleton(A),B) != empty_set,
inference(strip,[],[t49_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : set_union2(singleton(A),B) != empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A,B] : set_union2(singleton(A),B) = empty_set,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set,
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_11,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_13,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_2,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_3,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_5,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
in(X_20,singleton(X_20)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_7,plain,
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
( set_union2(A,B) != set_union2(A,B)
| ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(set_union2(A,B)))]]) ).
cnf(refute_0_9,plain,
set_union2(A,B) = set_union2(A,B),
introduced(tautology,[refl,[$fot(set_union2(A,B))]]) ).
cnf(refute_0_10,plain,
( ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(A,B)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ in(X_20,singleton(X_20))
| in(X_20,set_union2(X_18,singleton(X_20))) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_18)),bind(B,$fot(singleton(X_20))),bind(D,$fot(X_20))]]) ).
cnf(refute_0_12,plain,
in(X_20,set_union2(X_18,singleton(X_20))),
inference(resolve,[$cnf( in(X_20,singleton(X_20)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))),
inference(subst,[],[refute_0_12:[bind(X_18,$fot(skolemFOFtoCNF_B_1)),bind(X_20,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_14,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_20,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) = set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_22,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != empty_set
| set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) ),[0],$fot(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_23,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) != empty_set
| set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = empty_set ),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) = empty_set,
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),empty_set) )],[refute_0_14,refute_0_23]) ).
cnf(refute_0_25,plain,
( set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)) != empty_set
| ~ in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))
| in(skolemFOFtoCNF_A_2,empty_set) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_26,plain,
( ~ in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)))
| in(skolemFOFtoCNF_A_2,empty_set) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2)),empty_set) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
in(skolemFOFtoCNF_A_2,empty_set),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_2))) )],[refute_0_13,refute_0_26]) ).
cnf(refute_0_28,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_29,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_30,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_31,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
~ in(skolemFOFtoCNF_A_2,empty_set),
inference(subst,[],[refute_0_31:[bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_27,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 19:11:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------