TSTP Solution File: SET882+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:38:05 EDT 2022
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 12 unt; 0 def)
% Number of atoms : 111 ( 70 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 125 ( 56 ~; 46 |; 11 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) ) ).
fof(t23_zfmisc_1,conjecture,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ) ).
fof(subgoal_0,plain,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
inference(strip,[],[t23_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
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)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( A != B
& set_difference(unordered_pair(A,B),singleton(B)) != singleton(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2)
& skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(canonicalize,[],[l39_zfmisc_1]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) )
& ( A != B
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) )
& ( set_difference(unordered_pair(A,B),C) != singleton(A)
| A = B
| in(B,C) )
& ( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_2,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_3,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_5,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_8,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_9,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
in(X_33,singleton(X_33)),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_33))]]) ).
cnf(refute_0_12,plain,
( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( ~ in(X_33,singleton(X_33))
| set_difference(unordered_pair(X_32,X_33),singleton(X_33)) = singleton(X_32)
| in(X_32,singleton(X_33)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_32)),bind(B,$fot(X_33)),bind(C,$fot(singleton(X_33)))]]) ).
cnf(refute_0_14,plain,
( set_difference(unordered_pair(X_32,X_33),singleton(X_33)) = singleton(X_32)
| in(X_32,singleton(X_33)) ),
inference(resolve,[$cnf( in(X_33,singleton(X_33)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(skolemFOFtoCNF_A_2)),bind(X_33,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_16,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_17,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_17,refute_0_5]) ).
cnf(refute_0_19,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_20,plain,
in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_20,refute_0_4]) ).
cnf(refute_0_22,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_21,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n022.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 : Mon Jul 11 08:53:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.37
% 0.21/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.38
%------------------------------------------------------------------------------