TSTP Solution File: SET891+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 03:38:09 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 22 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l52_zfmisc_1,axiom,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B) ).
fof(t32_zfmisc_1,conjecture,
! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B) ).
fof(t41_enumset1,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ).
fof(subgoal_0,plain,
! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
inference(strip,[],[t32_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] : union(unordered_pair(singleton(A),singleton(B))) != unordered_pair(A,B),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(canonicalize,[],[t41_enumset1]) ).
fof(normalize_0_3,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
inference(canonicalize,[],[l52_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( unordered_pair(A,B) != set_union2(singleton(A),singleton(B))
| set_union2(singleton(A),singleton(B)) = unordered_pair(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(unordered_pair(A,B))),bind(Y,$fot(set_union2(singleton(A),singleton(B))))]]) ).
cnf(refute_0_6,plain,
set_union2(singleton(A),singleton(B)) = unordered_pair(A,B),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),set_union2(singleton(A),singleton(B))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
union(unordered_pair(A,B)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_9,plain,
union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) = set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_8:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_10,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_10]) ).
cnf(refute_0_12,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) != set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))
| union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))))),bind(Y,$fot(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)))),bind(Z,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_13,plain,
( set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))),set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
( union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_16,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(union(unordered_pair(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_18,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET891+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 : n011.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 15:52:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------