TSTP Solution File: SEU137+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU137+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:38:38 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 46 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 11 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ).
fof(t45_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
inference(strip,[],[t45_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( B != set_union2(A,set_difference(B,A))
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[t12_xboole_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[t39_xboole_1]) ).
fof(normalize_0_7,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_3,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_7,plain,
( set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))) ),[1],$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))),bind(Y,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_14,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) )],[refute_0_3,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU137+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 09:11:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41
%------------------------------------------------------------------------------